public Loan(int legs)
{
legs_ = new InitializedList<List<CashFlow>>(legs);
payer_ = new InitializedList<double>(legs);
notionals_ = new List<double>();
legNPV_ = new InitializedList<double?>(legs);
}
private void initialize()
{
// firstSeed is chosen based on clock() and used for the first rng
ulong firstSeed = (ulong)DateTime.Now.Ticks; // (std::time(0));
MersenneTwisterUniformRng first = new MersenneTwisterUniformRng(firstSeed);
// secondSeed is as random as it could be
// feel free to suggest improvements
ulong secondSeed = first.nextInt32();
MersenneTwisterUniformRng second = new MersenneTwisterUniformRng(secondSeed);
// use the second rng to initialize the final one
ulong skip = second.nextInt32() % 1000;
List<ulong> init = new InitializedList<ulong>(4);
init[0]=second.nextInt32();
init[1]=second.nextInt32();
init[2]=second.nextInt32();
init[3]=second.nextInt32();
rng_ = new MersenneTwisterUniformRng(init);
for (ulong i=0; i<skip ; i++)
rng_.nextInt32();
}
public override EndCriteria.Type minimize(Problem P, EndCriteria endCriteria) {
EndCriteria.Type ecType = EndCriteria.Type.None;
P.reset();
Vector x_ = P.currentValue();
currentProblem_ = P;
initCostValues_ = P.costFunction().values(x_);
int m = initCostValues_.size();
int n = x_.size();
Vector xx = new Vector(x_);
Vector fvec = new Vector(m), diag = new Vector(n);
int mode = 1;
double factor = 1;
int nprint = 0;
int info = 0;
int nfev =0;
Matrix fjac = new Matrix(m, n);
int ldfjac = m;
List<int> ipvt = new InitializedList<int>(n);
Vector qtf = new Vector(n), wa1 = new Vector(n), wa2 = new Vector(n), wa3 = new Vector(n), wa4 = new Vector(m);
// call lmdif to minimize the sum of the squares of m functions
// in n variables by the Levenberg-Marquardt algorithm.
MINPACK.lmdif(m, n, xx, ref fvec,
endCriteria.functionEpsilon(),
xtol_,
gtol_,
endCriteria.maxIterations(),
epsfcn_,
diag, mode, factor,
nprint, ref info, ref nfev, ref fjac,
ldfjac, ref ipvt, ref qtf,
wa1, wa2, wa3, wa4,
fcn);
info_ = info;
// check requirements & endCriteria evaluation
if(info == 0) throw new ApplicationException("MINPACK: improper input parameters");
//if(info == 6) throw new ApplicationException("MINPACK: ftol is too small. no further " +
// "reduction in the sum of squares is possible.");
if (info != 6) ecType = EndCriteria.Type.StationaryFunctionValue;
//QL_REQUIRE(info != 5, "MINPACK: number of calls to fcn has reached or exceeded maxfev.");
endCriteria.checkMaxIterations(nfev, ref ecType);
if(info == 7) throw new ApplicationException("MINPACK: xtol is too small. no further " +
"improvement in the approximate " +
"solution x is possible.");
if(info == 8) throw new ApplicationException("MINPACK: gtol is too small. fvec is " +
"orthogonal to the columns of the " +
"jacobian to machine precision.");
// set problem
x_ = new Vector(xx.GetRange(0, n));
P.setCurrentValue(x_);
P.setFunctionValue(P.costFunction().value(x_));
return ecType;
}
public AmericanExercise(Date latest, bool payoffAtExpiry)
: base(Type.American, payoffAtExpiry)
{
dates_ = new InitializedList<Date>(2);
dates_[0] = Date.minDate();
dates_[1] = latest;
}
//public List<CashFlow> interestCashflows()
//{
// List<CashFlow> icf = new List<CashFlow>();
// foreach (CashFlow cf in cashflows())
// {
// if (cf is QLNet.FixedRateCoupon)
// icf.Add(cf);
// }
// return icf;
//}
public List<CashFlow> expectedCashflows()
{
calcBondFactor();
List<CashFlow> expectedcashflows = new List<CashFlow>();
List<double> notionals = new InitializedList<double>(schedule_.Count);
notionals[0] = notionals_[0];
for (int i = 0; i < schedule_.Count - 1; ++i)
{
double currentNotional = notionals[i];
double smm = SMM(schedule_[i]);
double prepay = (notionals[i] * bondFactors_[i + 1]) / bondFactors_[i] * smm;
double actualamort = currentNotional * (1 - bondFactors_[i + 1] / bondFactors_[i]);
notionals[i + 1] = currentNotional - actualamort - prepay;
// ADD
CashFlow c1 = new VoluntaryPrepay(prepay, schedule_[i + 1]);
CashFlow c2 = new AmortizingPayment(actualamort, schedule_[i + 1]);
CashFlow c3 = new FixedRateCoupon(currentNotional, schedule_[i + 1], new InterestRate(PassThroughRate_, dCounter_, Compounding.Simple), schedule_[i], schedule_[i + 1]);
expectedcashflows.Add(c1);
expectedcashflows.Add(c2);
expectedcashflows.Add(c3);
}
notionals[notionals.Count - 1] = 0.0;
return expectedcashflows;
}
public static List<Func<Vector, double>> multiPathBasisSystem(int dim, int order, PolynomType polynomType)
{
List<Func<double, double>> b = pathBasisSystem(order, polynomType);
List<Func<Vector, double>> ret = new List<Func<Vector,double>>();
ret.Add((xx) => 1.0);
for (int i=1; i<=order; ++i) {
List<Func<Vector, double>> a = w(dim, i, polynomType, b);
foreach (var iter in a) {
ret.Add(iter);
}
}
// remove-o-zap: now remove redundant functions.
// usually we do have a lot of them due to the construction schema.
// We use a more "hands on" method here.
List<bool> rm = new InitializedList<bool>(ret.Count, true);
Vector x = new Vector(dim), v = new Vector(ret.Count);
MersenneTwisterUniformRng rng = new MersenneTwisterUniformRng(1234UL);
for (int i=0; i<10; ++i) {
int k;
// calculate random x vector
for (k=0; k<dim; ++k) {
x[k] = rng.next().value;
}
// get return values for all basis functions
for (k = 0; k < ret.Count; ++k) {
v[k] = ret[k](x);
}
// find duplicates
for (k = 0; k < ret.Count; ++k) {
if (v.First(xx => (Math.Abs(v[k] - xx) <= 10*v[k]*Const.QL_Epsilon)) == v.First() + k) {
// don't remove this item, it's unique!
rm[k] = false;
}
}
}
int iter2 = 0;
for (int i = 0; i < rm.Count; ++i) {
if (rm[i]) {
ret.RemoveAt(iter2);
}
else {
++iter2;
}
}
return ret;
}
public AmericanExercise(Date earliestDate, Date latestDate, bool payoffAtExpiry)
: base(Type.American, payoffAtExpiry)
{
if (!(earliestDate <= latestDate))
throw new ApplicationException("earliest > latest exercise date");
dates_ = new InitializedList<Date>(2);
dates_[0] = earliestDate;
dates_[1] = latestDate;
}
public override double value(double x, double y)
{
List<double> section = new InitializedList<double>( splines_.Count );
for (int i=0; i<splines_.Count; i++)
section[i]=splines_[i].value(x,true);
CubicInterpolation spline = new CubicInterpolation(this.yBegin_, this.ySize_, section,
CubicInterpolation.DerivativeApprox.Spline, false,
CubicInterpolation.BoundaryCondition.SecondDerivative, 0.0,
CubicInterpolation.BoundaryCondition.SecondDerivative, 0.0);
return spline.value(y,true);
}
//! generic times
/*! \note the starting time of the path is assumed to be 0 and must not be included */
public BrownianBridge(List<double> times) {
size_ = times.Count;
t_ = new InitializedList<double>(size_);
sqrtdt_ = new InitializedList<double>(size_);
bridgeIndex_ = new InitializedList<int>(size_);
leftIndex_ = new InitializedList<int>(size_);
rightIndex_ = new InitializedList<int>(size_);
leftWeight_ = new InitializedList<double>(size_);
rightWeight_ = new InitializedList<double>(size_);
stdDev_ = new InitializedList<double>(size_);
initialize();
}
public double secondDerivativeX(double x, double y)
{
List<double> section = new InitializedList<double>( this.zData_.columns() );
for (int i=0; i < section.Count; ++i)
{
section[i] = value(this.xBegin_[i], y);
}
return new CubicInterpolation( this.xBegin_, this.xSize_, section,
CubicInterpolation.DerivativeApprox.Spline, false,
CubicInterpolation.BoundaryCondition.SecondDerivative, 0.0,
CubicInterpolation.BoundaryCondition.SecondDerivative, 0.0).secondDerivative(x);
}
// Computes the size of the simplex
public static double computeSimplexSize(InitializedList<Vector> vertices)
{
Vector center = new Vector(vertices[0].Count, 0);
for (int i = 0; i < vertices.Count; ++i)
center += vertices[i];
center *= 1 / (double)(vertices.Count);
double result = 0;
for (int i = 0; i < vertices.Count; ++i)
{
Vector temp = vertices[i] - center;
result += Math.Sqrt(Vector.DotProduct(temp, temp));
}
return result / (double)(vertices.Count);
}
//! unit-time path
public BrownianBridge(int steps) {
size_ = steps;
t_ = new InitializedList<double>(size_);
sqrtdt_ = new InitializedList<double>(size_);
bridgeIndex_ = new InitializedList<int>(size_);
leftIndex_ = new InitializedList<int>(size_);
rightIndex_ = new InitializedList<int>(size_);
leftWeight_ = new InitializedList<double>(size_);
rightWeight_ = new InitializedList<double>(size_);
stdDev_ = new InitializedList<double>(size_);
for (int i=0; i<size_; ++i)
t_[i] = i+1;
initialize();
}
public DiscretizedSwaption(Swaption.Arguments args,
Date referenceDate,
DayCounter dayCounter)
: base(new DiscretizedSwap(args, referenceDate, dayCounter), args.exercise.type(), new List<double>())
{
arguments_=args;
exerciseTimes_ = new InitializedList<double>(arguments_.exercise.dates().Count);
for (int i = 0; i < exerciseTimes_.Count; ++i)
exerciseTimes_[i] =
dayCounter.yearFraction(referenceDate,
arguments_.exercise.date(i));
// Date adjustments can get time vectors out of synch.
// Here, we try and collapse similar dates which could cause
// a mispricing.
for (int i=0; i<arguments_.exercise.dates().Count; i++) {
Date exerciseDate = arguments_.exercise.date(i);
for (int j = 0; j < arguments_.fixedPayDates.Count; j++) {
if (withinNextWeek(exerciseDate,
arguments_.fixedPayDates[j])
// coupons in the future are dealt with below
&& arguments_.fixedResetDates[j] < referenceDate)
arguments_.fixedPayDates[j] = exerciseDate;
}
for (int j = 0; j < arguments_.fixedResetDates.Count; j++) {
if (withinPreviousWeek(exerciseDate,
arguments_.fixedResetDates[j]))
arguments_.fixedResetDates[j] = exerciseDate;
}
for (int j = 0; j < arguments_.floatingResetDates.Count; j++) {
if (withinPreviousWeek(exerciseDate,
arguments_.floatingResetDates[j]))
arguments_.floatingResetDates[j] = exerciseDate;
}
}
double lastFixedPayment =
dayCounter.yearFraction(referenceDate,
arguments_.fixedPayDates.Last() );
double lastFloatingPayment =
dayCounter.yearFraction(referenceDate,
arguments_.floatingPayDates.Last());
lastPayment_ = Math.Max(lastFixedPayment,lastFloatingPayment);
underlying_ = new DiscretizedSwap(arguments_,
referenceDate,
dayCounter);
}
public void test1dLinearRegression()
{
//BOOST_MESSAGE("Testing 1d simple linear least-squares regression...");
/* Example taken from the QuantLib-User list, see posting
* Multiple linear regression/weighted regression, Boris Skorodumov */
//SavedSettings backup;
List<double> x = new InitializedList<double>(9),
y = new InitializedList<double>(9);
x[0] = 2.4; x[1] = 1.8; x[2] = 2.5; x[3] = 3.0;
x[4] = 2.1; x[5] = 1.2; x[6] = 2.0; x[7] = 2.7; x[8] = 3.6;
y[0] = 7.8; y[1] = 5.5; y[2] = 8.0; y[3] = 9.0;
y[4] = 6.5; y[5] = 4.0; y[6] = 6.3; y[7] = 8.4; y[8] = 10.2;
List<Func<double, double>> v = new List<Func<double, double>>();
v.Add(a => 1.0);
v.Add(a => a);
LinearRegression m = new LinearRegression(x, y);
const double tol = 0.0002;
double[] coeffExpected = new double[] { 0.9448, 2.6853 };
double[] errorsExpected = new double[] { 0.3654, 0.1487 };
for (int i = 0; i < 2; ++i) {
if (Math.Abs(m.standardErrors()[i] - errorsExpected[i]) > tol) {
Assert.Fail("Failed to reproduce linear regression standard errors"
+ "\n calculated: " + m.standardErrors()[i]
+ "\n expected: " + errorsExpected[i]
+ "\n tolerance: " + tol);
}
if (Math.Abs(m.coefficients()[i] - coeffExpected[i]) > tol) {
Assert.Fail("Failed to reproduce linear regression coef."
+ "\n calculated: " + m.coefficients()[i]
+ "\n expected: " + coeffExpected[i]
+ "\n tolerance: " + tol);
}
}
}
public override void fetchResults(IPricingEngineResults r)
{
base.fetchResults(r);
LoanPricingEngineResults results = r as LoanPricingEngineResults;
if (results == null) throw new ArgumentException("wrong result type");
if (results.legNPV.Count != 0)
{
if (results.legNPV.Count != legNPV_.Count)
{
throw new ArgumentException("wrong number of leg NPV returned");
}
legNPV_ = results.legNPV;
}
else
{
legNPV_ = new InitializedList<double?>(legNPV_.Count);
}
}
public MersenneTwisterUniformRng(List<ulong> seeds) {
mt = new InitializedList<ulong>(N);
seedInitialization(19650218UL);
int i = 1, j = 0, k = (N > seeds.Count ? N : seeds.Count);
for (; k!=0; k--) {
mt[i] = (mt[i] ^ ((mt[i - 1] ^ (mt[i - 1] >> 30)) * 1664525UL)) + seeds[j] + (ulong)j; /* non linear */
mt[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */
i++; j++;
if (i>=N) { mt[0] = mt[N-1]; i=1; }
if (j>=seeds.Count) j=0;
}
for (k=N-1; k!=0; k--) {
mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 30)) * 1566083941UL)) - (ulong)i; /* non linear */
mt[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */
i++;
if (i>=N) { mt[0] = mt[N-1]; i=1; }
}
mt[0] = 0x80000000UL; /*MSB is 1; assuring non-zero initial array*/
}
// Instrument interface
public override void calculate() {
if (discountCurve_.empty()) throw new ArgumentException("no discounting term structure set");
results_.value = results_.cash = 0;
results_.errorEstimate = null;
results_.legNPV = new InitializedList<double?>(arguments_.legs.Count);
results_.legBPS = new InitializedList<double?>(arguments_.legs.Count);
List<double?> startDiscounts = new InitializedList<double?>(arguments_.legs.Count);
for (int i=0; i<arguments_.legs.Count; ++i) {
results_.legNPV[i] = arguments_.payer[i] * CashFlows.npv(arguments_.legs[i], discountCurve_);
results_.legBPS[i] = arguments_.payer[i] * CashFlows.bps(arguments_.legs[i], discountCurve_);
results_.value += results_.legNPV[i];
results_.cash += arguments_.payer[i] * CashFlows.cash(arguments_.legs[i]);
try {
Date d = CashFlows.startDate(arguments_.legs[i]);
startDiscounts[i] = discountCurve_.link.discount(d);
} catch {
startDiscounts[i] = null;
}
}
results_.additionalResults.Add("startDiscounts", startDiscounts);
}
public void setMarketData()
{
tenors = new SwaptionTenors();
//tenors.options.resize(6);
tenors.options = new InitializedList<Period>(6);
tenors.options[0] = new Period(1, TimeUnit.Months);
tenors.options[1] = new Period(6, TimeUnit.Months);
tenors.options[2] = new Period(1, TimeUnit.Years);
tenors.options[3] = new Period(5, TimeUnit.Years);
tenors.options[4] = new Period(10, TimeUnit.Years);
tenors.options[5] = new Period(30, TimeUnit.Years);
//tenors.swaps.resize(4);
tenors.swaps = new InitializedList<Period>(4);
tenors.swaps[0] = new Period(1, TimeUnit.Years);
tenors.swaps[1] = new Period(5, TimeUnit.Years);
tenors.swaps[2] = new Period(10, TimeUnit.Years);
tenors.swaps[3] = new Period(30, TimeUnit.Years);
vols = new Matrix(tenors.options.Count, tenors.swaps.Count);
vols[0, 0] = 0.1300; vols[0, 1] = 0.1560; vols[0, 2] = 0.1390; vols[0, 3] = 0.1220;
vols[1, 0] = 0.1440; vols[1, 1] = 0.1580; vols[1, 2] = 0.1460; vols[1, 3] = 0.1260;
vols[2, 0] = 0.1600; vols[2, 1] = 0.1590; vols[2, 2] = 0.1470; vols[2, 3] = 0.1290;
vols[3, 0] = 0.1640; vols[3, 1] = 0.1470; vols[3, 2] = 0.1370; vols[3, 3] = 0.1220;
vols[4, 0] = 0.1400; vols[4, 1] = 0.1300; vols[4, 2] = 0.1250; vols[4, 3] = 0.1100;
vols[5, 0] = 0.1130; vols[5, 1] = 0.1090; vols[5, 2] = 0.1070; vols[5, 3] = 0.0930;
volsHandle = new InitializedList<List<Handle<Quote>>>(tenors.options.Count);
for (int i = 0; i < tenors.options.Count; i++)
{
volsHandle[i] = new InitializedList<Handle<Quote>>(tenors.swaps.Count);
for (int j = 0; j < tenors.swaps.Count; j++)
// every handle must be reassigned, as the ones created by
// default are all linked together.
volsHandle[i][j] = new Handle<Quote>(new SimpleQuote(vols[i, j]));
}
}
public override void update()
{
Vector tmp = new Vector(size_);
List<double> dx = new InitializedList<double>(size_ - 1),
S = new InitializedList<double>(size_ - 1);
for (int i = 0; i < size_ - 1; ++i) {
dx[i] = xBegin_[i+1] - xBegin_[i];
S[i] = (yBegin_[i+1] - yBegin_[i])/dx[i];
}
// first derivative approximation
if (da_==CubicInterpolation.DerivativeApprox.Spline) {
TridiagonalOperator L = new TridiagonalOperator(size_);
for (int i = 1; i < size_ - 1; ++i) {
L.setMidRow(i, dx[i], 2.0*(dx[i]+dx[i-1]), dx[i-1]);
tmp[i] = 3.0*(dx[i]*S[i-1] + dx[i-1]*S[i]);
}
// left boundary condition
switch (leftType_) {
case CubicInterpolation.BoundaryCondition.NotAKnot:
// ignoring end condition value
L.setFirstRow(dx[1]*(dx[1]+dx[0]), (dx[0]+dx[1])*(dx[0]+dx[1]));
tmp[0] = S[0]*dx[1]*(2.0*dx[1]+3.0*dx[0]) + S[1]*dx[0]*dx[0];
break;
case CubicInterpolation.BoundaryCondition.FirstDerivative:
L.setFirstRow(1.0, 0.0);
tmp[0] = leftValue_;
break;
case CubicInterpolation.BoundaryCondition.SecondDerivative:
L.setFirstRow(2.0, 1.0);
tmp[0] = 3.0*S[0] - leftValue_*dx[0]/2.0;
break;
case CubicInterpolation.BoundaryCondition.Periodic:
case CubicInterpolation.BoundaryCondition.Lagrange:
// ignoring end condition value
throw new NotImplementedException("this end condition is not implemented yet");
default:
throw new ArgumentException("unknown end condition");
}
// right boundary condition
switch (rightType_) {
case CubicInterpolation.BoundaryCondition.NotAKnot:
// ignoring end condition value
L.setLastRow(-(dx[size_ - 2] + dx[size_ - 3]) * (dx[size_ - 2] + dx[size_ - 3]),
-dx[size_ - 3] * (dx[size_ - 3] + dx[size_ - 2]));
tmp[size_ - 1] = -S[size_ - 3] * dx[size_ - 2] * dx[size_ - 2] -
S[size_ - 2] * dx[size_ - 3] * (3.0 * dx[size_ - 2] + 2.0 * dx[size_ - 3]);
break;
case CubicInterpolation.BoundaryCondition.FirstDerivative:
L.setLastRow(0.0, 1.0);
tmp[size_ - 1] = rightValue_;
break;
case CubicInterpolation.BoundaryCondition.SecondDerivative:
L.setLastRow(1.0, 2.0);
tmp[size_ - 1] = 3.0 * S[size_ - 2] + rightValue_ * dx[size_ - 2] / 2.0;
break;
case CubicInterpolation.BoundaryCondition.Periodic:
case CubicInterpolation.BoundaryCondition.Lagrange:
// ignoring end condition value
throw new NotImplementedException("this end condition is not implemented yet");
default:
throw new ArgumentException("unknown end condition");
}
// solve the system
tmp = L.solveFor(tmp);
} else { // local schemes
if (size_ == 2)
tmp[0] = tmp[1] = S[0];
else {
switch (da_) {
case CubicInterpolation.DerivativeApprox.FourthOrder:
throw new NotImplementedException("FourthOrder not implemented yet");
break;
case CubicInterpolation.DerivativeApprox.Parabolic:
// intermediate points
for (int i = 1; i < size_ - 1; ++i) {
tmp[i] = (dx[i - 1] * S[i] + dx[i] * S[i - 1]) / (dx[i] + dx[i - 1]);
}
// end points
tmp[0] = ((2.0 * dx[0] + dx[1]) * S[0] - dx[0] * S[1]) / (dx[0] + dx[1]);
tmp[size_ - 1] = ((2.0 * dx[size_ - 2] + dx[size_ - 3]) * S[size_ - 2] - dx[size_ - 2] * S[size_ - 3]) / (dx[size_ - 2] + dx[size_ - 3]);
break;
break;
case CubicInterpolation.DerivativeApprox.FritschButland:
// intermediate points
for (int i=1; i<size_-1; ++i) {
double Smin = Math.Min(S[i-1], S[i]);
double Smax = Math.Max(S[i-1], S[i]);
tmp[i] = 3.0*Smin*Smax/(Smax+2.0*Smin);
}
// end points
tmp[0] = ((2.0*dx[ 0]+dx[ 1])*S[ 0] - dx[ 0]*S[ 1]) / (dx[ 0]+dx[ 1]);
tmp[size_-1] = ((2.0*dx[size_-2]+dx[size_-3])*S[size_-2] - dx[size_-2]*S[size_-3]) / (dx[size_-2]+dx[size_-3]);
break;
case CubicInterpolation.DerivativeApprox.Akima:
throw new NotImplementedException("Akima not implemented yet");
// end points
tmp[0] = ((2.0 * dx[0] + dx[1]) * S[0] - dx[0] * S[1]) / (dx[0] + dx[1]);
tmp[size_ - 1] = ((2.0 * dx[size_ - 2] + dx[size_ - 3]) * S[size_ - 2] - dx[size_ - 2] * S[size_ - 3]) / (dx[size_ - 2] + dx[size_ - 3]);
break;
case CubicInterpolation.DerivativeApprox.Kruger:
// intermediate points
for (int i = 1; i < size_ - 1; ++i) {
if (S[i-1]*S[i]<0.0)
// slope changes sign at point
tmp[i] = 0.0;
else
// slope will be between the slopes of the adjacent
// straight lines and should approach zero if the
// slope of either line approaches zero
tmp[i] = 2.0/(1.0/S[i-1]+1.0/S[i]);
}
// end points
tmp[0] = (3.0*S[0]-tmp[1])/2.0;
tmp[size_ - 1] = (3.0 * S[size_ - 2] - tmp[size_ - 2]) / 2.0;
break;
default:
throw new ArgumentException("unknown scheme");
}
}
}
monotonicityAdjustments_.Erase();
// Hyman monotonicity constrained filter
if (monotonic_) {
double correction;
double pm, pu, pd, M;
for (int i = 0; i < size_; ++i) {
if (i==0) {
if (tmp[i]*S[0]>0.0) {
correction = tmp[i]/Math.Abs(tmp[i]) *
Math.Min(Math.Abs(tmp[i]),
Math.Abs(3.0*S[0]));
} else {
correction = 0.0;
}
if (correction!=tmp[i]) {
tmp[i] = correction;
monotonicityAdjustments_[i] = true;
}
} else if (i == size_ - 1) {
if (tmp[i] * S[size_ - 2] > 0.0) {
correction = tmp[i]/Math.Abs(tmp[i]) *
Math.Min(Math.Abs(tmp[i]), Math.Abs(3.0 * S[size_ - 2]));
} else {
correction = 0.0;
}
if (correction!=tmp[i]) {
tmp[i] = correction;
monotonicityAdjustments_[i] = true;
}
} else {
pm=(S[i-1]*dx[i]+S[i]*dx[i-1])/
(dx[i-1]+dx[i]);
M = 3.0 * Math.Min(Math.Min(Math.Abs(S[i-1]), Math.Abs(S[i])),
Math.Abs(pm));
if (i>1) {
if ((S[i-1]-S[i-2])*(S[i]-S[i-1])>0.0) {
pd=(S[i-1]*(2.0*dx[i-1]+dx[i-2])
-S[i-2]*dx[i-1])/
(dx[i-2]+dx[i-1]);
if (pm*pd>0.0 && pm*(S[i-1]-S[i-2])>0.0) {
M = Math.Max(M, 1.5*Math.Min(
Math.Abs(pm),Math.Abs(pd)));
}
}
}
if (i < size_ - 2) {
if ((S[i]-S[i-1])*(S[i+1]-S[i])>0.0) {
pu=(S[i]*(2.0*dx[i]+dx[i+1])-S[i+1]*dx[i])/
(dx[i]+dx[i+1]);
if (pm*pu>0.0 && -pm*(S[i]-S[i-1])>0.0) {
M = Math.Max(M, 1.5*Math.Min(
Math.Abs(pm),Math.Abs(pu)));
}
}
}
if (tmp[i]*pm>0.0) {
correction = tmp[i]/Math.Abs(tmp[i]) *
Math.Min(Math.Abs(tmp[i]), M);
} else {
correction = 0.0;
}
if (correction!=tmp[i]) {
tmp[i] = correction;
monotonicityAdjustments_[i] = true;
}
}
}
}
// cubic coefficients
for (int i = 0; i < size_ - 1; ++i) {
a_[i] = tmp[i];
b_[i] = (3.0*S[i] - tmp[i+1] - 2.0*tmp[i])/dx[i];
c_[i] = (tmp[i+1] + tmp[i] - 2.0*S[i])/(dx[i]*dx[i]);
}
primitiveConst_[0] = 0.0;
for (int i = 1; i < size_ - 1; ++i) {
primitiveConst_[i] = primitiveConst_[i-1]
+ dx[i-1] *
(yBegin_[i-1] + dx[i-1] *
(a_[i-1]/2.0 + dx[i-1] *
(b_[i-1]/3.0 + dx[i-1] * c_[i-1]/4.0)));
}
}
public void testFdmLinearOpLayout()
{
int[] dims = new int[] { 5, 7, 8 };
List <int> dim = new List <int>(dims);
FdmLinearOpLayout layout = new FdmLinearOpLayout(dim);
int calculatedDim = layout.dim().Count;
int expectedDim = dim.Count;
if (calculatedDim != expectedDim)
{
QAssert.Fail("index.dimensions() should be " + expectedDim
+ ", but is " + calculatedDim);
}
int calculatedSize = layout.size();
int expectedSize = dim.accumulate(0, 3, 1, (x, y) => (x * y));
if (calculatedSize != expectedSize)
{
QAssert.Fail("index.size() should be "
+ expectedSize + ", but is " + calculatedSize);
}
for (int k = 0; k < dim[0]; ++k)
{
for (int l = 0; l < dim[1]; ++l)
{
for (int m = 0; m < dim[2]; ++m)
{
List <int> tmp = new InitializedList <int>(3);
tmp[0] = k; tmp[1] = l; tmp[2] = m;
int calculatedIndex = layout.index(tmp);
int expectedIndex = k + l * dim[0] + m * dim[0] * dim[1];
if (expectedIndex != layout.index(tmp))
{
QAssert.Fail("index.size() should be " + expectedIndex
+ ", but is " + calculatedIndex);
}
}
}
}
FdmLinearOpIterator iter = layout.begin();
for (int m = 0; m < dim[2]; ++m)
{
for (int l = 0; l < dim[1]; ++l)
{
for (int k = 0; k < dim[0]; ++k, ++iter)
{
for (int n = 1; n < 4; ++n)
{
int nn = layout.neighbourhood(iter, 1, n);
int calculatedIndex = k + m * dim[0] * dim[1]
+ ((l < dim[1] - n)? l + n
: dim[1] - 1 - (l + n - (dim[1] - 1))) * dim[0];
if (nn != calculatedIndex)
{
QAssert.Fail("next neighbourhood index is " + nn
+ " but should be " + calculatedIndex);
}
}
for (int n = 1; n < 7; ++n)
{
int nn = layout.neighbourhood(iter, 2, -n);
int calculatedIndex = k + l * dim[0]
+ ((m < n) ? n - m : m - n) * dim[0] * dim[1];
if (nn != calculatedIndex)
{
QAssert.Fail("next neighbourhood index is " + nn
+ " but should be " + calculatedIndex);
}
}
}
}
}
}
protected List<double> sinkingNotionals(Period maturityTenor,
Frequency sinkingFrequency,
double couponRate,
double initialNotional)
{
Period freqPeriod = new Period(sinkingFrequency);
int nPeriods = 0;
Utils.QL_REQUIRE(isSubPeriod(freqPeriod, maturityTenor, out nPeriods),() =>
"Bond frequency is incompatible with the maturity tenor");
List<double> notionals = new InitializedList<double>(nPeriods+1);
notionals[0] = initialNotional;
double coupon = couponRate / (double)sinkingFrequency;
double compoundedInterest = 1.0;
double totalValue = Math.Pow(1.0+coupon, nPeriods);
for(int i = 0; i < (int)nPeriods-1; ++i)
{
compoundedInterest *= (1.0 + coupon);
double currentNotional = 0.0;
if(coupon < 1.0e-12) {
currentNotional =
initialNotional*(1.0 - (i+1.0)/nPeriods);
}
else {
currentNotional =
initialNotional*(compoundedInterest - (compoundedInterest-1.0)/(1.0 - 1.0/totalValue));
}
notionals[i+1] = currentNotional;
}
notionals[notionals.Count-1] = 0.0;
return notionals;
}
public void testMonteCarloCapletPricing()
{
//"Testing caplet LMM Monte-Carlo caplet pricing..."
//SavedSettings backup;
/* factor loadings are taken from Hull & White article
plus extra normalisation to get orthogonal eigenvectors
http://www.rotman.utoronto.ca/~amackay/fin/libormktmodel2.pdf */
double[] compValues = {0.85549771, 0.46707264, 0.22353259,
0.91915359, 0.37716089, 0.11360610,
0.96438280, 0.26413316,-0.01412414,
0.97939148, 0.13492952,-0.15028753,
0.95970595,-0.00000000,-0.28100621,
0.97939148,-0.13492952,-0.15028753,
0.96438280,-0.26413316,-0.01412414,
0.91915359,-0.37716089, 0.11360610,
0.85549771,-0.46707264, 0.22353259};
Matrix volaComp=new Matrix(9,3);
List<double> lcompValues=new InitializedList<double>(27,0);
List<double> ltemp = new InitializedList<double>(3, 0);
lcompValues=compValues.ToList();
//std::copy(compValues, compValues+9*3, volaComp.begin());
for (int i = 0; i < 9; i++)
{
ltemp = lcompValues.GetRange(3*i, 3);
for (int j = 0; j < 3; j++)
volaComp[i, j] = ltemp[j];
}
LiborForwardModelProcess process1 = makeProcess();
LiborForwardModelProcess process2 = makeProcess(volaComp);
List<double> tmp = process1.fixingTimes();
TimeGrid grid=new TimeGrid(tmp ,12);
List<int> location=new List<int>();
for (int i=0; i < tmp.Count; ++i) {
location.Add(grid.index(tmp[i])) ;
}
// set-up a small Monte-Carlo simulation to price caplets
// and ratchet caps using a one- and a three factor libor market model
ulong seed = 42;
LowDiscrepancy.icInstance = new InverseCumulativeNormal();
IRNG rsg1 = (IRNG)new LowDiscrepancy().make_sequence_generator(
process1.factors()*(grid.size()-1), seed);
IRNG rsg2 = (IRNG)new LowDiscrepancy().make_sequence_generator(
process2.factors()*(grid.size()-1), seed);
MultiPathGenerator<IRNG> generator1=new MultiPathGenerator<IRNG> (process1, grid, rsg1, false);
MultiPathGenerator<IRNG> generator2=new MultiPathGenerator<IRNG> (process2, grid, rsg2, false);
const int nrTrails = 250000;
List<GeneralStatistics> stat1 = new InitializedList<GeneralStatistics>(process1.size());
List<GeneralStatistics> stat2 = new InitializedList<GeneralStatistics>(process2.size());
List<GeneralStatistics> stat3 = new InitializedList<GeneralStatistics>(process2.size() - 1);
for (int i=0; i<nrTrails; ++i) {
Sample<MultiPath> path1 = generator1.next();
Sample<MultiPath> path2 = generator2.next();
List<double> rates1=new InitializedList<double>(len);
List<double> rates2 = new InitializedList<double>(len);
for (int j=0; j<process1.size(); ++j) {
rates1[j] = path1.value[j][location[j]];
rates2[j] = path2.value[j][location[j]];
}
List<double> dis1 = process1.discountBond(rates1);
List<double> dis2 = process2.discountBond(rates2);
for (int k=0; k<process1.size(); ++k) {
double accrualPeriod = process1.accrualEndTimes()[k]
- process1.accrualStartTimes()[k];
// caplet payoff function, cap rate at 4%
double payoff1 = Math.Max(rates1[k] - 0.04, 0.0) * accrualPeriod;
double payoff2 = Math.Max(rates2[k] - 0.04, 0.0) * accrualPeriod;
stat1[k].add(dis1[k] * payoff1);
stat2[k].add(dis2[k] * payoff2);
if (k != 0) {
// ratchet cap payoff function
double payoff3 = Math.Max(rates2[k] - (rates2[k-1]+0.0025), 0.0)
* accrualPeriod;
stat3[k-1].add(dis2[k] * payoff3);
}
}
}
double[] capletNpv = {0.000000000000, 0.000002841629, 0.002533279333,
0.009577143571, 0.017746502618, 0.025216116835,
0.031608230268, 0.036645683881, 0.039792254012,
0.041829864365};
double[] ratchetNpv = {0.0082644895, 0.0082754754, 0.0082159966,
0.0082982822, 0.0083803357, 0.0084366961,
0.0084173270, 0.0081803406, 0.0079533814};
for (int k=0; k < process1.size(); ++k) {
double calculated1 = stat1[k].mean();
double tolerance1 = stat1[k].errorEstimate();
double expected = capletNpv[k];
if (Math.Abs(calculated1 - expected) > tolerance1) {
Assert.Fail("Failed to reproduce expected caplet NPV"
+ "\n calculated: " + calculated1
+ "\n error int: " + tolerance1
+ "\n expected: " + expected);
}
double calculated2 = stat2[k].mean();
double tolerance2 = stat2[k].errorEstimate();
if (Math.Abs(calculated2 - expected) > tolerance2) {
Assert.Fail("Failed to reproduce expected caplet NPV"
+ "\n calculated: " + calculated2
+ "\n error int: " + tolerance2
+ "\n expected: " + expected);
}
if (k != 0) {
double calculated3 = stat3[k-1].mean();
double tolerance3 = stat3[k-1].errorEstimate();
expected = ratchetNpv[k-1];
double refError = 1e-5; // 1e-5. error bars of the reference values
if (Math.Abs(calculated3 - expected) > tolerance3 + refError) {
Assert.Fail("Failed to reproduce expected caplet NPV"
+ "\n calculated: " + calculated3
+ "\n error int: " + tolerance3 + refError
+ "\n expected: " + expected);
}
}
}
}
public void testCachedFloating()
{
// "Testing floating-rate bond prices against cached values...");
CommonVars vars = new CommonVars();
Date today = new Date(22, Month.November, 2004);
Settings.setEvaluationDate(today);
int settlementDays = 1;
var riskFreeRate = new Handle <YieldTermStructure>(Utilities.flatRate(today, 0.025, new Actual360()));
var discountCurve = new Handle <YieldTermStructure>(Utilities.flatRate(today, 0.03, new Actual360()));
IborIndex index = new USDLibor(new Period(6, TimeUnit.Months), riskFreeRate);
int fixingDays = 1;
double tolerance = 1.0e-6;
IborCouponPricer pricer = new BlackIborCouponPricer(new Handle <OptionletVolatilityStructure>());
// plain
Schedule sch = new Schedule(new Date(30, Month.November, 2004), new Date(30, Month.November, 2008),
new Period(Frequency.Semiannual), new UnitedStates(UnitedStates.Market.GovernmentBond),
BusinessDayConvention.ModifiedFollowing, BusinessDayConvention.ModifiedFollowing,
DateGeneration.Rule.Backward, false);
FloatingRateBond bond1 = new FloatingRateBond(settlementDays, vars.faceAmount, sch,
index, new ActualActual(ActualActual.Convention.ISMA),
BusinessDayConvention.ModifiedFollowing, fixingDays,
new List <double>(), new List <double>(),
new List <double>(), new List <double>(),
false,
100.0, new Date(30, Month.November, 2004));
IPricingEngine bondEngine = new DiscountingBondEngine(riskFreeRate);
bond1.setPricingEngine(bondEngine);
Utils.setCouponPricer(bond1.cashflows(), pricer);
#if QL_USE_INDEXED_COUPON
double cachedPrice1 = 99.874645;
#else
double cachedPrice1 = 99.874646;
#endif
double price = bond1.cleanPrice();
if (Math.Abs(price - cachedPrice1) > tolerance)
{
Assert.Fail("failed to reproduce cached price:\n"
+ " calculated: " + price + "\n"
+ " expected: " + cachedPrice1 + "\n"
+ " error: " + (price - cachedPrice1));
}
// different risk-free and discount curve
FloatingRateBond bond2 = new FloatingRateBond(settlementDays, vars.faceAmount, sch,
index, new ActualActual(ActualActual.Convention.ISMA),
BusinessDayConvention.ModifiedFollowing, fixingDays,
new List <double>(), new List <double>(),
new List <double>(), new List <double>(),
false,
100.0, new Date(30, Month.November, 2004));
IPricingEngine bondEngine2 = new DiscountingBondEngine(discountCurve);
bond2.setPricingEngine(bondEngine2);
Utils.setCouponPricer(bond2.cashflows(), pricer);
#if QL_USE_INDEXED_COUPON
double cachedPrice2 = 97.955904;
#else
double cachedPrice2 = 97.955904;
#endif
price = bond2.cleanPrice();
if (Math.Abs(price - cachedPrice2) > tolerance)
{
Assert.Fail("failed to reproduce cached price:\n"
+ " calculated: " + price + "\n"
+ " expected: " + cachedPrice2 + "\n"
+ " error: " + (price - cachedPrice2));
}
// varying spread
InitializedList <double> spreads = new InitializedList <double>(4);
spreads[0] = 0.001;
spreads[1] = 0.0012;
spreads[2] = 0.0014;
spreads[3] = 0.0016;
FloatingRateBond bond3 = new FloatingRateBond(settlementDays, vars.faceAmount, sch,
index, new ActualActual(ActualActual.Convention.ISMA),
BusinessDayConvention.ModifiedFollowing, fixingDays,
new List <double>(), spreads,
new List <double>(), new List <double>(),
false,
100.0, new Date(30, Month.November, 2004));
bond3.setPricingEngine(bondEngine2);
Utils.setCouponPricer(bond3.cashflows(), pricer);
#if QL_USE_INDEXED_COUPON
double cachedPrice3 = 98.495458;
#else
double cachedPrice3 = 98.495459;
#endif
price = bond3.cleanPrice();
if (Math.Abs(price - cachedPrice3) > tolerance)
{
Assert.Fail("failed to reproduce cached price:\n"
+ " calculated: " + price + "\n"
+ " expected: " + cachedPrice3 + "\n"
+ " error: " + (price - cachedPrice3));
}
}
public void testStrikeDependency()
{
//("Testing swaption dependency on strike......");
CommonVars vars = new CommonVars();
double[] strikes = new double[] { 0.03, 0.04, 0.05, 0.06, 0.07 };
for (int i = 0; i < exercises.Length; i++) {
for (int j = 0; j < lengths.Length; j++) {
for (int k=0; k < type.Length ; k++) {
Date exerciseDate = vars.calendar.advance(vars.today,
exercises[i]);
Date startDate = vars.calendar.advance(exerciseDate,
vars.settlementDays, TimeUnit.Days);
// store the results for different rates...
List<double> values = new InitializedList<double>(strikes.Length);
List<double> values_cash = new InitializedList<double>(strikes.Length);
double vol = 0.20;
for (int l=0; l< strikes.Length ; l++) {
VanillaSwap swap = new MakeVanillaSwap(lengths[j], vars.index, strikes[l])
.withEffectiveDate(startDate)
.withFloatingLegSpread(0.0)
.withType(type[k]);
Swaption swaption = vars.makeSwaption(swap,exerciseDate,vol);
// FLOATING_POINT_EXCEPTION
values[l]=swaption.NPV();
Swaption swaption_cash = vars.makeSwaption( swap,exerciseDate,vol,
Settlement.Type.Cash);
values_cash[l]=swaption_cash.NPV();
}
// and check that they go the right way
if (type[k]==VanillaSwap.Type.Payer) {
for (int z = 0; z < values.Count - 1; z++)
{
if( values[z]<values[z+1]){
Assert.Fail("NPV of Payer swaption with delivery settlement"+
"is increasing with the strike:" +
"\noption tenor: " + exercises[i] +
"\noption date: " + exerciseDate +
"\nvolatility: " + vol +
"\nswap tenor: " + lengths[j] +
"\nvalue: " + values[z ] +" at strike: " + strikes[z ] +
"\nvalue: " + values[z+1] + " at strike: " + strikes[z+1]);
}
}
for (int z = 0; z < values_cash.Count - 1; z++)
{
if (values_cash[z] < values_cash[z + 1])
{
Assert.Fail("NPV of Payer swaption with cash settlement" +
"is increasing with the strike:" +
"\noption tenor: " + exercises[i] +
"\noption date: " + exerciseDate +
"\nvolatility: " + vol +
"\nswap tenor: " + lengths[j] +
"\nvalue: " + values_cash[z] + " at strike: " + strikes[z] +
"\nvalue: " + values_cash[z + 1] + " at strike: " + strikes[z + 1]);
}
}
}
else {
for (int z = 0; z < values.Count - 1; z++){
if (values[z] > values[z+1]){
Assert.Fail("NPV of Receiver swaption with delivery settlement" +
"is increasing with the strike:" +
"\noption tenor: " + exercises[i] +
"\noption date: " + exerciseDate +
"\nvolatility: " + vol +
"\nswap tenor: " + lengths[j] +
"\nvalue: " + values[z] + " at strike: " + strikes[z] +
"\nvalue: " + values[z + 1] + " at strike: " + strikes[z + 1]);
}
}
for (int z = 0; z < values_cash.Count - 1; z++)
{
if (values[z] > values[z+1])
{
Assert.Fail("NPV of Receiver swaption with cash settlement" +
"is increasing with the strike:" +
"\noption tenor: " + exercises[i] +
"\noption date: " + exerciseDate +
"\nvolatility: " + vol +
"\nswap tenor: " + lengths[j] +
"\nvalue: " + values_cash[z] + " at strike: " + strikes[z] +
"\nvalue: " + values_cash[z + 1] + " at strike: " + strikes[z + 1]);
}
}
}
}
}
}
}
public void testCachedFixed()
{
// "Testing fixed-coupon bond prices against cached values...");
CommonVars vars = new CommonVars();
Date today = new Date(22, Month.November, 2004);
Settings.setEvaluationDate(today);
int settlementDays = 1;
var discountCurve = new Handle<YieldTermStructure>(Utilities.flatRate(today, 0.03, new Actual360()));
double tolerance = 1.0e-6;
// plain
Schedule sch = new Schedule(new Date(30, Month.November, 2004),
new Date(30, Month.November, 2008), new Period(Frequency.Semiannual),
new UnitedStates(UnitedStates.Market.GovernmentBond),
BusinessDayConvention.Unadjusted, BusinessDayConvention.Unadjusted, DateGeneration.Rule.Backward, false);
FixedRateBond bond1 = new FixedRateBond(settlementDays, vars.faceAmount, sch, new List<double>() { 0.02875 },
new ActualActual(ActualActual.Convention.ISMA), BusinessDayConvention.ModifiedFollowing,
100.0, new Date(30, Month.November, 2004));
IPricingEngine bondEngine = new DiscountingBondEngine(discountCurve);
bond1.setPricingEngine(bondEngine);
double cachedPrice1 = 99.298100;
double price = bond1.cleanPrice();
if (Math.Abs(price - cachedPrice1) > tolerance)
{
Console.WriteLine("failed to reproduce cached price:\n"
+ " calculated: " + price + "\n"
+ " expected: " + cachedPrice1 + "\n"
+ " error: " + (price - cachedPrice1));
}
// varying coupons
InitializedList<double> couponRates = new InitializedList<double>(4);
couponRates[0] = 0.02875;
couponRates[1] = 0.03;
couponRates[2] = 0.03125;
couponRates[3] = 0.0325;
FixedRateBond bond2 = new FixedRateBond(settlementDays, vars.faceAmount, sch, couponRates,
new ActualActual(ActualActual.Convention.ISMA),
BusinessDayConvention.ModifiedFollowing,
100.0, new Date(30, Month.November, 2004));
bond2.setPricingEngine(bondEngine);
double cachedPrice2 = 100.334149;
price = bond2.cleanPrice();
if (Math.Abs(price - cachedPrice2) > tolerance)
{
Console.WriteLine("failed to reproduce cached price:\n"
+ " calculated: " + price + "\n"
+ " expected: " + cachedPrice2 + "\n"
+ " error: " + (price - cachedPrice2));
}
// stub date
Schedule sch3 = new Schedule(new Date(30, Month.November, 2004),
new Date(30, Month.March, 2009), new Period(Frequency.Semiannual),
new UnitedStates(UnitedStates.Market.GovernmentBond),
BusinessDayConvention.Unadjusted, BusinessDayConvention.Unadjusted, DateGeneration.Rule.Backward, false,
null, new Date(30, Month.November, 2008));
FixedRateBond bond3 = new FixedRateBond(settlementDays, vars.faceAmount, sch3,
couponRates, new ActualActual(ActualActual.Convention.ISMA),
BusinessDayConvention.ModifiedFollowing,
100.0, new Date(30, Month.November, 2004));
bond3.setPricingEngine(bondEngine);
double cachedPrice3 = 100.382794;
price = bond3.cleanPrice();
if (Math.Abs(price - cachedPrice3) > tolerance)
{
Assert.Fail("failed to reproduce cached price:\n"
+ " calculated: " + price + "\n"
+ " expected: " + cachedPrice3 + "\n"
+ " error: " + (price - cachedPrice3));
}
}
public void testObservability()
{
// Testing volatility cube observability
CommonVars vars = new CommonVars();
List <List <Handle <Quote> > > parametersGuess =
new InitializedList <List <Handle <Quote> > >(vars.cube.tenors.options.Count * vars.cube.tenors.swaps.Count);
for (int i = 0; i < vars.cube.tenors.options.Count * vars.cube.tenors.swaps.Count; i++)
{
parametersGuess[i] = new InitializedList <Handle <Quote> >(4);
parametersGuess[i][0] = new Handle <Quote>(new SimpleQuote(0.2));
parametersGuess[i][1] = new Handle <Quote>(new SimpleQuote(0.5));
parametersGuess[i][2] = new Handle <Quote>(new SimpleQuote(0.4));
parametersGuess[i][3] = new Handle <Quote>(new SimpleQuote(0.0));
}
List <bool> isParameterFixed = new InitializedList <bool>(4, false);
SwaptionVolCube1x volCube1_0, volCube1_1;
// VolCube created before change of reference date
volCube1_0 = new SwaptionVolCube1x(vars.atmVolMatrix,
vars.cube.tenors.options,
vars.cube.tenors.swaps,
vars.cube.strikeSpreads,
vars.cube.volSpreadsHandle,
vars.swapIndexBase,
vars.shortSwapIndexBase,
vars.vegaWeighedSmileFit,
parametersGuess,
isParameterFixed,
true);
Date referenceDate = Settings.evaluationDate();
Settings.setEvaluationDate(vars.conventions.calendar.advance(referenceDate, new Period(1, TimeUnit.Days),
vars.conventions.optionBdc));
// VolCube created after change of reference date
volCube1_1 = new SwaptionVolCube1x(vars.atmVolMatrix,
vars.cube.tenors.options,
vars.cube.tenors.swaps,
vars.cube.strikeSpreads,
vars.cube.volSpreadsHandle,
vars.swapIndexBase,
vars.shortSwapIndexBase,
vars.vegaWeighedSmileFit,
parametersGuess,
isParameterFixed,
true);
double dummyStrike = 0.03;
for (int i = 0; i < vars.cube.tenors.options.Count; i++)
{
for (int j = 0; j < vars.cube.tenors.swaps.Count; j++)
{
for (int k = 0; k < vars.cube.strikeSpreads.Count; k++)
{
double v0 = volCube1_0.volatility(vars.cube.tenors.options[i],
vars.cube.tenors.swaps[j],
dummyStrike + vars.cube.strikeSpreads[k],
false);
double v1 = volCube1_1.volatility(vars.cube.tenors.options[i],
vars.cube.tenors.swaps[j],
dummyStrike + vars.cube.strikeSpreads[k],
false);
if (Math.Abs(v0 - v1) > 1e-14)
{
QAssert.Fail(" option tenor = " + vars.cube.tenors.options[i] +
" swap tenor = " + vars.cube.tenors.swaps[j] +
" strike = " + (dummyStrike + vars.cube.strikeSpreads[k]) +
" v0 = " + (v0) +
" v1 = " + (v1) +
" error = " + Math.Abs(v1 - v0));
}
}
}
}
Settings.setEvaluationDate(referenceDate);
SwaptionVolCube2 volCube2_0, volCube2_1;
// VolCube created before change of reference date
volCube2_0 = new SwaptionVolCube2(vars.atmVolMatrix,
vars.cube.tenors.options,
vars.cube.tenors.swaps,
vars.cube.strikeSpreads,
vars.cube.volSpreadsHandle,
vars.swapIndexBase,
vars.shortSwapIndexBase,
vars.vegaWeighedSmileFit);
Settings.setEvaluationDate(vars.conventions.calendar.advance(referenceDate, new Period(1, TimeUnit.Days),
vars.conventions.optionBdc));
// VolCube created after change of reference date
volCube2_1 = new SwaptionVolCube2(vars.atmVolMatrix,
vars.cube.tenors.options,
vars.cube.tenors.swaps,
vars.cube.strikeSpreads,
vars.cube.volSpreadsHandle,
vars.swapIndexBase,
vars.shortSwapIndexBase,
vars.vegaWeighedSmileFit);
for (int i = 0; i < vars.cube.tenors.options.Count; i++)
{
for (int j = 0; j < vars.cube.tenors.swaps.Count; j++)
{
for (int k = 0; k < vars.cube.strikeSpreads.Count; k++)
{
double v0 = volCube2_0.volatility(vars.cube.tenors.options[i],
vars.cube.tenors.swaps[j],
dummyStrike + vars.cube.strikeSpreads[k],
false);
double v1 = volCube2_1.volatility(vars.cube.tenors.options[i],
vars.cube.tenors.swaps[j],
dummyStrike + vars.cube.strikeSpreads[k],
false);
if (Math.Abs(v0 - v1) > 1e-14)
{
QAssert.Fail(" option tenor = " + vars.cube.tenors.options[i] +
" swap tenor = " + vars.cube.tenors.swaps[j] +
" strike = " + (dummyStrike + vars.cube.strikeSpreads[k]) +
" v0 = " + (v0) +
" v1 = " + (v1) +
" error = " + Math.Abs(v1 - v0));
}
}
}
}
Settings.setEvaluationDate(referenceDate);
}
static void Main(string[] args)
{
DateTime timer = DateTime.Now;
//////////////// DATES //////////////////////////////////////////////
Calendar calendar = new TARGET();
Date todaysDate = new Date(15, Month.January, 2017);
Date settlementDate = new Date(todaysDate);
Settings.setEvaluationDate(todaysDate);
DayCounter dayCounter = new Actual365Fixed();
//////////////// MARKET //////////////////////////////////////////////
// Spot
double underlying = 1.0;
Handle <Quote> underlyingH = new Handle <Quote>(new SimpleQuote(underlying));
// Curves
double riskFreeRate = 0.01;
double dividendYield = 0.035;
double cstVol = 0.2;
double hazardRate = 0.02;
Handle <YieldTermStructure> flatTermStructure = new Handle <YieldTermStructure>(new FlatForward(settlementDate, riskFreeRate, dayCounter));
Handle <YieldTermStructure> flatDividendTS = new Handle <YieldTermStructure>(new FlatForward(settlementDate, dividendYield, dayCounter));
Handle <BlackVolTermStructure> mySurfaceH = new Handle <BlackVolTermStructure>(new BlackConstantVol(settlementDate, calendar, cstVol, dayCounter));
Handle <DefaultProbabilityTermStructure> defaultTSH = new Handle <DefaultProbabilityTermStructure>(new FlatHazardRate(settlementDate, hazardRate, dayCounter));
// Process
GeneralizedBlackScholesProcessTolerance bsmProcess = new GeneralizedBlackScholesProcessTolerance(underlyingH, flatDividendTS, flatTermStructure, mySurfaceH);
//////////////// INSTRUMENT //////////////////////////////////////////////
List <Date> fixings = new InitializedList <Date>();
for (int i = 1; i <= 8; i++)
{
fixings.Add(settlementDate + new Period(i * 3, TimeUnit.Months));
}
double couponBond = 0.0525;
double couponBinary = 0.077;
double barrierlvl = 0.7;
double strike = 1.0;
double recovery = 0.4;
double absoluteTolerance = 0.0001;
GenericScriptRepack repack = new GenericScriptRepack(fixings, couponBond, couponBinary, barrierlvl, strike, recovery);
IPricingEngine mcengine = new MakeMCGenericScriptInstrument <PseudoRandom>(bsmProcess)
.withAbsoluteTolerance(absoluteTolerance)
.withStepsPerYear(52)
.withSeed(50)
.withCredit(defaultTSH)
.value();
repack.setPricingEngine(mcengine);
Console.WriteLine("Repack pricing = {0:0.0000}", repack.NPV());
repack.inspout(5, true);
//////////////// END TEST //////////////////////////////////////////////
Console.WriteLine();
Console.WriteLine(" \nRun completed in {0}", DateTime.Now - timer);
Console.WriteLine();
Console.Write("Press any key to continue ...");
Console.ReadKey();
}
public void testRegression()
{
//("Testing linear least-squares regression...");
//SavedSettings backup;
const int nr = 100000;
var rng = new InverseCumulativeRng <MersenneTwisterUniformRng, InverseCumulativeNormal>(
new MersenneTwisterUniformRng(1234u));
List <Func <double, double> > v = new List <Func <double, double> >();
v.Add(x => 1.0);
v.Add(x => x);
v.Add(x => x * x);
v.Add(Math.Sin);
List <Func <double, double> > w = new List <Func <double, double> >(v);
w.Add(x => x * x);
for (int k = 0; k < 3; ++k)
{
int i;
double[] a = { rng.next().value,
rng.next().value,
rng.next().value,
rng.next().value };
List <double> x = new InitializedList <double>(nr), y = new InitializedList <double>(nr);
for (i = 0; i < nr; ++i)
{
x[i] = rng.next().value;
// regression in y = a_1 + a_2*x + a_3*x^2 + a_4*sin(x) + eps
y[i] = a[0] * v[0](x[i]) + a[1] * v[1](x[i]) + a[2] * v[2](x[i])
+ a[3] * v[3](x[i]) + rng.next().value;
}
LinearLeastSquaresRegression m = new LinearLeastSquaresRegression(x, y, v);
for (i = 0; i < v.Count; ++i)
{
if (m.standardErrors()[i] > tolerance)
{
Assert.Fail("Failed to reproduce linear regression coef."
+ "\n error: " + m.standardErrors()[i]
+ "\n tolerance: " + tolerance);
}
if (Math.Abs(m.coefficients()[i] - a[i]) > 3 * m.error()[i])
{
Assert.Fail("Failed to reproduce linear regression coef."
+ "\n calculated: " + m.coefficients()[i]
+ "\n error: " + m.standardErrors()[i]
+ "\n expected: " + a[i]);
}
}
m = new LinearLeastSquaresRegression(x, y, w);
double[] ma = { m.coefficients()[0], m.coefficients()[1], m.coefficients()[2] + m.coefficients()[4], m.coefficients()[3] };
double[] err = { m.standardErrors()[0], m.standardErrors()[1],
Math.Sqrt(m.standardErrors()[2] * m.standardErrors()[2]
+ m.standardErrors()[4] * m.standardErrors()[4]),
m.standardErrors()[3] };
for (i = 0; i < v.Count; ++i)
{
if (Math.Abs(ma[i] - a[i]) > 3 * err[i])
{
Assert.Fail("Failed to reproduce linear regression coef."
+ "\n calculated: " + ma[i]
+ "\n error: " + err[i]
+ "\n expected: " + a[i]);
}
}
}
}
public void testSpreadedCube()
{
// Testing spreaded swaption volatility cube
CommonVars vars = new CommonVars();
List <List <Handle <Quote> > > parametersGuess =
new InitializedList <List <Handle <Quote> > >(vars.cube.tenors.options.Count * vars.cube.tenors.swaps.Count);
for (int i = 0; i < vars.cube.tenors.options.Count * vars.cube.tenors.swaps.Count; i++)
{
parametersGuess[i] = new InitializedList <Handle <Quote> >(4);
parametersGuess[i][0] = new Handle <Quote>(new SimpleQuote(0.2));
parametersGuess[i][1] = new Handle <Quote>(new SimpleQuote(0.5));
parametersGuess[i][2] = new Handle <Quote>(new SimpleQuote(0.4));
parametersGuess[i][3] = new Handle <Quote>(new SimpleQuote(0.0));
}
List <bool> isParameterFixed = new InitializedList <bool>(4, false);
Handle <SwaptionVolatilityStructure> volCube = new Handle <SwaptionVolatilityStructure>(
new SwaptionVolCube1x(vars.atmVolMatrix,
vars.cube.tenors.options,
vars.cube.tenors.swaps,
vars.cube.strikeSpreads,
vars.cube.volSpreadsHandle,
vars.swapIndexBase,
vars.shortSwapIndexBase,
vars.vegaWeighedSmileFit,
parametersGuess,
isParameterFixed,
true));
SimpleQuote spread = new SimpleQuote(0.0001);
Handle <Quote> spreadHandle = new Handle <Quote>(spread);
SwaptionVolatilityStructure spreadedVolCube = new SpreadedSwaptionVolatility(volCube, spreadHandle);
List <double> strikes = new List <double>();
for (int k = 1; k < 100; k++)
{
strikes.Add(k * .01);
}
for (int i = 0; i < vars.cube.tenors.options.Count; i++)
{
for (int j = 0; j < vars.cube.tenors.swaps.Count; j++)
{
SmileSection smileSectionByCube = volCube.link.smileSection(vars.cube.tenors.options[i],
vars.cube.tenors.swaps[j]);
SmileSection smileSectionBySpreadedCube = spreadedVolCube.smileSection(vars.cube.tenors.options[i],
vars.cube.tenors.swaps[j]);
for (int k = 0; k < strikes.Count; k++)
{
double strike = strikes[k];
double diff = spreadedVolCube.volatility(vars.cube.tenors.options[i], vars.cube.tenors.swaps[j], strike)
- volCube.link.volatility(vars.cube.tenors.options[i], vars.cube.tenors.swaps[j], strike);
if (Math.Abs(diff - spread.value()) > 1e-16)
{
QAssert.Fail("\ndiff!=spread in volatility method:" +
"\nexpiry time = " + vars.cube.tenors.options[i] +
"\nswap length = " + vars.cube.tenors.swaps[j] +
"\n atm strike = " + (strike) +
"\ndiff = " + diff +
"\nspread = " + spread.value());
}
diff = smileSectionBySpreadedCube.volatility(strike) - smileSectionByCube.volatility(strike);
if (Math.Abs(diff - spread.value()) > 1e-16)
{
QAssert.Fail("\ndiff!=spread in smile section method:" +
"\nexpiry time = " + vars.cube.tenors.options[i] +
"\nswap length = " + vars.cube.tenors.swaps[j] +
"\n atm strike = " + (strike) +
"\ndiff = " + diff +
"\nspread = " + spread.value());
}
}
}
}
//testing observability
Flag f = new Flag();
spreadedVolCube.registerWith(f.update);
volCube.link.update();
if (!f.isUp())
{
QAssert.Fail("SpreadedSwaptionVolatilityStructure does not propagate notifications");
}
f.lower();
spread.setValue(.001);
if (!f.isUp())
{
QAssert.Fail("SpreadedSwaptionVolatilityStructure does not propagate notifications");
}
}
public void testMultiDimRegression()
{
//BOOST_MESSAGE("Testing linear least-squares regression...");
//SavedSettings backup;
const int nr = 100000;
const int dims = 4;
const double tolerance = 0.01;
var rng = new InverseCumulativeRng <MersenneTwisterUniformRng, InverseCumulativeNormal>(
new MersenneTwisterUniformRng(1234u));
List <Func <Vector, double> > v = new List <Func <Vector, double> >();
v.Add(xx => 1.0);
for (int i = 0; i < dims; ++i)
{
int jj = i; // c# delegate work-around vs. boost bind; jj has to be evaluted before add delegate to the list
v.Add(vv => vv[jj]);
}
Vector coeff = new Vector(v.Count);
for (int i = 0; i < v.Count; ++i)
{
coeff[i] = rng.next().value;
}
List <double> y = new InitializedList <double>(nr, 0.0);
List <Vector> x = new InitializedList <Vector>(nr);
for (int i = 0; i < nr; ++i)
{
x[i] = new Vector(dims);
for (int j = 0; j < dims; ++j)
{
x[i][j] = rng.next().value;
}
for (int j = 0; j < v.Count; ++j)
{
y[i] += coeff[j] * v[j](x[i]);
}
y[i] += rng.next().value;
}
LinearLeastSquaresRegression <Vector> m = new LinearLeastSquaresRegression <Vector>(x, y, v);
for (int i = 0; i < v.Count; ++i)
{
if (m.standardErrors()[i] > tolerance)
{
Assert.Fail("Failed to reproduce linear regression coef."
+ "\n error: " + m.standardErrors()[i]
+ "\n tolerance: " + tolerance);
}
if (Math.Abs(m.coefficients()[i] - coeff[i]) > 3 * tolerance)
{
Assert.Fail("Failed to reproduce linear regression coef."
+ "\n calculated: " + m.coefficients()[i]
+ "\n error: " + m.standardErrors()[i]
+ "\n expected: " + coeff[i]);
}
}
}
public void testCallableEquityPricing()
{
// Testing the pricing of a callable equity product
/*
* For the definition of the example product see
* Alexander Giese, On the Pricing of Auto-Callable Equity
* Structures in the Presence of Stochastic Volatility and
* Stochastic Interest Rates .
* http://workshop.mathfinance.de/2006/papers/giese/slides.pdf
*/
int maturity = 7;
DayCounter dc = new Actual365Fixed();
Date today = Date.Today;
Settings.Instance.setEvaluationDate(today);
Handle <Quote> spot = new Handle <Quote>(new SimpleQuote(100.0));
SimpleQuote qRate = new SimpleQuote(0.04);
Handle <YieldTermStructure> qTS = new Handle <YieldTermStructure>(Utilities.flatRate(today, qRate, dc));
SimpleQuote rRate = new SimpleQuote(0.04);
Handle <YieldTermStructure> rTS = new Handle <YieldTermStructure>(Utilities.flatRate(today, rRate, dc));
HestonProcess hestonProcess = new HestonProcess(rTS, qTS, spot, 0.0625, 1.0, 0.24 * 0.24, 1e-4, 0.0);
// FLOATING_POINT_EXCEPTION
HullWhiteForwardProcess hwProcess = new HullWhiteForwardProcess(rTS, 0.00883, 0.00526);
hwProcess.setForwardMeasureTime(dc.yearFraction(today, today + new Period(maturity + 1, TimeUnit.Years)));
HybridHestonHullWhiteProcess jointProcess = new HybridHestonHullWhiteProcess(hestonProcess, hwProcess, -0.4);
Schedule schedule = new Schedule(today, today + new Period(maturity, TimeUnit.Years), new Period(1, TimeUnit.Years),
new TARGET(), BusinessDayConvention.Following, BusinessDayConvention.Following, DateGeneration.Rule.Forward, false);
List <double> times = new InitializedList <double>(maturity + 1);
for (int i = 0; i <= maturity; ++i)
{
times[i] = i;
}
TimeGrid grid = new TimeGrid(times, times.Count);
List <double> redemption = new InitializedList <double>(maturity);
for (int i = 0; i < maturity; ++i)
{
redemption[i] = 1.07 + 0.03 * i;
}
ulong seed = 42;
IRNG rsg = (InverseCumulativeRsg <RandomSequenceGenerator <MersenneTwisterUniformRng>
, InverseCumulativeNormal>)
new PseudoRandom().make_sequence_generator(jointProcess.factors() * (grid.size() - 1), seed);
MultiPathGenerator <IRNG> generator = new MultiPathGenerator <IRNG>(jointProcess, grid, rsg, false);
GeneralStatistics stat = new GeneralStatistics();
double antitheticPayoff = 0;
int nrTrails = 40000;
for (int i = 0; i < nrTrails; ++i)
{
bool antithetic = (i % 2) != 0;
Sample <IPath> path = antithetic ? generator.antithetic() : generator.next();
MultiPath value = path.value as MultiPath;
Utils.QL_REQUIRE(value != null, () => "Invalid Path");
double payoff = 0;
for (int j = 1; j <= maturity; ++j)
{
if (value[0][j] > spot.link.value())
{
Vector states = new Vector(3);
for (int k = 0; k < 3; ++k)
{
states[k] = value[k][j];
}
payoff = redemption[j - 1] / jointProcess.numeraire(grid[j], states);
break;
}
else if (j == maturity)
{
Vector states = new Vector(3);
for (int k = 0; k < 3; ++k)
{
states[k] = value[k][j];
}
payoff = 1.0 / jointProcess.numeraire(grid[j], states);
}
}
if (antithetic)
{
stat.add(0.5 * (antitheticPayoff + payoff));
}
else
{
antitheticPayoff = payoff;
}
}
double expected = 0.938;
double calculated = stat.mean();
double error = stat.errorEstimate();
if (Math.Abs(expected - calculated) > 3 * error)
{
QAssert.Fail("Failed to reproduce auto-callable equity structure price"
+ "\n calculated: " + calculated
+ "\n error: " + error
+ "\n expected: " + expected);
}
}
public void testZeroBondPricing()
{
// Testing Monte-Carlo zero bond pricing
DayCounter dc = new Actual360();
Date today = Date.Today;
Settings.Instance.setEvaluationDate(today);
// construct a strange yield curve to check drifts and discounting
// of the joint stochastic process
List <Date> dates = new List <Date>();
List <double> times = new List <double>();
List <double> rates = new List <double>();
dates.Add(today);
rates.Add(0.02);
times.Add(0.0);
for (int i = 120; i < 240; ++i)
{
dates.Add(today + new Period(i, TimeUnit.Months));
rates.Add(0.02 + 0.0002 * Math.Exp(Math.Sin(i / 8.0)));
times.Add(dc.yearFraction(today, dates.Last()));
}
Date maturity = dates.Last() + new Period(10, TimeUnit.Years);
dates.Add(maturity);
rates.Add(0.04);
//times.Add(dc.yearFraction(today, dates.Last()));
Handle <Quote> s0 = new Handle <Quote>(new SimpleQuote(100));
Handle <YieldTermStructure> ts = new Handle <YieldTermStructure>(new InterpolatedZeroCurve <Linear>(dates, rates, dc));
Handle <YieldTermStructure> ds = new Handle <YieldTermStructure>(Utilities.flatRate(today, 0.0, dc));
HestonProcess hestonProcess = new HestonProcess(ts, ds, s0, 0.02, 1.0, 0.2, 0.5, -0.8);
HullWhiteForwardProcess hwProcess = new HullWhiteForwardProcess(ts, 0.05, 0.05);
hwProcess.setForwardMeasureTime(dc.yearFraction(today, maturity));
HullWhite hwModel = new HullWhite(ts, 0.05, 0.05);
HybridHestonHullWhiteProcess jointProcess = new HybridHestonHullWhiteProcess(hestonProcess, hwProcess, -0.4);
TimeGrid grid = new TimeGrid(times);
int factors = jointProcess.factors();
int steps = grid.size() - 1;
SobolBrownianBridgeRsg rsg = new SobolBrownianBridgeRsg(factors, steps);
MultiPathGenerator <SobolBrownianBridgeRsg> generator = new MultiPathGenerator <SobolBrownianBridgeRsg>(
jointProcess, grid, rsg, false);
int m = 90;
List <GeneralStatistics> zeroStat = new InitializedList <GeneralStatistics>(m);
List <GeneralStatistics> optionStat = new InitializedList <GeneralStatistics>(m);
int nrTrails = 8191;
int optionTenor = 24;
double strike = 0.5;
for (int i = 0; i < nrTrails; ++i)
{
Sample <IPath> path = generator.next();
MultiPath value = path.value as MultiPath;
Utils.QL_REQUIRE(value != null, () => "Invalid Path");
for (int j = 1; j < m; ++j)
{
double t = grid[j]; // zero end and option maturity
double T = grid[j + optionTenor]; // maturity of zero bond
// of option
Vector states = new Vector(3);
Vector optionStates = new Vector(3);
for (int k = 0; k < jointProcess.size(); ++k)
{
states[k] = value[k][j];
optionStates[k] = value[k][j + optionTenor];
}
double zeroBond
= 1.0 / jointProcess.numeraire(t, states);
double zeroOption = zeroBond * Math.Max(0.0, hwModel.discountBond(t, T, states[2]) - strike);
zeroStat[j].add(zeroBond);
optionStat[j].add(zeroOption);
}
}
for (int j = 1; j < m; ++j)
{
double t = grid[j];
double calculated = zeroStat[j].mean();
double expected = ts.link.discount(t);
if (Math.Abs(calculated - expected) > 0.03)
{
QAssert.Fail("Failed to reproduce expected zero bond prices"
+ "\n t: " + t
+ "\n calculated: " + calculated
+ "\n expected: " + expected);
}
double T = grid[j + optionTenor];
calculated = optionStat[j].mean();
expected = hwModel.discountBondOption(Option.Type.Call, strike, t, T);
if (Math.Abs(calculated - expected) > 0.0035)
{
QAssert.Fail("Failed to reproduce expected zero bond option prices"
+ "\n t: " + t
+ "\n T: " + T
+ "\n calculated: " + calculated
+ "\n expected: " + expected);
}
}
}
public void cpibondconsistency()
{
CommonVars common = new CommonVars();
// ZeroInflationSwap aka CPISwap
CPISwap.Type type = CPISwap.Type.Payer;
double nominal = 1000000.0;
bool subtractInflationNominal = true;
// float+spread leg
double spread = 0.0;
DayCounter floatDayCount = new Actual365Fixed();
BusinessDayConvention floatPaymentConvention = BusinessDayConvention.ModifiedFollowing;
int fixingDays = 0;
IborIndex floatIndex = new GBPLibor(new Period(6, TimeUnit.Months), common.nominalUK);
// fixed x inflation leg
double fixedRate = 0.1; //1% would be 0.01
double baseCPI = 206.1; // would be 206.13871 if we were interpolating
DayCounter fixedDayCount = new Actual365Fixed();
BusinessDayConvention fixedPaymentConvention = BusinessDayConvention.ModifiedFollowing;
Calendar fixedPaymentCalendar = new UnitedKingdom();
ZeroInflationIndex fixedIndex = common.ii;
Period contractObservationLag = common.contractObservationLag;
InterpolationType observationInterpolation = common.contractObservationInterpolation;
// set the schedules
Date startDate = new Date(2, Month.October, 2007);
Date endDate = new Date(2, Month.October, 2052);
Schedule floatSchedule = new MakeSchedule().from(startDate).to(endDate)
.withTenor(new Period(6, TimeUnit.Months))
.withCalendar(new UnitedKingdom())
.withConvention(floatPaymentConvention)
.backwards().value();
Schedule fixedSchedule = new MakeSchedule().from(startDate).to(endDate)
.withTenor(new Period(6, TimeUnit.Months))
.withCalendar(new UnitedKingdom())
.withConvention(BusinessDayConvention.Unadjusted)
.backwards().value();
CPISwap zisV = new CPISwap(type, nominal, subtractInflationNominal,
spread, floatDayCount, floatSchedule,
floatPaymentConvention, fixingDays, floatIndex,
fixedRate, baseCPI, fixedDayCount, fixedSchedule,
fixedPaymentConvention, contractObservationLag,
fixedIndex, observationInterpolation);
double[] floatFix = { 0.06255, 0.05975, 0.0637, 0.018425, 0.0073438, -1, -1 };
double[] cpiFix = { 211.4, 217.2, 211.4, 213.4, -2, -2 };
for (int i = 0; i < floatSchedule.Count; i++)
{
if (floatSchedule[i] < common.evaluationDate)
{
floatIndex.addFixing(floatSchedule[i], floatFix[i], true);//true=overwrite
}
CPICoupon zic = zisV.cpiLeg()[i] as CPICoupon;
if (zic != null)
{
if (zic.fixingDate() < (common.evaluationDate - new Period(1, TimeUnit.Months)))
{
fixedIndex.addFixing(zic.fixingDate(), cpiFix[i], true);
}
}
}
// simple structure so simple pricing engine - most work done by index
DiscountingSwapEngine dse = new DiscountingSwapEngine(common.nominalUK);
zisV.setPricingEngine(dse);
// now do the bond equivalent
List <double> fixedRates = new InitializedList <double>(1, fixedRate);
int settlementDays = 1;// cannot be zero!
bool growthOnly = true;
CPIBond cpiB = new CPIBond(settlementDays, nominal, growthOnly,
baseCPI, contractObservationLag, fixedIndex,
observationInterpolation, fixedSchedule,
fixedRates, fixedDayCount, fixedPaymentConvention);
DiscountingBondEngine dbe = new DiscountingBondEngine(common.nominalUK);
cpiB.setPricingEngine(dbe);
QAssert.IsTrue(Math.Abs(cpiB.NPV() - zisV.legNPV(0).GetValueOrDefault()) < 1e-5,
"cpi bond does not equal equivalent cpi swap leg");
// remove circular refernce
common.hcpi.linkTo(null);
}
public LoanPricingEngineResults()
{
legNPV = new InitializedList <double?>();
}
public void testSpreadDependency()
{
//"Testing swaption dependency on spread...";
CommonVars vars = new CommonVars();
double[] spreads = { -0.002, -0.001, 0.0, 0.001, 0.002 };
for (int i=0; i<exercises.Length ; i++) {
for (int j=0; j<lengths.Length ; j++) {
for (int k=0; k<type.Length ; k++) {
Date exerciseDate = vars.calendar.advance(vars.today,
exercises[i]);
Date startDate =
vars.calendar.advance(exerciseDate,
vars.settlementDays,TimeUnit.Days);
// store the results for different rates...
List<double> values=new InitializedList<double>(spreads.Length);
List<double> values_cash = new InitializedList<double>(spreads.Length);
for (int l=0; l<spreads.Length; l++) {
VanillaSwap swap =
new MakeVanillaSwap(lengths[j], vars.index, 0.06)
.withEffectiveDate(startDate)
.withFloatingLegSpread(spreads[l])
.withType(type[k]);
Swaption swaption =
vars.makeSwaption(swap,exerciseDate,0.20);
// FLOATING_POINT_EXCEPTION
values[l]=swaption.NPV();
Swaption swaption_cash =
vars.makeSwaption(swap,exerciseDate,0.20,
Settlement.Type.Cash);
values_cash[l]=swaption_cash.NPV();
}
// and check that they go the right way
if (type[k]==VanillaSwap.Type.Payer) {
for (int n = 0; n < spreads.Length - 1; n++)
{
if (values[n] > values[n + 1])
Assert.Fail("NPV is decreasing with the spread " +
"in a payer swaption (physical delivered):" +
"\nexercise date: " + exerciseDate +
"\nlength: " + lengths[j] +
"\nvalue: " + values[n] + " for spread: " + spreads[n] +
"\nvalue: " + values[n + 1] + " for spread: " + spreads[n + 1]);
if (values_cash[n] > values_cash[n + 1])
Assert.Fail("NPV is decreasing with the spread " +
"in a payer swaption (cash delivered):" +
"\nexercise date: " + exerciseDate +
"\nlength: " + lengths[j] +
"\nvalue: " + values_cash[n] + " for spread: " + spreads[n] +
"\nvalue: " + values_cash[n + 1] + " for spread: " + spreads[n + 1]);
}
}
else
{
for (int n = 0; n < spreads.Length - 1; n++)
{
if (values[n] < values[n + 1])
Assert.Fail("NPV is increasing with the spread " +
"in a receiver swaption (physical delivered):" +
"\nexercise date: " + exerciseDate +
"\nlength: " + lengths[j] +
"\nvalue: " + values[n] + " for spread: " + spreads[n] +
"\nvalue: " + values[n + 1] + " for spread: " + spreads[n + 1]);
if (values_cash[n] < values_cash[n+1])
Assert.Fail("NPV is increasing with the spread " +
"in a receiver swaption (cash delivered):" +
"\nexercise date: " + exerciseDate +
"\nlength: " + lengths[j] +
"\nvalue: " + values_cash[n ] + " for spread: " + spreads[n] +
"\nvalue: " + values_cash[n+1] + " for spread: " + spreads[n+1]);
}
}
}
}
}
}
public void testSwaptionPricing()
{
// Testing forward swap and swaption pricing
const int size = 10;
const int steps = 8 * size;
#if QL_USE_INDEXED_COUPON
const double tolerance = 1e-6;
#else
const double tolerance = 1e-12;
#endif
List <Date> dates = new List <Date>();
List <double> rates = new List <double>();
dates.Add(new Date(4, 9, 2005));
dates.Add(new Date(4, 9, 2011));
rates.Add(0.04);
rates.Add(0.08);
IborIndex index = makeIndex(dates, rates);
LiborForwardModelProcess process = new LiborForwardModelProcess(size, index);
LmCorrelationModel corrModel = new LmExponentialCorrelationModel(size, 0.5);
LmVolatilityModel volaModel = new LmLinearExponentialVolatilityModel(process.fixingTimes(),
0.291, 1.483, 0.116, 0.00001);
// set-up pricing engine
process.setCovarParam((LfmCovarianceParameterization)
new LfmCovarianceProxy(volaModel, corrModel));
// set-up a small Monte-Carlo simulation to price swations
List <double> tmp = process.fixingTimes();
TimeGrid grid = new TimeGrid(tmp, tmp.Count, steps);
List <int> location = new List <int>();
for (int i = 0; i < tmp.Count; ++i)
{
location.Add(grid.index(tmp[i]));
}
ulong seed = 42;
const int nrTrails = 5000;
LowDiscrepancy.icInstance = new InverseCumulativeNormal();
IRNG rsg = (InverseCumulativeRsg <RandomSequenceGenerator <MersenneTwisterUniformRng>
, InverseCumulativeNormal>)
new PseudoRandom().make_sequence_generator(process.factors() * (grid.size() - 1), seed);
MultiPathGenerator <IRNG> generator = new MultiPathGenerator <IRNG>(process,
grid,
rsg, false);
LiborForwardModel liborModel = new LiborForwardModel(process, volaModel, corrModel);
Calendar calendar = index.fixingCalendar();
DayCounter dayCounter = index.forwardingTermStructure().link.dayCounter();
BusinessDayConvention convention = index.businessDayConvention();
Date settlement = index.forwardingTermStructure().link.referenceDate();
SwaptionVolatilityMatrix m = liborModel.getSwaptionVolatilityMatrix();
for (int i = 1; i < size; ++i)
{
for (int j = 1; j <= size - i; ++j)
{
Date fwdStart = settlement + new Period(6 * i, TimeUnit.Months);
Date fwdMaturity = fwdStart + new Period(6 * j, TimeUnit.Months);
Schedule schedule = new Schedule(fwdStart, fwdMaturity, index.tenor(), calendar,
convention, convention, DateGeneration.Rule.Forward, false);
double swapRate = 0.0404;
VanillaSwap forwardSwap = new VanillaSwap(VanillaSwap.Type.Receiver, 1.0,
schedule, swapRate, dayCounter,
schedule, index, 0.0, index.dayCounter());
forwardSwap.setPricingEngine(new DiscountingSwapEngine(index.forwardingTermStructure()));
// check forward pricing first
double expected = forwardSwap.fairRate();
double calculated = liborModel.S_0(i - 1, i + j - 1);
if (Math.Abs(expected - calculated) > tolerance)
{
QAssert.Fail("Failed to reproduce fair forward swap rate"
+ "\n calculated: " + calculated
+ "\n expected: " + expected);
}
swapRate = forwardSwap.fairRate();
forwardSwap =
new VanillaSwap(VanillaSwap.Type.Receiver, 1.0,
schedule, swapRate, dayCounter,
schedule, index, 0.0, index.dayCounter());
forwardSwap.setPricingEngine(new DiscountingSwapEngine(index.forwardingTermStructure()));
if (i == j && i <= size / 2)
{
IPricingEngine engine =
new LfmSwaptionEngine(liborModel, index.forwardingTermStructure());
Exercise exercise =
new EuropeanExercise(process.fixingDates()[i]);
Swaption swaption =
new Swaption(forwardSwap, exercise);
swaption.setPricingEngine(engine);
GeneralStatistics stat = new GeneralStatistics();
for (int n = 0; n < nrTrails; ++n)
{
Sample <IPath> path = (n % 2 != 0) ? generator.antithetic()
: generator.next();
MultiPath value = path.value as MultiPath;
Utils.QL_REQUIRE(value != null, () => "Invalid Path");
//Sample<MultiPath> path = generator.next();
List <double> rates_ = new InitializedList <double>(size);
for (int k = 0; k < process.size(); ++k)
{
rates_[k] = value[k][location[i]];
}
List <double> dis = process.discountBond(rates_);
double npv = 0.0;
for (int k = i; k < i + j; ++k)
{
npv += (swapRate - rates_[k])
* (process.accrualEndTimes()[k]
- process.accrualStartTimes()[k]) * dis[k];
}
stat.add(Math.Max(npv, 0.0));
}
if (Math.Abs(swaption.NPV() - stat.mean())
> stat.errorEstimate() * 2.35)
{
QAssert.Fail("Failed to reproduce swaption npv"
+ "\n calculated: " + stat.mean()
+ "\n expected: " + swaption.NPV());
}
}
}
}
}
public void testBrazilianCached()
{
//("Testing Brazilian public bond prices against cached values...");
CommonVars vars = new CommonVars();
double faceAmount = 1000.0;
double redemption = 100.0;
Date issueDate = new Date(1, Month.January, 2007);
Date today = new Date(6, Month.June, 2007);
Settings.setEvaluationDate(today);
// NTN-F maturity dates
InitializedList<Date> maturityDates = new InitializedList<Date>(6);
maturityDates[0] = new Date(1, Month.January, 2008);
maturityDates[1] = new Date(1, Month.January, 2010);
maturityDates[2] = new Date(1, Month.July, 2010);
maturityDates[3] = new Date(1, Month.January, 2012);
maturityDates[4] = new Date(1, Month.January, 2014);
maturityDates[5] = new Date(1, Month.January, 2017);
// NTN-F yields
InitializedList<double> yields = new InitializedList<double>(6);
yields[0] = 0.114614;
yields[1] = 0.105726;
yields[2] = 0.105328;
yields[3] = 0.104283;
yields[4] = 0.103218;
yields[5] = 0.102948;
// NTN-F prices
InitializedList<double> prices = new InitializedList<double>(6);
prices[0] = 1034.63031372;
prices[1] = 1030.09919487;
prices[2] = 1029.98307160;
prices[3] = 1028.13585068;
prices[4] = 1028.33383817;
prices[5] = 1026.19716497;
int settlementDays = 1;
vars.faceAmount = 1000.0;
// The tolerance is high because Andima truncate yields
double tolerance = 1.0e-4;
InitializedList<InterestRate> couponRates = new InitializedList<InterestRate>(1);
couponRates[0] = new InterestRate(0.1, new Thirty360(), Compounding.Compounded, Frequency.Annual);
for (int bondIndex = 0; bondIndex < maturityDates.Count; bondIndex++)
{
// plain
InterestRate yield = new InterestRate(yields[bondIndex], new Business252(new Brazil()),
Compounding.Compounded, Frequency.Annual);
Schedule schedule = new Schedule(new Date(1, Month.January, 2007),
maturityDates[bondIndex], new Period(Frequency.Semiannual),
new Brazil(Brazil.Market.Settlement),
BusinessDayConvention.Unadjusted, BusinessDayConvention.Unadjusted,
DateGeneration.Rule.Backward, false);
FixedRateBond bond = new FixedRateBond(settlementDays,
faceAmount,
schedule,
couponRates,
BusinessDayConvention.Following,
redemption,
issueDate);
double cachedPrice = prices[bondIndex];
double price = vars.faceAmount * (bond.cleanPrice(yield.rate(),
yield.dayCounter(),
yield.compounding(),
yield.frequency(),
today) + bond.accruedAmount(today)) / 100;
if (Math.Abs(price - cachedPrice) > tolerance)
{
Assert.Fail("failed to reproduce cached price:\n"
+ " calculated: " + price + "\n"
+ " expected: " + cachedPrice + "\n"
+ " error: " + (price - cachedPrice) + "\n"
);
}
}
}
static void Main(string[] args)
{
DateTime timer = DateTime.Now;
/*********************
*** MARKET DATA ***
*********************/
Calendar calendar = new TARGET();
Date settlementDate = new Date(18, Month.September, 2008);
// must be a business day
settlementDate = calendar.adjust(settlementDate);
int fixingDays = 3;
int settlementDays = 3;
Date todaysDate = calendar.advance(settlementDate, -fixingDays, TimeUnit.Days);
// nothing to do with Date::todaysDate
Settings.setEvaluationDate(todaysDate);
Console.WriteLine("Today: {0}, {1}", todaysDate.DayOfWeek, todaysDate);
Console.WriteLine("Settlement date: {0}, {1}", settlementDate.DayOfWeek, settlementDate);
// Building of the bonds discounting yield curve
/*********************
*** RATE HELPERS ***
*********************/
// RateHelpers are built from the above quotes together with
// other instrument dependant infos. Quotes are passed in
// relinkable handles which could be relinked to some other
// data source later.
// Common data
// ZC rates for the short end
double zc3mQuote = 0.0096;
double zc6mQuote = 0.0145;
double zc1yQuote = 0.0194;
Quote zc3mRate = new SimpleQuote(zc3mQuote);
Quote zc6mRate = new SimpleQuote(zc6mQuote);
Quote zc1yRate = new SimpleQuote(zc1yQuote);
DayCounter zcBondsDayCounter = new Actual365Fixed();
RateHelper zc3m = new DepositRateHelper(new Handle <Quote>(zc3mRate),
new Period(3, TimeUnit.Months), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, zcBondsDayCounter);
RateHelper zc6m = new DepositRateHelper(new Handle <Quote>(zc6mRate),
new Period(6, TimeUnit.Months), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, zcBondsDayCounter);
RateHelper zc1y = new DepositRateHelper(new Handle <Quote>(zc1yRate),
new Period(1, TimeUnit.Years), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, zcBondsDayCounter);
// setup bonds
double redemption = 100.0;
const int numberOfBonds = 5;
Date[] issueDates =
{
new Date(15, Month.March, 2005),
new Date(15, Month.June, 2005),
new Date(30, Month.June, 2006),
new Date(15, Month.November, 2002),
new Date(15, Month.May, 1987)
};
Date[] maturities =
{
new Date(31, Month.August, 2010),
new Date(31, Month.August, 2011),
new Date(31, Month.August, 2013),
new Date(15, Month.August, 2018),
new Date(15, Month.May, 2038)
};
double[] couponRates =
{
0.02375,
0.04625,
0.03125,
0.04000,
0.04500
};
double[] marketQuotes =
{
100.390625,
106.21875,
100.59375,
101.6875,
102.140625
};
List <SimpleQuote> quote = new List <SimpleQuote>();
for (int i = 0; i < numberOfBonds; i++)
{
SimpleQuote cp = new SimpleQuote(marketQuotes[i]);
quote.Add(cp);
}
List <RelinkableHandle <Quote> > quoteHandle = new InitializedList <RelinkableHandle <Quote> >(numberOfBonds);
for (int i = 0; i < numberOfBonds; i++)
{
quoteHandle[i].linkTo(quote[i]);
}
// Definition of the rate helpers
List <FixedRateBondHelper> bondsHelpers = new List <FixedRateBondHelper>();
for (int i = 0; i < numberOfBonds; i++)
{
Schedule schedule = new Schedule(issueDates[i], maturities[i], new Period(Frequency.Semiannual),
new UnitedStates(UnitedStates.Market.GovernmentBond),
BusinessDayConvention.Unadjusted, BusinessDayConvention.Unadjusted,
DateGeneration.Rule.Backward, false);
FixedRateBondHelper bondHelper = new FixedRateBondHelper(quoteHandle[i],
settlementDays,
100.0,
schedule,
new List <double>()
{
couponRates[i]
},
new ActualActual(ActualActual.Convention.Bond),
BusinessDayConvention.Unadjusted,
redemption,
issueDates[i]);
bondsHelpers.Add(bondHelper);
}
/*********************
** CURVE BUILDING **
*********************/
// Any DayCounter would be fine.
// ActualActual::ISDA ensures that 30 years is 30.0
DayCounter termStructureDayCounter = new ActualActual(ActualActual.Convention.ISDA);
double tolerance = 1.0e-15;
// A depo-bond curve
List <RateHelper> bondInstruments = new List <RateHelper>();
// Adding the ZC bonds to the curve for the short end
bondInstruments.Add(zc3m);
bondInstruments.Add(zc6m);
bondInstruments.Add(zc1y);
// Adding the Fixed rate bonds to the curve for the long end
for (int i = 0; i < numberOfBonds; i++)
{
bondInstruments.Add(bondsHelpers[i]);
}
YieldTermStructure bondDiscountingTermStructure = new PiecewiseYieldCurve <Discount, LogLinear>(
settlementDate, bondInstruments,
termStructureDayCounter,
new List <Handle <Quote> >(),
new List <Date>(),
tolerance);
// Building of the Libor forecasting curve
// deposits
double d1wQuote = 0.043375;
double d1mQuote = 0.031875;
double d3mQuote = 0.0320375;
double d6mQuote = 0.03385;
double d9mQuote = 0.0338125;
double d1yQuote = 0.0335125;
// swaps
double s2yQuote = 0.0295;
double s3yQuote = 0.0323;
double s5yQuote = 0.0359;
double s10yQuote = 0.0412;
double s15yQuote = 0.0433;
/********************
*** QUOTES ***
********************/
// SimpleQuote stores a value which can be manually changed;
// other Quote subclasses could read the value from a database
// or some kind of data feed.
// deposits
Quote d1wRate = new SimpleQuote(d1wQuote);
Quote d1mRate = new SimpleQuote(d1mQuote);
Quote d3mRate = new SimpleQuote(d3mQuote);
Quote d6mRate = new SimpleQuote(d6mQuote);
Quote d9mRate = new SimpleQuote(d9mQuote);
Quote d1yRate = new SimpleQuote(d1yQuote);
// swaps
Quote s2yRate = new SimpleQuote(s2yQuote);
Quote s3yRate = new SimpleQuote(s3yQuote);
Quote s5yRate = new SimpleQuote(s5yQuote);
Quote s10yRate = new SimpleQuote(s10yQuote);
Quote s15yRate = new SimpleQuote(s15yQuote);
/*********************
*** RATE HELPERS ***
*********************/
// RateHelpers are built from the above quotes together with
// other instrument dependant infos. Quotes are passed in
// relinkable handles which could be relinked to some other
// data source later.
// deposits
DayCounter depositDayCounter = new Actual360();
RateHelper d1w = new DepositRateHelper(
new Handle <Quote>(d1wRate),
new Period(1, TimeUnit.Weeks), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, depositDayCounter);
RateHelper d1m = new DepositRateHelper(
new Handle <Quote>(d1mRate),
new Period(1, TimeUnit.Months), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, depositDayCounter);
RateHelper d3m = new DepositRateHelper(
new Handle <Quote>(d3mRate),
new Period(3, TimeUnit.Months), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, depositDayCounter);
RateHelper d6m = new DepositRateHelper(
new Handle <Quote>(d6mRate),
new Period(6, TimeUnit.Months), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, depositDayCounter);
RateHelper d9m = new DepositRateHelper(
new Handle <Quote>(d9mRate),
new Period(9, TimeUnit.Months), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, depositDayCounter);
RateHelper d1y = new DepositRateHelper(
new Handle <Quote>(d1yRate),
new Period(1, TimeUnit.Years), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, depositDayCounter);
// setup swaps
Frequency swFixedLegFrequency = Frequency.Annual;
BusinessDayConvention swFixedLegConvention = BusinessDayConvention.Unadjusted;
DayCounter swFixedLegDayCounter = new Thirty360(Thirty360.Thirty360Convention.European);
IborIndex swFloatingLegIndex = new Euribor6M();
Period forwardStart = new Period(1, TimeUnit.Days);
RateHelper s2y = new SwapRateHelper(
new Handle <Quote>(s2yRate), new Period(2, TimeUnit.Years),
calendar, swFixedLegFrequency,
swFixedLegConvention, swFixedLegDayCounter,
swFloatingLegIndex, new Handle <Quote>(), forwardStart);
RateHelper s3y = new SwapRateHelper(
new Handle <Quote>(s3yRate), new Period(3, TimeUnit.Years),
calendar, swFixedLegFrequency,
swFixedLegConvention, swFixedLegDayCounter,
swFloatingLegIndex, new Handle <Quote>(), forwardStart);
RateHelper s5y = new SwapRateHelper(
new Handle <Quote>(s5yRate), new Period(5, TimeUnit.Years),
calendar, swFixedLegFrequency,
swFixedLegConvention, swFixedLegDayCounter,
swFloatingLegIndex, new Handle <Quote>(), forwardStart);
RateHelper s10y = new SwapRateHelper(
new Handle <Quote>(s10yRate), new Period(10, TimeUnit.Years),
calendar, swFixedLegFrequency,
swFixedLegConvention, swFixedLegDayCounter,
swFloatingLegIndex, new Handle <Quote>(), forwardStart);
RateHelper s15y = new SwapRateHelper(
new Handle <Quote>(s15yRate), new Period(15, TimeUnit.Years),
calendar, swFixedLegFrequency,
swFixedLegConvention, swFixedLegDayCounter,
swFloatingLegIndex, new Handle <Quote>(), forwardStart);
/*********************
** CURVE BUILDING **
*********************/
// Any DayCounter would be fine.
// ActualActual::ISDA ensures that 30 years is 30.0
// A depo-swap curve
List <RateHelper> depoSwapInstruments = new List <RateHelper>();
depoSwapInstruments.Add(d1w);
depoSwapInstruments.Add(d1m);
depoSwapInstruments.Add(d3m);
depoSwapInstruments.Add(d6m);
depoSwapInstruments.Add(d9m);
depoSwapInstruments.Add(d1y);
depoSwapInstruments.Add(s2y);
depoSwapInstruments.Add(s3y);
depoSwapInstruments.Add(s5y);
depoSwapInstruments.Add(s10y);
depoSwapInstruments.Add(s15y);
YieldTermStructure depoSwapTermStructure = new PiecewiseYieldCurve <Discount, LogLinear>(
settlementDate, depoSwapInstruments,
termStructureDayCounter,
new List <Handle <Quote> >(),
new List <Date>(),
tolerance);
// Term structures that will be used for pricing:
// the one used for discounting cash flows
RelinkableHandle <YieldTermStructure> discountingTermStructure = new RelinkableHandle <YieldTermStructure>();
// the one used for forward rate forecasting
RelinkableHandle <YieldTermStructure> forecastingTermStructure = new RelinkableHandle <YieldTermStructure>();
/*********************
* BONDS TO BE PRICED *
**********************/
// Common data
double faceAmount = 100;
// Pricing engine
IPricingEngine bondEngine = new DiscountingBondEngine(discountingTermStructure);
// Zero coupon bond
ZeroCouponBond zeroCouponBond = new ZeroCouponBond(
settlementDays,
new UnitedStates(UnitedStates.Market.GovernmentBond),
faceAmount,
new Date(15, Month.August, 2013),
BusinessDayConvention.Following,
116.92,
new Date(15, Month.August, 2003));
zeroCouponBond.setPricingEngine(bondEngine);
// Fixed 4.5% US Treasury Note
Schedule fixedBondSchedule = new Schedule(new Date(15, Month.May, 2007),
new Date(15, Month.May, 2017), new Period(Frequency.Semiannual),
new UnitedStates(UnitedStates.Market.GovernmentBond),
BusinessDayConvention.Unadjusted, BusinessDayConvention.Unadjusted, DateGeneration.Rule.Backward, false);
FixedRateBond fixedRateBond = new FixedRateBond(
settlementDays,
faceAmount,
fixedBondSchedule,
new List <double>()
{
0.045
},
new ActualActual(ActualActual.Convention.Bond),
BusinessDayConvention.ModifiedFollowing,
100.0, new Date(15, Month.May, 2007));
fixedRateBond.setPricingEngine(bondEngine);
// Floating rate bond (3M USD Libor + 0.1%)
// Should and will be priced on another curve later...
RelinkableHandle <YieldTermStructure> liborTermStructure = new RelinkableHandle <YieldTermStructure>();
IborIndex libor3m = new USDLibor(new Period(3, TimeUnit.Months), liborTermStructure);
libor3m.addFixing(new Date(17, Month.July, 2008), 0.0278625);
Schedule floatingBondSchedule = new Schedule(new Date(21, Month.October, 2005),
new Date(21, Month.October, 2010), new Period(Frequency.Quarterly),
new UnitedStates(UnitedStates.Market.NYSE),
BusinessDayConvention.Unadjusted, BusinessDayConvention.Unadjusted, DateGeneration.Rule.Backward, true);
FloatingRateBond floatingRateBond = new FloatingRateBond(
settlementDays,
faceAmount,
floatingBondSchedule,
libor3m,
new Actual360(),
BusinessDayConvention.ModifiedFollowing,
2,
// Gearings
new List <double>()
{
1.0
},
// Spreads
new List <double>()
{
0.001
},
// Caps
new List <double?>(),
// Floors
new List <double?>(),
// Fixing in arrears
true,
100.0,
new Date(21, Month.October, 2005));
floatingRateBond.setPricingEngine(bondEngine);
// Coupon pricers
IborCouponPricer pricer = new BlackIborCouponPricer();
// optionLet volatilities
double volatility = 0.0;
Handle <OptionletVolatilityStructure> vol;
vol = new Handle <OptionletVolatilityStructure>(
new ConstantOptionletVolatility(
settlementDays,
calendar,
BusinessDayConvention.ModifiedFollowing,
volatility,
new Actual365Fixed()));
pricer.setCapletVolatility(vol);
Utils.setCouponPricer(floatingRateBond.cashflows(), pricer);
// Yield curve bootstrapping
forecastingTermStructure.linkTo(depoSwapTermStructure);
discountingTermStructure.linkTo(bondDiscountingTermStructure);
// We are using the depo & swap curve to estimate the future Libor rates
liborTermStructure.linkTo(depoSwapTermStructure);
/***************
* BOND PRICING *
****************/
// write column headings
int[] widths = { 18, 10, 10, 10 };
Console.WriteLine("{0,18}{1,10}{2,10}{3,10}", "", "ZC", "Fixed", "Floating");
int width = widths[0]
+ widths[1]
+ widths[2]
+ widths[3];
string rule = "".PadLeft(width, '-'), dblrule = "".PadLeft(width, '=');
string tab = "".PadLeft(8, ' ');
Console.WriteLine(rule);
Console.WriteLine("Net present value".PadLeft(widths[0]) + "{0,10:n2}{1,10:n2}{2,10:n2}",
zeroCouponBond.NPV(),
fixedRateBond.NPV(),
floatingRateBond.NPV());
Console.WriteLine("Clean price".PadLeft(widths[0]) + "{0,10:n2}{1,10:n2}{2,10:n2}",
zeroCouponBond.cleanPrice(),
fixedRateBond.cleanPrice(),
floatingRateBond.cleanPrice());
Console.WriteLine("Dirty price".PadLeft(widths[0]) + "{0,10:n2}{1,10:n2}{2,10:n2}",
zeroCouponBond.dirtyPrice(),
fixedRateBond.dirtyPrice(),
floatingRateBond.dirtyPrice());
Console.WriteLine("Accrued coupon".PadLeft(widths[0]) + "{0,10:n2}{1,10:n2}{2,10:n2}",
zeroCouponBond.accruedAmount(),
fixedRateBond.accruedAmount(),
floatingRateBond.accruedAmount());
Console.WriteLine("Previous coupon".PadLeft(widths[0]) + "{0,10:0.00%}{1,10:0.00%}{2,10:0.00%}",
"N/A",
fixedRateBond.previousCouponRate(),
floatingRateBond.previousCouponRate());
Console.WriteLine("Next coupon".PadLeft(widths[0]) + "{0,10:0.00%}{1,10:0.00%}{2,10:0.00%}",
"N/A",
fixedRateBond.nextCouponRate(),
floatingRateBond.nextCouponRate());
Console.WriteLine("Yield".PadLeft(widths[0]) + "{0,10:0.00%}{1,10:0.00%}{2,10:0.00%}",
zeroCouponBond.yield(new Actual360(), Compounding.Compounded, Frequency.Annual),
fixedRateBond.yield(new Actual360(), Compounding.Compounded, Frequency.Annual),
floatingRateBond.yield(new Actual360(), Compounding.Compounded, Frequency.Annual));
Console.WriteLine();
// Other computations
Console.WriteLine("Sample indirect computations (for the floating rate bond): ");
Console.WriteLine(rule);
Console.WriteLine("Yield to Clean Price: {0:n2}",
floatingRateBond.cleanPrice(floatingRateBond.yield(new Actual360(), Compounding.Compounded, Frequency.Annual),
new Actual360(), Compounding.Compounded, Frequency.Annual,
settlementDate));
Console.WriteLine("Clean Price to Yield: {0:0.00%}",
floatingRateBond.yield(floatingRateBond.cleanPrice(), new Actual360(), Compounding.Compounded, Frequency.Annual,
settlementDate));
/* "Yield to Price"
* "Price to Yield" */
Console.WriteLine(" \nRun completed in {0}", DateTime.Now - timer);
Console.WriteLine();
Console.Write("Press any key to continue ...");
Console.ReadKey();
}
public void testCachedFloating()
{
// "Testing floating-rate bond prices against cached values...");
CommonVars vars = new CommonVars();
Date today = new Date(22, Month.November, 2004);
Settings.setEvaluationDate(today);
int settlementDays = 1;
var riskFreeRate = new Handle<YieldTermStructure>(Utilities.flatRate(today, 0.025, new Actual360()));
var discountCurve = new Handle<YieldTermStructure>(Utilities.flatRate(today, 0.03, new Actual360()));
IborIndex index = new USDLibor(new Period(6, TimeUnit.Months), riskFreeRate);
int fixingDays = 1;
double tolerance = 1.0e-6;
IborCouponPricer pricer = new BlackIborCouponPricer(new Handle<OptionletVolatilityStructure>());
// plain
Schedule sch = new Schedule(new Date(30, Month.November, 2004), new Date(30, Month.November, 2008),
new Period(Frequency.Semiannual), new UnitedStates(UnitedStates.Market.GovernmentBond),
BusinessDayConvention.ModifiedFollowing, BusinessDayConvention.ModifiedFollowing,
DateGeneration.Rule.Backward, false);
FloatingRateBond bond1 = new FloatingRateBond(settlementDays, vars.faceAmount, sch,
index, new ActualActual(ActualActual.Convention.ISMA),
BusinessDayConvention.ModifiedFollowing, fixingDays,
new List<double>(), new List<double>(),
new List<double>(), new List<double>(),
false,
100.0, new Date(30, Month.November, 2004));
IPricingEngine bondEngine = new DiscountingBondEngine(riskFreeRate);
bond1.setPricingEngine(bondEngine);
Utils.setCouponPricer(bond1.cashflows(), pricer);
#if QL_USE_INDEXED_COUPON
double cachedPrice1 = 99.874645;
#else
double cachedPrice1 = 99.874646;
#endif
double price = bond1.cleanPrice();
if (Math.Abs(price - cachedPrice1) > tolerance)
{
Assert.Fail("failed to reproduce cached price:\n"
+ " calculated: " + price + "\n"
+ " expected: " + cachedPrice1 + "\n"
+ " error: " + (price - cachedPrice1));
}
// different risk-free and discount curve
FloatingRateBond bond2 = new FloatingRateBond(settlementDays, vars.faceAmount, sch,
index, new ActualActual(ActualActual.Convention.ISMA),
BusinessDayConvention.ModifiedFollowing, fixingDays,
new List<double>(), new List<double>(),
new List<double>(), new List<double>(),
false,
100.0, new Date(30, Month.November, 2004));
IPricingEngine bondEngine2 = new DiscountingBondEngine(discountCurve);
bond2.setPricingEngine(bondEngine2);
Utils.setCouponPricer(bond2.cashflows(), pricer);
#if QL_USE_INDEXED_COUPON
double cachedPrice2 = 97.955904;
#else
double cachedPrice2 = 97.955904;
#endif
price = bond2.cleanPrice();
if (Math.Abs(price - cachedPrice2) > tolerance)
{
Assert.Fail("failed to reproduce cached price:\n"
+ " calculated: " + price + "\n"
+ " expected: " + cachedPrice2 + "\n"
+ " error: " + (price - cachedPrice2));
}
// varying spread
InitializedList<double> spreads = new InitializedList<double>(4);
spreads[0] = 0.001;
spreads[1] = 0.0012;
spreads[2] = 0.0014;
spreads[3] = 0.0016;
FloatingRateBond bond3 = new FloatingRateBond(settlementDays, vars.faceAmount, sch,
index, new ActualActual(ActualActual.Convention.ISMA),
BusinessDayConvention.ModifiedFollowing, fixingDays,
new List<double>(), spreads,
new List<double>(), new List<double>(),
false,
100.0, new Date(30, Month.November, 2004));
bond3.setPricingEngine(bondEngine2);
Utils.setCouponPricer(bond3.cashflows(), pricer);
#if QL_USE_INDEXED_COUPON
double cachedPrice3 = 98.495458;
#else
double cachedPrice3 = 98.495459;
#endif
price = bond3.cleanPrice();
if (Math.Abs(price - cachedPrice3) > tolerance)
{
Assert.Fail("failed to reproduce cached price:\n"
+ " calculated: " + price + "\n"
+ " expected: " + cachedPrice3 + "\n"
+ " error: " + (price - cachedPrice3));
}
}
public void testDecomposition()
{
// Testing collared coupon against its decomposition...
CommonVars vars = new CommonVars();
double tolerance = 1e-10;
double npvVanilla, npvCappedLeg, npvFlooredLeg, npvCollaredLeg, npvCap, npvFloor, npvCollar;
double error;
double floorstrike = 0.05;
double capstrike = 0.10;
List <double> caps = new InitializedList <double>(vars.length, capstrike);
List <double> caps0 = new List <double>();
List <double> floors = new InitializedList <double>(vars.length, floorstrike);
List <double> floors0 = new List <double>();
double gearing_p = 0.5;
double spread_p = 0.002;
double gearing_n = -1.5;
double spread_n = 0.12;
// fixed leg with zero rate
List <CashFlow> fixedLeg = vars.makeFixedLeg(vars.startDate, vars.length);
// floating leg with gearing=1 and spread=0
List <CashFlow> floatLeg = vars.makeYoYLeg(vars.startDate, vars.length);
// floating leg with positive gearing (gearing_p) and spread<>0
List <CashFlow> floatLeg_p = vars.makeYoYLeg(vars.startDate, vars.length, gearing_p, spread_p);
// floating leg with negative gearing (gearing_n) and spread<>0
List <CashFlow> floatLeg_n = vars.makeYoYLeg(vars.startDate, vars.length, gearing_n, spread_n);
// Swap with null fixed leg and floating leg with gearing=1 and spread=0
Swap vanillaLeg = new Swap(fixedLeg, floatLeg);
// Swap with null fixed leg and floating leg with positive gearing and spread<>0
Swap vanillaLeg_p = new Swap(fixedLeg, floatLeg_p);
// Swap with null fixed leg and floating leg with negative gearing and spread<>0
Swap vanillaLeg_n = new Swap(fixedLeg, floatLeg_n);
IPricingEngine engine = new DiscountingSwapEngine(vars.nominalTS);
vanillaLeg.setPricingEngine(engine); // here use the autoset feature
vanillaLeg_p.setPricingEngine(engine);
vanillaLeg_n.setPricingEngine(engine);
// CAPPED coupon - Decomposition of payoff
// Payoff = Nom * Min(rate,strike) * accrualperiod =
// = Nom * [rate + Min(0,strike-rate)] * accrualperiod =
// = Nom * rate * accrualperiod - Nom * Max(rate-strike,0) * accrualperiod =
// = VanillaFloatingLeg - Call
//
int whichPricer = 0;
// Case gearing = 1 and spread = 0
List <CashFlow> cappedLeg = vars.makeYoYCapFlooredLeg(whichPricer, vars.startDate, vars.length,
caps, floors0, vars.volatility);
Swap capLeg = new Swap(fixedLeg, cappedLeg);
capLeg.setPricingEngine(engine);
YoYInflationCap cap = new YoYInflationCap(floatLeg, new List <double>()
{
capstrike
});
cap.setPricingEngine(vars.makeEngine(vars.volatility, whichPricer));
npvVanilla = vanillaLeg.NPV();
npvCappedLeg = capLeg.NPV();
npvCap = cap.NPV();
error = Math.Abs(npvCappedLeg - (npvVanilla - npvCap));
if (error > tolerance)
{
QAssert.Fail("\nYoY Capped Leg: gearing=1, spread=0%, strike=" + capstrike * 100 +
"%\n" +
" Capped Floating Leg NPV: " + npvCappedLeg + "\n" +
" Floating Leg NPV - Cap NPV: " + (npvVanilla - npvCap) + "\n" +
" Diff: " + error);
}
// gearing = 1 and spread = 0
// FLOORED coupon - Decomposition of payoff
// Payoff = Nom * Max(rate,strike) * accrualperiod =
// = Nom * [rate + Max(0,strike-rate)] * accrualperiod =
// = Nom * rate * accrualperiod + Nom * Max(strike-rate,0) * accrualperiod =
// = VanillaFloatingLeg + Put
//
List <CashFlow> flooredLeg = vars.makeYoYCapFlooredLeg(whichPricer, vars.startDate, vars.length,
caps0, floors, vars.volatility);
Swap floorLeg = new Swap(fixedLeg, flooredLeg);
floorLeg.setPricingEngine(engine);
YoYInflationFloor floor = new YoYInflationFloor(floatLeg, new List <double>()
{
floorstrike
});
floor.setPricingEngine(vars.makeEngine(vars.volatility, whichPricer));
npvFlooredLeg = floorLeg.NPV();
npvFloor = floor.NPV();
error = Math.Abs(npvFlooredLeg - (npvVanilla + npvFloor));
if (error > tolerance)
{
QAssert.Fail("YoY Floored Leg: gearing=1, spread=0%, strike=" + floorstrike * 100 +
"%\n" +
" Floored Floating Leg NPV: " + npvFlooredLeg + "\n" +
" Floating Leg NPV + Floor NPV: " + (npvVanilla + npvFloor) + "\n" +
" Diff: " + error);
}
// gearing = 1 and spread = 0
// COLLARED coupon - Decomposition of payoff
// Payoff = Nom * Min(strikem,Max(rate,strikeM)) * accrualperiod =
// = VanillaFloatingLeg - Collar
//
List <CashFlow> collaredLeg = vars.makeYoYCapFlooredLeg(whichPricer, vars.startDate, vars.length,
caps, floors, vars.volatility);
Swap collarLeg = new Swap(fixedLeg, collaredLeg);
collarLeg.setPricingEngine(engine);
YoYInflationCollar collar = new YoYInflationCollar(floatLeg,
new List <double>()
{
capstrike
},
new List <double>()
{
floorstrike
});
collar.setPricingEngine(vars.makeEngine(vars.volatility, whichPricer));
npvCollaredLeg = collarLeg.NPV();
npvCollar = collar.NPV();
error = Math.Abs(npvCollaredLeg - (npvVanilla - npvCollar));
if (error > tolerance)
{
QAssert.Fail("\nYoY Collared Leg: gearing=1, spread=0%, strike=" +
floorstrike * 100 + "% and " + capstrike * 100 + "%\n" +
" Collared Floating Leg NPV: " + npvCollaredLeg + "\n" +
" Floating Leg NPV - Collar NPV: " + (npvVanilla - npvCollar) + "\n" +
" Diff: " + error);
}
// gearing = a and spread = b
// CAPPED coupon - Decomposition of payoff
// Payoff
// = Nom * Min(a*rate+b,strike) * accrualperiod =
// = Nom * [a*rate+b + Min(0,strike-a*rate-b)] * accrualperiod =
// = Nom * a*rate+b * accrualperiod + Nom * Min(strike-b-a*rate,0) * accrualperiod
// --> If a>0 (assuming positive effective strike):
// Payoff = VanillaFloatingLeg - Call(a*rate+b,strike)
// --> If a<0 (assuming positive effective strike):
// Payoff = VanillaFloatingLeg + Nom * Min(strike-b+|a|*rate+,0) * accrualperiod =
// = VanillaFloatingLeg + Put(|a|*rate+b,strike)
//
// Positive gearing
List <CashFlow> cappedLeg_p = vars.makeYoYCapFlooredLeg(whichPricer, vars.startDate, vars.length, caps, floors0,
vars.volatility, gearing_p, spread_p);
Swap capLeg_p = new Swap(fixedLeg, cappedLeg_p);
capLeg_p.setPricingEngine(engine);
YoYInflationCap cap_p = new YoYInflationCap(floatLeg_p, new List <double>()
{
capstrike
});
cap_p.setPricingEngine(vars.makeEngine(vars.volatility, whichPricer));
npvVanilla = vanillaLeg_p.NPV();
npvCappedLeg = capLeg_p.NPV();
npvCap = cap_p.NPV();
error = Math.Abs(npvCappedLeg - (npvVanilla - npvCap));
if (error > tolerance)
{
QAssert.Fail("\nYoY Capped Leg: gearing=" + gearing_p + ", " +
"spread= " + spread_p * 100 +
"%, strike=" + capstrike * 100 + "%, " +
"effective strike= " + (capstrike - spread_p) / gearing_p * 100 +
"%\n" +
" Capped Floating Leg NPV: " + npvCappedLeg + "\n" +
" Vanilla Leg NPV: " + npvVanilla + "\n" +
" Cap NPV: " + npvCap + "\n" +
" Floating Leg NPV - Cap NPV: " + (npvVanilla - npvCap) + "\n" +
" Diff: " + error);
}
// Negative gearing
List <CashFlow> cappedLeg_n = vars.makeYoYCapFlooredLeg(whichPricer, vars.startDate, vars.length, caps, floors0,
vars.volatility, gearing_n, spread_n);
Swap capLeg_n = new Swap(fixedLeg, cappedLeg_n);
capLeg_n.setPricingEngine(engine);
YoYInflationFloor floor_n = new YoYInflationFloor(floatLeg, new List <double>()
{
(capstrike - spread_n) / gearing_n
});
floor_n.setPricingEngine(vars.makeEngine(vars.volatility, whichPricer));
npvVanilla = vanillaLeg_n.NPV();
npvCappedLeg = capLeg_n.NPV();
npvFloor = floor_n.NPV();
error = Math.Abs(npvCappedLeg - (npvVanilla + gearing_n * npvFloor));
if (error > tolerance)
{
QAssert.Fail("\nYoY Capped Leg: gearing=" + gearing_n + ", " +
"spread= " + spread_n * 100 +
"%, strike=" + capstrike * 100 + "%, " +
"effective strike= " + ((capstrike - spread_n) / gearing_n * 100) +
"%\n" +
" Capped Floating Leg NPV: " + npvCappedLeg + "\n" +
" npv Vanilla: " + npvVanilla + "\n" +
" npvFloor: " + npvFloor + "\n" +
" Floating Leg NPV - Cap NPV: " + (npvVanilla + gearing_n * npvFloor) + "\n" +
" Diff: " + error);
}
// gearing = a and spread = b
// FLOORED coupon - Decomposition of payoff
// Payoff
// = Nom * Max(a*rate+b,strike) * accrualperiod =
// = Nom * [a*rate+b + Max(0,strike-a*rate-b)] * accrualperiod =
// = Nom * a*rate+b * accrualperiod + Nom * Max(strike-b-a*rate,0) * accrualperiod
// --> If a>0 (assuming positive effective strike):
// Payoff = VanillaFloatingLeg + Put(a*rate+b,strike)
// --> If a<0 (assuming positive effective strike):
// Payoff = VanillaFloatingLeg + Nom * Max(strike-b+|a|*rate+,0) * accrualperiod =
// = VanillaFloatingLeg - Call(|a|*rate+b,strike)
//
// Positive gearing
List <CashFlow> flooredLeg_p1 = vars.makeYoYCapFlooredLeg(whichPricer, vars.startDate, vars.length, caps0, floors,
vars.volatility, gearing_p, spread_p);
Swap floorLeg_p1 = new Swap(fixedLeg, flooredLeg_p1);
floorLeg_p1.setPricingEngine(engine);
YoYInflationFloor floor_p1 = new YoYInflationFloor(floatLeg_p, new List <double>()
{
floorstrike
});
floor_p1.setPricingEngine(vars.makeEngine(vars.volatility, whichPricer));
npvVanilla = vanillaLeg_p.NPV();
npvFlooredLeg = floorLeg_p1.NPV();
npvFloor = floor_p1.NPV();
error = Math.Abs(npvFlooredLeg - (npvVanilla + npvFloor));
if (error > tolerance)
{
QAssert.Fail("\nYoY Floored Leg: gearing=" + gearing_p + ", "
+ "spread= " + spread_p * 100 + "%, strike=" + floorstrike * 100 + "%, "
+ "effective strike= " + (floorstrike - spread_p) / gearing_p * 100
+ "%\n" +
" Floored Floating Leg NPV: " + npvFlooredLeg
+ "\n" +
" Floating Leg NPV + Floor NPV: " + (npvVanilla + npvFloor)
+ "\n" +
" Diff: " + error);
}
// Negative gearing
List <CashFlow> flooredLeg_n = vars.makeYoYCapFlooredLeg(whichPricer, vars.startDate, vars.length, caps0, floors,
vars.volatility, gearing_n, spread_n);
Swap floorLeg_n = new Swap(fixedLeg, flooredLeg_n);
floorLeg_n.setPricingEngine(engine);
YoYInflationCap cap_n = new YoYInflationCap(floatLeg, new List <double>()
{
(floorstrike - spread_n) / gearing_n
});
cap_n.setPricingEngine(vars.makeEngine(vars.volatility, whichPricer));
npvVanilla = vanillaLeg_n.NPV();
npvFlooredLeg = floorLeg_n.NPV();
npvCap = cap_n.NPV();
error = Math.Abs(npvFlooredLeg - (npvVanilla - gearing_n * npvCap));
if (error > tolerance)
{
QAssert.Fail("\nYoY Capped Leg: gearing=" + gearing_n + ", " +
"spread= " + spread_n * 100 +
"%, strike=" + floorstrike * 100 + "%, " +
"effective strike= " + (floorstrike - spread_n) / gearing_n * 100 +
"%\n" +
" Capped Floating Leg NPV: " + npvFlooredLeg + "\n" +
" Floating Leg NPV - Cap NPV: " + (npvVanilla - gearing_n * npvCap) + "\n" +
" Diff: " + error);
}
// gearing = a and spread = b
// COLLARED coupon - Decomposition of payoff
// Payoff = Nom * Min(caprate,Max(a*rate+b,floorrate)) * accrualperiod
// --> If a>0 (assuming positive effective strike):
// Payoff = VanillaFloatingLeg - Collar(a*rate+b, floorrate, caprate)
// --> If a<0 (assuming positive effective strike):
// Payoff = VanillaFloatingLeg + Collar(|a|*rate+b, caprate, floorrate)
//
// Positive gearing
List <CashFlow> collaredLeg_p = vars.makeYoYCapFlooredLeg(whichPricer, vars.startDate, vars.length, caps, floors,
vars.volatility, gearing_p, spread_p);
Swap collarLeg_p1 = new Swap(fixedLeg, collaredLeg_p);
collarLeg_p1.setPricingEngine(engine);
YoYInflationCollar collar_p = new YoYInflationCollar(floatLeg_p,
new List <double>()
{
capstrike
},
new List <double>()
{
floorstrike
});
collar_p.setPricingEngine(vars.makeEngine(vars.volatility, whichPricer));
npvVanilla = vanillaLeg_p.NPV();
npvCollaredLeg = collarLeg_p1.NPV();
npvCollar = collar_p.NPV();
error = Math.Abs(npvCollaredLeg - (npvVanilla - npvCollar));
if (error > tolerance)
{
QAssert.Fail("\nYoY Collared Leg: gearing=" + gearing_p + ", "
+ "spread= " + spread_p * 100 + "%, strike="
+ floorstrike * 100 + "% and " + capstrike * 100
+ "%, "
+ "effective strike=" + (floorstrike - spread_p) / gearing_p * 100
+ "% and " + (capstrike - spread_p) / gearing_p * 100
+ "%\n" +
" Collared Floating Leg NPV: " + npvCollaredLeg
+ "\n" +
" Floating Leg NPV - Collar NPV: " + (npvVanilla - npvCollar)
+ "\n" +
" Diff: " + error);
}
// Negative gearing
List <CashFlow> collaredLeg_n = vars.makeYoYCapFlooredLeg(whichPricer, vars.startDate, vars.length, caps, floors,
vars.volatility, gearing_n, spread_n);
Swap collarLeg_n1 = new Swap(fixedLeg, collaredLeg_n);
collarLeg_n1.setPricingEngine(engine);
YoYInflationCollar collar_n = new YoYInflationCollar(floatLeg,
new List <double>()
{
(floorstrike - spread_n) / gearing_n
},
new List <double>()
{
(capstrike - spread_n) / gearing_n
});
collar_n.setPricingEngine(vars.makeEngine(vars.volatility, whichPricer));
npvVanilla = vanillaLeg_n.NPV();
npvCollaredLeg = collarLeg_n1.NPV();
npvCollar = collar_n.NPV();
error = Math.Abs(npvCollaredLeg - (npvVanilla - gearing_n * npvCollar));
if (error > tolerance)
{
QAssert.Fail("\nYoY Collared Leg: gearing=" + gearing_n + ", "
+ "spread= " + spread_n * 100 + "%, strike="
+ floorstrike * 100 + "% and " + capstrike * 100
+ "%, "
+ "effective strike=" + (floorstrike - spread_n) / gearing_n * 100
+ "% and " + (capstrike - spread_n) / gearing_n * 100
+ "%\n" +
" Collared Floating Leg NPV: " + npvCollaredLeg
+ "\n" +
" Floating Leg NPV - Collar NPV: " + (npvVanilla - gearing_n * npvCollar)
+ "\n" +
" Diff: " + error);
}
// remove circular refernce
vars.hy.linkTo(null);
}
void checkSequence <S>(string name, int dimension) where S : IGeneralStatistics, new ()
{
GenericSequenceStatistics <S> ss = new GenericSequenceStatistics <S>(dimension);
int i;
for (i = 0; i < data.Length; i++)
{
List <double> temp = new InitializedList <double>(dimension, data[i]);
ss.add(temp, weights[i]);
}
List <double> calculated;
double expected, tolerance;
if (ss.samples() != data.Length)
{
QAssert.Fail("SequenceStatistics<" + name + ">: "
+ "wrong number of samples\n"
+ " calculated: " + ss.samples() + "\n"
+ " expected: " + data.Length);
}
expected = weights.Sum();
if (ss.weightSum() != expected)
{
QAssert.Fail("SequenceStatistics<" + name + ">: "
+ "wrong sum of weights\n"
+ " calculated: " + ss.weightSum() + "\n"
+ " expected: " + expected);
}
expected = data.Min();
calculated = ss.min();
for (i = 0; i < dimension; i++)
{
if (calculated[i] != expected)
{
QAssert.Fail("SequenceStatistics<" + name + ">: "
+ (i + 1) + " dimension: "
+ "wrong minimum value\n"
+ " calculated: " + calculated[i] + "\n"
+ " expected: " + expected);
}
}
expected = data.Max();
calculated = ss.max();
for (i = 0; i < dimension; i++)
{
if (calculated[i] != expected)
{
QAssert.Fail("SequenceStatistics<" + name + ">: "
+ (i + 1) + " dimension: "
+ "wrong maximun value\n"
+ " calculated: " + calculated[i] + "\n"
+ " expected: " + expected);
}
}
expected = 4.3;
tolerance = 1.0e-9;
calculated = ss.mean();
for (i = 0; i < dimension; i++)
{
if (Math.Abs(calculated[i] - expected) > tolerance)
{
QAssert.Fail("SequenceStatistics<" + name + ">: "
+ (i + 1) + " dimension: "
+ "wrong mean value\n"
+ " calculated: " + calculated[i] + "\n"
+ " expected: " + expected);
}
}
expected = 2.23333333333;
calculated = ss.variance();
for (i = 0; i < dimension; i++)
{
if (Math.Abs(calculated[i] - expected) > tolerance)
{
QAssert.Fail("SequenceStatistics<" + name + ">: "
+ (i + 1) + " dimension: "
+ "wrong variance\n"
+ " calculated: " + calculated[i] + "\n"
+ " expected: " + expected);
}
}
expected = 1.4944341181;
calculated = ss.standardDeviation();
for (i = 0; i < dimension; i++)
{
if (Math.Abs(calculated[i] - expected) > tolerance)
{
QAssert.Fail("SequenceStatistics<" + name + ">: "
+ (i + 1) + " dimension: "
+ "wrong standard deviation\n"
+ " calculated: " + calculated[i] + "\n"
+ " expected: " + expected);
}
}
expected = 0.359543071407;
calculated = ss.skewness();
for (i = 0; i < dimension; i++)
{
if (Math.Abs(calculated[i] - expected) > tolerance)
{
QAssert.Fail("SequenceStatistics<" + name + ">: "
+ (i + 1) + " dimension: "
+ "wrong skewness\n"
+ " calculated: " + calculated[i] + "\n"
+ " expected: " + expected);
}
}
expected = -0.151799637209;
calculated = ss.kurtosis();
for (i = 0; i < dimension; i++)
{
if (Math.Abs(calculated[i] - expected) > tolerance)
{
QAssert.Fail("SequenceStatistics<" + name + ">: "
+ (i + 1) + " dimension: "
+ "wrong kurtosis\n"
+ " calculated: " + calculated[i] + "\n"
+ " expected: " + expected);
}
}
}
public void testCalibration()
{
double forward = 0.03;
double tau = 1.0;
//Real a = 0.04;
//Real b = 0.1;
//Real rho = -0.5;
//Real sigma = 0.1;
//Real m = 0.0;
double a = 0.1;
double b = 0.06;
double rho = -0.9;
double m = 0.24;
double sigma = 0.06;
List <double> strikes = new List <double>();
strikes.Add(0.01);
strikes.Add(0.015);
strikes.Add(0.02);
strikes.Add(0.025);
strikes.Add(0.03);
strikes.Add(0.035);
strikes.Add(0.04);
strikes.Add(0.045);
strikes.Add(0.05);
List <double> vols = new InitializedList <double>(strikes.Count, 0.20); //dummy vols (we do not calibrate here)
SviInterpolation svi = new SviInterpolation(strikes, strikes.Count, vols, tau,
forward, a, b, sigma, rho, m, true, true, true,
true, true);
svi.enableExtrapolation();
List <double> sviVols = new InitializedList <double>(strikes.Count, 0.0);
for (int i = 0; i < strikes.Count; ++i)
{
sviVols[i] = svi.value(strikes[i]);
}
SviInterpolation svi2 = new SviInterpolation(strikes, strikes.Count, sviVols, tau,
forward, null, null, null,
null, null, false, false, false,
false, false, false, null,
null, 1E-8, false,
0); //don't allow for random start values
svi2.enableExtrapolation();
svi2.update();
Console.WriteLine("a=" + svi2.a());
if (!Utils.close_enough(a, svi2.a(), 100))
{
QAssert.Fail("error in a coefficient estimation");
}
Console.WriteLine("b=" + svi2.b());
if (!Utils.close_enough(b, svi2.b(), 100))
{
QAssert.Fail("error in b coefficient estimation");
}
Console.WriteLine("sigma=" + svi2.sigma());
if (!Utils.close_enough(sigma, svi2.sigma(), 100))
{
QAssert.Fail("error in sigma coefficient estimation");
}
Console.WriteLine("rho=" + svi2.rho());
if (!Utils.close_enough(rho, svi2.rho(), 100))
{
QAssert.Fail("error in rho coefficient estimation");
}
Console.WriteLine("m=" + svi2.m());
if (!Utils.close_enough(m, svi2.m(), 100))
{
QAssert.Fail("error in m coefficient estimation");
}
Console.WriteLine("error=" + svi2.rmsError());
}
public void testDecomposition()
{
// Testing collared coupon against its decomposition
CommonVars vars = new CommonVars();
double tolerance = 1e-12;
double npvVanilla, npvCappedLeg, npvFlooredLeg, npvCollaredLeg, npvCap, npvFloor, npvCollar;
double error;
double floorstrike = 0.05;
double capstrike = 0.10;
List <double?> caps = new InitializedList <double?>(vars.length, capstrike);
List <double?> caps0 = new List <double?>();
List <double?> floors = new InitializedList <double?>(vars.length, floorstrike);
List <double?> floors0 = new List <double?>();
double gearing_p = 0.5;
double spread_p = 0.002;
double gearing_n = -1.5;
double spread_n = 0.12;
// fixed leg with zero rate
List <CashFlow> fixedLeg = vars.makeFixedLeg(vars.startDate, vars.length);
// floating leg with gearing=1 and spread=0
List <CashFlow> floatLeg = vars.makeFloatingLeg(vars.startDate, vars.length);
// floating leg with positive gearing (gearing_p) and spread<>0
List <CashFlow> floatLeg_p = vars.makeFloatingLeg(vars.startDate, vars.length, gearing_p, spread_p);
// floating leg with negative gearing (gearing_n) and spread<>0
List <CashFlow> floatLeg_n = vars.makeFloatingLeg(vars.startDate, vars.length, gearing_n, spread_n);
// Swap with null fixed leg and floating leg with gearing=1 and spread=0
Swap vanillaLeg = new Swap(fixedLeg, floatLeg);
// Swap with null fixed leg and floating leg with positive gearing and spread<>0
Swap vanillaLeg_p = new Swap(fixedLeg, floatLeg_p);
// Swap with null fixed leg and floating leg with negative gearing and spread<>0
Swap vanillaLeg_n = new Swap(fixedLeg, floatLeg_n);
IPricingEngine engine = new DiscountingSwapEngine(vars.termStructure);
vanillaLeg.setPricingEngine(engine);
vanillaLeg_p.setPricingEngine(engine);
vanillaLeg_n.setPricingEngine(engine);
/* CAPPED coupon - Decomposition of payoff
* Payoff = Nom * Min(rate,strike) * accrualperiod =
* = Nom * [rate + Min(0,strike-rate)] * accrualperiod =
* = Nom * rate * accrualperiod - Nom * Max(rate-strike,0) * accrualperiod =
* = VanillaFloatingLeg - Call
*/
// Case gearing = 1 and spread = 0
List <CashFlow> cappedLeg = vars.makeCapFlooredLeg(vars.startDate, vars.length, caps, floors0, vars.volatility);
Swap capLeg = new Swap(fixedLeg, cappedLeg);
capLeg.setPricingEngine(engine);
Cap cap = new Cap(floatLeg, new InitializedList <double>(1, capstrike));
cap.setPricingEngine(vars.makeEngine(vars.volatility));
npvVanilla = vanillaLeg.NPV();
npvCappedLeg = capLeg.NPV();
npvCap = cap.NPV();
error = Math.Abs(npvCappedLeg - (npvVanilla - npvCap));
if (error > tolerance)
{
QAssert.Fail("\nCapped Leg: gearing=1, spread=0%, strike=" + capstrike * 100 +
"%\n" +
" Capped Floating Leg NPV: " + npvCappedLeg + "\n" +
" Floating Leg NPV - Cap NPV: " + (npvVanilla - npvCap) + "\n" +
" Diff: " + error);
}
/* gearing = 1 and spread = 0
* FLOORED coupon - Decomposition of payoff
* Payoff = Nom * Max(rate,strike) * accrualperiod =
* = Nom * [rate + Max(0,strike-rate)] * accrualperiod =
* = Nom * rate * accrualperiod + Nom * Max(strike-rate,0) * accrualperiod =
* = VanillaFloatingLeg + Put
*/
List <CashFlow> flooredLeg = vars.makeCapFlooredLeg(vars.startDate, vars.length, caps0, floors, vars.volatility);
Swap floorLeg = new Swap(fixedLeg, flooredLeg);
floorLeg.setPricingEngine(engine);
Floor floor = new Floor(floatLeg, new InitializedList <double>(1, floorstrike));
floor.setPricingEngine(vars.makeEngine(vars.volatility));
npvFlooredLeg = floorLeg.NPV();
npvFloor = floor.NPV();
error = Math.Abs(npvFlooredLeg - (npvVanilla + npvFloor));
if (error > tolerance)
{
QAssert.Fail("Floored Leg: gearing=1, spread=0%, strike=" + floorstrike * 100 +
"%\n" +
" Floored Floating Leg NPV: " + npvFlooredLeg + "\n" +
" Floating Leg NPV + Floor NPV: " + (npvVanilla + npvFloor) + "\n" +
" Diff: " + error);
}
/* gearing = 1 and spread = 0
* COLLARED coupon - Decomposition of payoff
* Payoff = Nom * Min(strikem,Max(rate,strikeM)) * accrualperiod =
* = VanillaFloatingLeg - Collar
*/
List <CashFlow> collaredLeg = vars.makeCapFlooredLeg(vars.startDate, vars.length, caps, floors, vars.volatility);
Swap collarLeg = new Swap(fixedLeg, collaredLeg);
collarLeg.setPricingEngine(engine);
Collar collar = new Collar(floatLeg, new InitializedList <double>(1, capstrike),
new InitializedList <double>(1, floorstrike));
collar.setPricingEngine(vars.makeEngine(vars.volatility));
npvCollaredLeg = collarLeg.NPV();
npvCollar = collar.NPV();
error = Math.Abs(npvCollaredLeg - (npvVanilla - npvCollar));
if (error > tolerance)
{
QAssert.Fail("\nCollared Leg: gearing=1, spread=0%, strike=" +
floorstrike * 100 + "% and " + capstrike * 100 + "%\n" +
" Collared Floating Leg NPV: " + npvCollaredLeg + "\n" +
" Floating Leg NPV - Collar NPV: " + (npvVanilla - npvCollar) + "\n" +
" Diff: " + error);
}
/* gearing = a and spread = b
* CAPPED coupon - Decomposition of payoff
* Payoff
* = Nom * Min(a*rate+b,strike) * accrualperiod =
* = Nom * [a*rate+b + Min(0,strike-a*rate-b)] * accrualperiod =
* = Nom * a*rate+b * accrualperiod + Nom * Min(strike-b-a*rate,0) * accrualperiod
* --> If a>0 (assuming positive effective strike):
* Payoff = VanillaFloatingLeg - Call(a*rate+b,strike)
* --> If a<0 (assuming positive effective strike):
* Payoff = VanillaFloatingLeg + Nom * Min(strike-b+|a|*rate+,0) * accrualperiod =
* = VanillaFloatingLeg + Put(|a|*rate+b,strike)
*/
// Positive gearing
List <CashFlow> cappedLeg_p = vars.makeCapFlooredLeg(vars.startDate, vars.length, caps, floors0,
vars.volatility, gearing_p, spread_p);
Swap capLeg_p = new Swap(fixedLeg, cappedLeg_p);
capLeg_p.setPricingEngine(engine);
Cap cap_p = new Cap(floatLeg_p, new InitializedList <double>(1, capstrike));
cap_p.setPricingEngine(vars.makeEngine(vars.volatility));
npvVanilla = vanillaLeg_p.NPV();
npvCappedLeg = capLeg_p.NPV();
npvCap = cap_p.NPV();
error = Math.Abs(npvCappedLeg - (npvVanilla - npvCap));
if (error > tolerance)
{
QAssert.Fail("\nCapped Leg: gearing=" + gearing_p + ", " +
"spread= " + spread_p * 100 +
"%, strike=" + capstrike * 100 + "%, " +
"effective strike= " + (capstrike - spread_p) / gearing_p * 100 +
"%\n" +
" Capped Floating Leg NPV: " + npvCappedLeg + "\n" +
" Vanilla Leg NPV: " + npvVanilla + "\n" +
" Cap NPV: " + npvCap + "\n" +
" Floating Leg NPV - Cap NPV: " + (npvVanilla - npvCap) + "\n" +
" Diff: " + error);
}
// Negative gearing
List <CashFlow> cappedLeg_n = vars.makeCapFlooredLeg(vars.startDate, vars.length, caps, floors0,
vars.volatility, gearing_n, spread_n);
Swap capLeg_n = new Swap(fixedLeg, cappedLeg_n);
capLeg_n.setPricingEngine(engine);
Floor floor_n = new Floor(floatLeg, new InitializedList <double>(1, (capstrike - spread_n) / gearing_n));
floor_n.setPricingEngine(vars.makeEngine(vars.volatility));
npvVanilla = vanillaLeg_n.NPV();
npvCappedLeg = capLeg_n.NPV();
npvFloor = floor_n.NPV();
error = Math.Abs(npvCappedLeg - (npvVanilla + gearing_n * npvFloor));
if (error > tolerance)
{
QAssert.Fail("\nCapped Leg: gearing=" + gearing_n + ", " +
"spread= " + spread_n * 100 +
"%, strike=" + capstrike * 100 + "%, " +
"effective strike= " + (capstrike - spread_n) / gearing_n * 100 +
"%\n" +
" Capped Floating Leg NPV: " + npvCappedLeg + "\n" +
" npv Vanilla: " + npvVanilla + "\n" +
" npvFloor: " + npvFloor + "\n" +
" Floating Leg NPV - Cap NPV: " + (npvVanilla + gearing_n * npvFloor) + "\n" +
" Diff: " + error);
}
/* gearing = a and spread = b
* FLOORED coupon - Decomposition of payoff
* Payoff
* = Nom * Max(a*rate+b,strike) * accrualperiod =
* = Nom * [a*rate+b + Max(0,strike-a*rate-b)] * accrualperiod =
* = Nom * a*rate+b * accrualperiod + Nom * Max(strike-b-a*rate,0) * accrualperiod
* --> If a>0 (assuming positive effective strike):
* Payoff = VanillaFloatingLeg + Put(a*rate+b,strike)
* --> If a<0 (assuming positive effective strike):
* Payoff = VanillaFloatingLeg + Nom * Max(strike-b+|a|*rate+,0) * accrualperiod =
* = VanillaFloatingLeg - Call(|a|*rate+b,strike)
*/
// Positive gearing
List <CashFlow> flooredLeg_p1 = vars.makeCapFlooredLeg(vars.startDate, vars.length, caps0, floors,
vars.volatility, gearing_p, spread_p);
Swap floorLeg_p1 = new Swap(fixedLeg, flooredLeg_p1);
floorLeg_p1.setPricingEngine(engine);
Floor floor_p1 = new Floor(floatLeg_p, new InitializedList <double>(1, floorstrike));
floor_p1.setPricingEngine(vars.makeEngine(vars.volatility));
npvVanilla = vanillaLeg_p.NPV();
npvFlooredLeg = floorLeg_p1.NPV();
npvFloor = floor_p1.NPV();
error = Math.Abs(npvFlooredLeg - (npvVanilla + npvFloor));
if (error > tolerance)
{
QAssert.Fail("\nFloored Leg: gearing=" + gearing_p + ", "
+ "spread= " + spread_p * 100 + "%, strike=" + floorstrike * 100 + "%, "
+ "effective strike= " + (floorstrike - spread_p) / gearing_p * 100
+ "%\n" +
" Floored Floating Leg NPV: " + npvFlooredLeg
+ "\n" +
" Floating Leg NPV + Floor NPV: " + (npvVanilla + npvFloor)
+ "\n" +
" Diff: " + error);
}
// Negative gearing
List <CashFlow> flooredLeg_n = vars.makeCapFlooredLeg(vars.startDate, vars.length, caps0, floors,
vars.volatility, gearing_n, spread_n);
Swap floorLeg_n = new Swap(fixedLeg, flooredLeg_n);
floorLeg_n.setPricingEngine(engine);
Cap cap_n = new Cap(floatLeg, new InitializedList <double>(1, (floorstrike - spread_n) / gearing_n));
cap_n.setPricingEngine(vars.makeEngine(vars.volatility));
npvVanilla = vanillaLeg_n.NPV();
npvFlooredLeg = floorLeg_n.NPV();
npvCap = cap_n.NPV();
error = Math.Abs(npvFlooredLeg - (npvVanilla - gearing_n * npvCap));
if (error > tolerance)
{
QAssert.Fail("\nCapped Leg: gearing=" + gearing_n + ", " +
"spread= " + spread_n * 100 +
"%, strike=" + floorstrike * 100 + "%, " +
"effective strike= " + (floorstrike - spread_n) / gearing_n * 100 +
"%\n" +
" Capped Floating Leg NPV: " + npvFlooredLeg + "\n" +
" Floating Leg NPV - Cap NPV: " + (npvVanilla - gearing_n * npvCap) + "\n" +
" Diff: " + error);
}
/* gearing = a and spread = b
* COLLARED coupon - Decomposition of payoff
* Payoff = Nom * Min(caprate,Max(a*rate+b,floorrate)) * accrualperiod
* --> If a>0 (assuming positive effective strike):
* Payoff = VanillaFloatingLeg - Collar(a*rate+b, floorrate, caprate)
* --> If a<0 (assuming positive effective strike):
* Payoff = VanillaFloatingLeg + Collar(|a|*rate+b, caprate, floorrate)
*/
// Positive gearing
List <CashFlow> collaredLeg_p = vars.makeCapFlooredLeg(vars.startDate, vars.length, caps, floors,
vars.volatility, gearing_p, spread_p);
Swap collarLeg_p1 = new Swap(fixedLeg, collaredLeg_p);
collarLeg_p1.setPricingEngine(engine);
Collar collar_p = new Collar(floatLeg_p, new InitializedList <double>(1, capstrike),
new InitializedList <double>(1, floorstrike));
collar_p.setPricingEngine(vars.makeEngine(vars.volatility));
npvVanilla = vanillaLeg_p.NPV();
npvCollaredLeg = collarLeg_p1.NPV();
npvCollar = collar_p.NPV();
error = Math.Abs(npvCollaredLeg - (npvVanilla - npvCollar));
if (error > tolerance)
{
QAssert.Fail("\nCollared Leg: gearing=" + gearing_p + ", "
+ "spread= " + spread_p * 100 + "%, strike="
+ floorstrike * 100 + "% and " + capstrike * 100
+ "%, "
+ "effective strike=" + (floorstrike - spread_p) / gearing_p * 100
+ "% and " + (capstrike - spread_p) / gearing_p * 100
+ "%\n" +
" Collared Floating Leg NPV: " + npvCollaredLeg
+ "\n" +
" Floating Leg NPV - Collar NPV: " + (npvVanilla - npvCollar)
+ "\n" +
" Diff: " + error);
}
// Negative gearing
List <CashFlow> collaredLeg_n = vars.makeCapFlooredLeg(vars.startDate, vars.length, caps, floors,
vars.volatility, gearing_n, spread_n);
Swap collarLeg_n1 = new Swap(fixedLeg, collaredLeg_n);
collarLeg_n1.setPricingEngine(engine);
Collar collar_n = new Collar(floatLeg, new InitializedList <double>(1, (floorstrike - spread_n) / gearing_n),
new InitializedList <double>(1, (capstrike - spread_n) / gearing_n));
collar_n.setPricingEngine(vars.makeEngine(vars.volatility));
npvVanilla = vanillaLeg_n.NPV();
npvCollaredLeg = collarLeg_n1.NPV();
npvCollar = collar_n.NPV();
error = Math.Abs(npvCollaredLeg - (npvVanilla - gearing_n * npvCollar));
if (error > tolerance)
{
QAssert.Fail("\nCollared Leg: gearing=" + gearing_n + ", "
+ "spread= " + spread_n * 100 + "%, strike="
+ floorstrike * 100 + "% and " + capstrike * 100
+ "%, "
+ "effective strike=" + (floorstrike - spread_n) / gearing_n * 100
+ "% and " + (capstrike - spread_n) / gearing_n * 100
+ "%\n" +
" Collared Floating Leg NPV: " + npvCollaredLeg
+ "\n" +
" Floating Leg NPV - Collar NPV: " + (npvVanilla - gearing_n * npvCollar)
+ "\n" +
" Diff: " + error);
}
}
// setup
public CommonVars()
{
backup = new SavedSettings();
Calendar calendar = new TARGET();
Date referenceDate = calendar.adjust(Date.Today);
Settings.Instance.setEvaluationDate(referenceDate);
termStructure = new RelinkableHandle <YieldTermStructure>();
termStructure.linkTo(Utilities.flatRate(referenceDate, 0.05, new Actual365Fixed()));
// ATM Volatility structure
List <Period> atmOptionTenors = new List <Period>();
atmOptionTenors.Add(new Period(1, TimeUnit.Months));
atmOptionTenors.Add(new Period(6, TimeUnit.Months));
atmOptionTenors.Add(new Period(1, TimeUnit.Years));
atmOptionTenors.Add(new Period(5, TimeUnit.Years));
atmOptionTenors.Add(new Period(10, TimeUnit.Years));
atmOptionTenors.Add(new Period(30, TimeUnit.Years));
List <Period> atmSwapTenors = new List <Period>();
atmSwapTenors.Add(new Period(1, TimeUnit.Years));
atmSwapTenors.Add(new Period(5, TimeUnit.Years));
atmSwapTenors.Add(new Period(10, TimeUnit.Years));
atmSwapTenors.Add(new Period(30, TimeUnit.Years));
Matrix m = new Matrix(atmOptionTenors.Count, atmSwapTenors.Count);
m[0, 0] = 0.1300; m[0, 1] = 0.1560; m[0, 2] = 0.1390; m[0, 3] = 0.1220;
m[1, 0] = 0.1440; m[1, 1] = 0.1580; m[1, 2] = 0.1460; m[1, 3] = 0.1260;
m[2, 0] = 0.1600; m[2, 1] = 0.1590; m[2, 2] = 0.1470; m[2, 3] = 0.1290;
m[3, 0] = 0.1640; m[3, 1] = 0.1470; m[3, 2] = 0.1370; m[3, 3] = 0.1220;
m[4, 0] = 0.1400; m[4, 1] = 0.1300; m[4, 2] = 0.1250; m[4, 3] = 0.1100;
m[5, 0] = 0.1130; m[5, 1] = 0.1090; m[5, 2] = 0.1070; m[5, 3] = 0.0930;
atmVol = new Handle <SwaptionVolatilityStructure>(
new SwaptionVolatilityMatrix(calendar, BusinessDayConvention.Following, atmOptionTenors,
atmSwapTenors, m, new Actual365Fixed()));
// Vol cubes
List <Period> optionTenors = new List <Period>();
optionTenors.Add(new Period(1, TimeUnit.Years));
optionTenors.Add(new Period(10, TimeUnit.Years));
optionTenors.Add(new Period(30, TimeUnit.Years));
List <Period> swapTenors = new List <Period>();
swapTenors.Add(new Period(2, TimeUnit.Years));
swapTenors.Add(new Period(10, TimeUnit.Years));
swapTenors.Add(new Period(30, TimeUnit.Years));
List <double> strikeSpreads = new List <double>();
strikeSpreads.Add(-0.020);
strikeSpreads.Add(-0.005);
strikeSpreads.Add(+0.000);
strikeSpreads.Add(+0.005);
strikeSpreads.Add(+0.020);
int nRows = optionTenors.Count * swapTenors.Count;
int nCols = strikeSpreads.Count;
Matrix volSpreadsMatrix = new Matrix(nRows, nCols);
volSpreadsMatrix[0, 0] = 0.0599;
volSpreadsMatrix[0, 1] = 0.0049;
volSpreadsMatrix[0, 2] = 0.0000;
volSpreadsMatrix[0, 3] = -0.0001;
volSpreadsMatrix[0, 4] = 0.0127;
volSpreadsMatrix[1, 0] = 0.0729;
volSpreadsMatrix[1, 1] = 0.0086;
volSpreadsMatrix[1, 2] = 0.0000;
volSpreadsMatrix[1, 3] = -0.0024;
volSpreadsMatrix[1, 4] = 0.0098;
volSpreadsMatrix[2, 0] = 0.0738;
volSpreadsMatrix[2, 1] = 0.0102;
volSpreadsMatrix[2, 2] = 0.0000;
volSpreadsMatrix[2, 3] = -0.0039;
volSpreadsMatrix[2, 4] = 0.0065;
volSpreadsMatrix[3, 0] = 0.0465;
volSpreadsMatrix[3, 1] = 0.0063;
volSpreadsMatrix[3, 2] = 0.0000;
volSpreadsMatrix[3, 3] = -0.0032;
volSpreadsMatrix[3, 4] = -0.0010;
volSpreadsMatrix[4, 0] = 0.0558;
volSpreadsMatrix[4, 1] = 0.0084;
volSpreadsMatrix[4, 2] = 0.0000;
volSpreadsMatrix[4, 3] = -0.0050;
volSpreadsMatrix[4, 4] = -0.0057;
volSpreadsMatrix[5, 0] = 0.0576;
volSpreadsMatrix[5, 1] = 0.0083;
volSpreadsMatrix[5, 2] = 0.0000;
volSpreadsMatrix[5, 3] = -0.0043;
volSpreadsMatrix[5, 4] = -0.0014;
volSpreadsMatrix[6, 0] = 0.0437;
volSpreadsMatrix[6, 1] = 0.0059;
volSpreadsMatrix[6, 2] = 0.0000;
volSpreadsMatrix[6, 3] = -0.0030;
volSpreadsMatrix[6, 4] = -0.0006;
volSpreadsMatrix[7, 0] = 0.0533;
volSpreadsMatrix[7, 1] = 0.0078;
volSpreadsMatrix[7, 2] = 0.0000;
volSpreadsMatrix[7, 3] = -0.0045;
volSpreadsMatrix[7, 4] = -0.0046;
volSpreadsMatrix[8, 0] = 0.0545;
volSpreadsMatrix[8, 1] = 0.0079;
volSpreadsMatrix[8, 2] = 0.0000;
volSpreadsMatrix[8, 3] = -0.0042;
volSpreadsMatrix[8, 4] = -0.0020;
List <List <Handle <Quote> > > volSpreads = new InitializedList <List <Handle <Quote> > >(nRows);
for (int i = 0; i < nRows; ++i)
{
volSpreads[i] = new InitializedList <Handle <Quote> >(nCols);
for (int j = 0; j < nCols; ++j)
{
volSpreads[i][j] = new Handle <Quote>(new SimpleQuote(volSpreadsMatrix[i, j]));
}
}
iborIndex = new Euribor6M(termStructure);
SwapIndex swapIndexBase = new EuriborSwapIsdaFixA(new Period(10, TimeUnit.Years), termStructure);
SwapIndex shortSwapIndexBase = new EuriborSwapIsdaFixA(new Period(2, TimeUnit.Years), termStructure);
bool vegaWeightedSmileFit = false;
SabrVolCube2 = new Handle <SwaptionVolatilityStructure>(
new SwaptionVolCube2(atmVol,
optionTenors,
swapTenors,
strikeSpreads,
volSpreads,
swapIndexBase,
shortSwapIndexBase,
vegaWeightedSmileFit));
SabrVolCube2.link.enableExtrapolation();
List <List <Handle <Quote> > > guess = new InitializedList <List <Handle <Quote> > >(nRows);
for (int i = 0; i < nRows; ++i)
{
guess[i] = new InitializedList <Handle <Quote> >(4);
guess[i][0] = new Handle <Quote>(new SimpleQuote(0.2));
guess[i][1] = new Handle <Quote>(new SimpleQuote(0.5));
guess[i][2] = new Handle <Quote>(new SimpleQuote(0.4));
guess[i][3] = new Handle <Quote>(new SimpleQuote(0.0));
}
List <bool> isParameterFixed = new InitializedList <bool>(4, false);
isParameterFixed[1] = true;
// FIXME
bool isAtmCalibrated = false;
SabrVolCube1 = new Handle <SwaptionVolatilityStructure>(
new SwaptionVolCube1x(atmVol,
optionTenors,
swapTenors,
strikeSpreads,
volSpreads,
swapIndexBase,
shortSwapIndexBase,
vegaWeightedSmileFit,
guess,
isParameterFixed,
isAtmCalibrated));
SabrVolCube1.link.enableExtrapolation();
yieldCurveModels = new List <GFunctionFactory.YieldCurveModel>();
yieldCurveModels.Add(GFunctionFactory.YieldCurveModel.Standard);
yieldCurveModels.Add(GFunctionFactory.YieldCurveModel.ExactYield);
yieldCurveModels.Add(GFunctionFactory.YieldCurveModel.ParallelShifts);
yieldCurveModels.Add(GFunctionFactory.YieldCurveModel.NonParallelShifts);
yieldCurveModels.Add(GFunctionFactory.YieldCurveModel.NonParallelShifts); // for linear tsr model
Handle <Quote> zeroMeanRev = new Handle <Quote>(new SimpleQuote(0.0));
numericalPricers = new List <CmsCouponPricer>();
analyticPricers = new List <CmsCouponPricer>();
for (int j = 0; j < yieldCurveModels.Count; ++j)
{
if (j < yieldCurveModels.Count - 1)
{
numericalPricers.Add(new NumericHaganPricer(atmVol, yieldCurveModels[j], zeroMeanRev));
}
else
{
numericalPricers.Add(new LinearTsrPricer(atmVol, zeroMeanRev));
}
analyticPricers.Add(new AnalyticHaganPricer(atmVol, yieldCurveModels[j], zeroMeanRev));
}
}
public void testCrankNicolsonWithDamping()
{
SavedSettings backup = new SavedSettings();
DayCounter dc = new Actual360();
Date today = Date.Today;
SimpleQuote spot = new SimpleQuote(100.0);
YieldTermStructure qTS = Utilities.flatRate(today, 0.06, dc);
YieldTermStructure rTS = Utilities.flatRate(today, 0.06, dc);
BlackVolTermStructure volTS = Utilities.flatVol(today, 0.35, dc);
StrikedTypePayoff payoff =
new CashOrNothingPayoff(Option.Type.Put, 100, 10.0);
double maturity = 0.75;
Date exDate = today + Convert.ToInt32(maturity * 360 + 0.5);
Exercise exercise = new EuropeanExercise(exDate);
BlackScholesMertonProcess process = new
BlackScholesMertonProcess(new Handle <Quote>(spot),
new Handle <YieldTermStructure>(qTS),
new Handle <YieldTermStructure>(rTS),
new Handle <BlackVolTermStructure>(volTS));
IPricingEngine engine =
new AnalyticEuropeanEngine(process);
VanillaOption opt = new VanillaOption(payoff, exercise);
opt.setPricingEngine(engine);
double expectedPV = opt.NPV();
double expectedGamma = opt.gamma();
// fd pricing using implicit damping steps and Crank Nicolson
int csSteps = 25, dampingSteps = 3, xGrid = 400;
List <int> dim = new InitializedList <int>(1, xGrid);
FdmLinearOpLayout layout = new FdmLinearOpLayout(dim);
Fdm1dMesher equityMesher =
new FdmBlackScholesMesher(
dim[0], process, maturity, payoff.strike(),
null, null, 0.0001, 1.5,
new Pair <double?, double?>(payoff.strike(), 0.01));
FdmMesher mesher =
new FdmMesherComposite(equityMesher);
FdmBlackScholesOp map =
new FdmBlackScholesOp(mesher, process, payoff.strike());
FdmInnerValueCalculator calculator =
new FdmLogInnerValue(payoff, mesher, 0);
object rhs = new Vector(layout.size());
Vector x = new Vector(layout.size());
FdmLinearOpIterator endIter = layout.end();
for (FdmLinearOpIterator iter = layout.begin(); iter != endIter;
++iter)
{
(rhs as Vector)[iter.index()] = calculator.avgInnerValue(iter, maturity);
x[iter.index()] = mesher.location(iter, 0);
}
FdmBackwardSolver solver = new FdmBackwardSolver(map, new FdmBoundaryConditionSet(),
new FdmStepConditionComposite(),
new FdmSchemeDesc().Douglas());
solver.rollback(ref rhs, maturity, 0.0, csSteps, dampingSteps);
MonotonicCubicNaturalSpline spline = new MonotonicCubicNaturalSpline(x, x.Count, rhs as Vector);
double s = spot.value();
double calculatedPV = spline.value(Math.Log(s));
double calculatedGamma = (spline.secondDerivative(Math.Log(s))
- spline.derivative(Math.Log(s))) / (s * s);
double relTol = 2e-3;
if (Math.Abs(calculatedPV - expectedPV) > relTol * expectedPV)
{
QAssert.Fail("Error calculating the PV of the digital option" +
"\n rel. tolerance: " + relTol +
"\n expected: " + expectedPV +
"\n calculated: " + calculatedPV);
}
if (Math.Abs(calculatedGamma - expectedGamma) > relTol * expectedGamma)
{
QAssert.Fail("Error calculating the Gamma of the digital option" +
"\n rel. tolerance: " + relTol +
"\n expected: " + expectedGamma +
"\n calculated: " + calculatedGamma);
}
}
public void testStrikeDependency()
{
//("Testing swaption dependency on strike......");
CommonVars vars = new CommonVars();
double[] strikes = new double[] { 0.03, 0.04, 0.05, 0.06, 0.07 };
for (int i = 0; i < exercises.Length; i++)
{
for (int j = 0; j < lengths.Length; j++)
{
for (int k = 0; k < type.Length; k++)
{
Date exerciseDate = vars.calendar.advance(vars.today,
exercises[i]);
Date startDate = vars.calendar.advance(exerciseDate,
vars.settlementDays, TimeUnit.Days);
// store the results for different rates...
List <double> values = new InitializedList <double>(strikes.Length);
List <double> values_cash = new InitializedList <double>(strikes.Length);
double vol = 0.20;
for (int l = 0; l < strikes.Length; l++)
{
VanillaSwap swap = new MakeVanillaSwap(lengths[j], vars.index, strikes[l])
.withEffectiveDate(startDate)
.withFloatingLegSpread(0.0)
.withType(type[k]);
Swaption swaption = vars.makeSwaption(swap, exerciseDate, vol);
// FLOATING_POINT_EXCEPTION
values[l] = swaption.NPV();
Swaption swaption_cash = vars.makeSwaption(swap, exerciseDate, vol,
Settlement.Type.Cash);
values_cash[l] = swaption_cash.NPV();
}
// and check that they go the right way
if (type[k] == VanillaSwap.Type.Payer)
{
for (int z = 0; z < values.Count - 1; z++)
{
if (values[z] < values[z + 1])
{
Assert.Fail("NPV of Payer swaption with delivery settlement" +
"is increasing with the strike:" +
"\noption tenor: " + exercises[i] +
"\noption date: " + exerciseDate +
"\nvolatility: " + vol +
"\nswap tenor: " + lengths[j] +
"\nvalue: " + values[z] + " at strike: " + strikes[z] +
"\nvalue: " + values[z + 1] + " at strike: " + strikes[z + 1]);
}
}
for (int z = 0; z < values_cash.Count - 1; z++)
{
if (values_cash[z] < values_cash[z + 1])
{
Assert.Fail("NPV of Payer swaption with cash settlement" +
"is increasing with the strike:" +
"\noption tenor: " + exercises[i] +
"\noption date: " + exerciseDate +
"\nvolatility: " + vol +
"\nswap tenor: " + lengths[j] +
"\nvalue: " + values_cash[z] + " at strike: " + strikes[z] +
"\nvalue: " + values_cash[z + 1] + " at strike: " + strikes[z + 1]);
}
}
}
else
{
for (int z = 0; z < values.Count - 1; z++)
{
if (values[z] > values[z + 1])
{
Assert.Fail("NPV of Receiver swaption with delivery settlement" +
"is increasing with the strike:" +
"\noption tenor: " + exercises[i] +
"\noption date: " + exerciseDate +
"\nvolatility: " + vol +
"\nswap tenor: " + lengths[j] +
"\nvalue: " + values[z] + " at strike: " + strikes[z] +
"\nvalue: " + values[z + 1] + " at strike: " + strikes[z + 1]);
}
}
for (int z = 0; z < values_cash.Count - 1; z++)
{
if (values[z] > values[z + 1])
{
Assert.Fail("NPV of Receiver swaption with cash settlement" +
"is increasing with the strike:" +
"\noption tenor: " + exercises[i] +
"\noption date: " + exerciseDate +
"\nvolatility: " + vol +
"\nswap tenor: " + lengths[j] +
"\nvalue: " + values_cash[z] + " at strike: " + strikes[z] +
"\nvalue: " + values_cash[z + 1] + " at strike: " + strikes[z + 1]);
}
}
}
}
}
}
}
public CubicInterpolationImpl(List<double> xBegin, int size, List<double> yBegin,
CubicInterpolation.DerivativeApprox da,
bool monotonic,
CubicInterpolation.BoundaryCondition leftCondition,
double leftConditionValue,
CubicInterpolation.BoundaryCondition rightCondition,
double rightConditionValue)
: base(xBegin, size, yBegin)
{
da_ = da;
monotonic_ = monotonic;
leftType_ = leftCondition;
rightType_ = rightCondition;
leftValue_ = leftConditionValue;
rightValue_ = rightConditionValue;
// coefficients
primitiveConst_ = new InitializedList<double>(size - 1);
a_ = new InitializedList<double>(size - 1);
b_ = new InitializedList<double>(size - 1);
c_ = new InitializedList<double>(size - 1);
monotonicityAdjustments_ = new InitializedList<bool>(size);
}
public double value(Vector p, List<CalibrationHelper> instruments)
{
List<double> w = new InitializedList<double>(instruments.Count, 1.0);
CalibrationFunction f = new CalibrationFunction(this, instruments, w);
return f.value(p);
}
public List <CashFlow> makeYoYCapFlooredLeg(int which, Date startDate,
int length,
List <double> caps,
List <double> floors,
double volatility,
double gearing = 1.0,
double spread = 0.0)
{
Handle <YoYOptionletVolatilitySurface> vol = new Handle <YoYOptionletVolatilitySurface>(
new ConstantYoYOptionletVolatility(volatility,
settlementDays,
calendar,
convention,
dc,
observationLag,
frequency,
iir.interpolated()));
YoYInflationCouponPricer pricer = null;
switch (which)
{
case 0:
pricer = new BlackYoYInflationCouponPricer(vol);
break;
case 1:
pricer = new UnitDisplacedBlackYoYInflationCouponPricer(vol);
break;
case 2:
pricer = new BachelierYoYInflationCouponPricer(vol);
break;
default:
QAssert.Fail("unknown coupon pricer request: which = " + which
+ "should be 0=Black,1=DD,2=Bachelier");
break;
}
List <double> gearingVector = new InitializedList <double>(length, gearing);
List <double> spreadVector = new InitializedList <double>(length, spread);
YoYInflationIndex ii = iir as YoYInflationIndex;
Date endDate = calendar.advance(startDate, new Period(length, TimeUnit.Years), BusinessDayConvention.Unadjusted);
Schedule schedule = new Schedule(startDate, endDate, new Period(frequency), calendar,
BusinessDayConvention.Unadjusted,
BusinessDayConvention.Unadjusted,// ref periods & acc periods
DateGeneration.Rule.Forward, false);
List <CashFlow> yoyLeg = new yoyInflationLeg(schedule, calendar, ii, observationLag)
.withPaymentDayCounter(dc)
.withGearings(gearingVector)
.withSpreads(spreadVector)
.withCaps(caps)
.withFloors(floors)
.withNotionals(nominals)
.withPaymentAdjustment(convention);
for (int i = 0; i < yoyLeg.Count; i++)
{
((YoYInflationCoupon)(yoyLeg[i])).setPricer(pricer);
}
//setCouponPricer(iborLeg, pricer);
return(yoyLeg);
}
public void testBrazilianCached()
{
//("Testing Brazilian public bond prices against cached values...");
CommonVars vars = new CommonVars();
double faceAmount = 1000.0;
double redemption = 100.0;
Date issueDate = new Date(1, Month.January, 2007);
Date today = new Date(6, Month.June, 2007);
Settings.setEvaluationDate(today);
// NTN-F maturity dates
InitializedList <Date> maturityDates = new InitializedList <Date>(6);
maturityDates[0] = new Date(1, Month.January, 2008);
maturityDates[1] = new Date(1, Month.January, 2010);
maturityDates[2] = new Date(1, Month.July, 2010);
maturityDates[3] = new Date(1, Month.January, 2012);
maturityDates[4] = new Date(1, Month.January, 2014);
maturityDates[5] = new Date(1, Month.January, 2017);
// NTN-F yields
InitializedList <double> yields = new InitializedList <double>(6);
yields[0] = 0.114614;
yields[1] = 0.105726;
yields[2] = 0.105328;
yields[3] = 0.104283;
yields[4] = 0.103218;
yields[5] = 0.102948;
// NTN-F prices
InitializedList <double> prices = new InitializedList <double>(6);
prices[0] = 1034.63031372;
prices[1] = 1030.09919487;
prices[2] = 1029.98307160;
prices[3] = 1028.13585068;
prices[4] = 1028.33383817;
prices[5] = 1026.19716497;
int settlementDays = 1;
vars.faceAmount = 1000.0;
// The tolerance is high because Andima truncate yields
double tolerance = 1.0e-4;
InitializedList <InterestRate> couponRates = new InitializedList <InterestRate>(1);
couponRates[0] = new InterestRate(0.1, new Thirty360(), Compounding.Compounded, Frequency.Annual);
for (int bondIndex = 0; bondIndex < maturityDates.Count; bondIndex++)
{
// plain
InterestRate yield = new InterestRate(yields[bondIndex], new Business252(new Brazil()),
Compounding.Compounded, Frequency.Annual);
Schedule schedule = new Schedule(new Date(1, Month.January, 2007),
maturityDates[bondIndex], new Period(Frequency.Semiannual),
new Brazil(Brazil.Market.Settlement),
BusinessDayConvention.Unadjusted, BusinessDayConvention.Unadjusted,
DateGeneration.Rule.Backward, false);
FixedRateBond bond = new FixedRateBond(settlementDays,
faceAmount,
schedule,
couponRates,
BusinessDayConvention.Following,
redemption,
issueDate);
double cachedPrice = prices[bondIndex];
double price = vars.faceAmount * (bond.cleanPrice(yield.rate(),
yield.dayCounter(),
yield.compounding(),
yield.frequency(),
today) + bond.accruedAmount(today)) / 100;
if (Math.Abs(price - cachedPrice) > tolerance)
{
Assert.Fail("failed to reproduce cached price:\n"
+ " calculated: " + price + "\n"
+ " expected: " + cachedPrice + "\n"
+ " error: " + (price - cachedPrice) + "\n"
);
}
}
}
public EuropeanExercise(Date date)
: base(Type.European)
{
dates_ = new InitializedList<Date>(1, date);
}
public void testRegression()
{
// Testing fixed-coupon convertible bond in known regression case
Date today = new Date(23, Month.December, 2008);
Date tomorrow = today + 1;
Settings.Instance.setEvaluationDate(tomorrow);
Handle <Quote> u = new Handle <Quote>(new SimpleQuote(2.9084382818797443));
List <Date> dates = new InitializedList <Date>(25);
List <double> forwards = new InitializedList <double>(25);
dates[0] = new Date(29, Month.December, 2008); forwards[0] = 0.0025999342800;
dates[1] = new Date(5, Month.January, 2009); forwards[1] = 0.0025999342800;
dates[2] = new Date(29, Month.January, 2009); forwards[2] = 0.0053123275500;
dates[3] = new Date(27, Month.February, 2009); forwards[3] = 0.0197049598721;
dates[4] = new Date(30, Month.March, 2009); forwards[4] = 0.0220524845296;
dates[5] = new Date(29, Month.June, 2009); forwards[5] = 0.0217076395643;
dates[6] = new Date(29, Month.December, 2009); forwards[6] = 0.0230349627478;
dates[7] = new Date(29, Month.December, 2010); forwards[7] = 0.0087631647476;
dates[8] = new Date(29, Month.December, 2011); forwards[8] = 0.0219084299499;
dates[9] = new Date(31, Month.December, 2012); forwards[9] = 0.0244798766219;
dates[10] = new Date(30, Month.December, 2013); forwards[10] = 0.0267885498456;
dates[11] = new Date(29, Month.December, 2014); forwards[11] = 0.0266922867562;
dates[12] = new Date(29, Month.December, 2015); forwards[12] = 0.0271052126386;
dates[13] = new Date(29, Month.December, 2016); forwards[13] = 0.0268829891648;
dates[14] = new Date(29, Month.December, 2017); forwards[14] = 0.0264594744498;
dates[15] = new Date(31, Month.December, 2018); forwards[15] = 0.0273450367424;
dates[16] = new Date(30, Month.December, 2019); forwards[16] = 0.0294852614749;
dates[17] = new Date(29, Month.December, 2020); forwards[17] = 0.0285556119719;
dates[18] = new Date(29, Month.December, 2021); forwards[18] = 0.0305557764659;
dates[19] = new Date(29, Month.December, 2022); forwards[19] = 0.0292244738422;
dates[20] = new Date(29, Month.December, 2023); forwards[20] = 0.0263917004194;
dates[21] = new Date(29, Month.December, 2028); forwards[21] = 0.0239626970243;
dates[22] = new Date(29, Month.December, 2033); forwards[22] = 0.0216417108090;
dates[23] = new Date(29, Month.December, 2038); forwards[23] = 0.0228343838422;
dates[24] = new Date(31, Month.December, 2199); forwards[24] = 0.0228343838422;
Handle <YieldTermStructure> r = new Handle <YieldTermStructure>(new InterpolatedForwardCurve <BackwardFlat>(dates, forwards, new Actual360()));
Handle <BlackVolTermStructure> sigma = new Handle <BlackVolTermStructure>(new BlackConstantVol(tomorrow, new NullCalendar(), 21.685235548092248,
new Thirty360(Thirty360.Thirty360Convention.BondBasis)));
BlackProcess process = new BlackProcess(u, r, sigma);
Handle <Quote> spread = new Handle <Quote>(new SimpleQuote(0.11498700678012874));
Date issueDate = new Date(23, Month.July, 2008);
Date maturityDate = new Date(1, Month.August, 2013);
Calendar calendar = new UnitedStates();
Schedule schedule = new MakeSchedule().from(issueDate)
.to(maturityDate)
.withTenor(new Period(6, TimeUnit.Months))
.withCalendar(calendar)
.withConvention(BusinessDayConvention.Unadjusted).value();
int settlementDays = 3;
Exercise exercise = new EuropeanExercise(maturityDate);
double conversionRatio = 100.0 / 20.3175;
List <double> coupons = new InitializedList <double>(schedule.size() - 1, 0.05);
DayCounter dayCounter = new Thirty360(Thirty360.Thirty360Convention.BondBasis);
CallabilitySchedule no_callability = new CallabilitySchedule();
DividendSchedule no_dividends = new DividendSchedule();
double redemption = 100.0;
ConvertibleFixedCouponBond bond = new ConvertibleFixedCouponBond(exercise, conversionRatio,
no_dividends, no_callability,
spread, issueDate, settlementDays,
coupons, dayCounter,
schedule, redemption);
bond.setPricingEngine(new BinomialConvertibleEngine <CoxRossRubinstein> (process, 600));
try
{
double x = bond.NPV(); // should throw; if not, an INF was not detected.
QAssert.Fail("INF result was not detected: " + x + " returned");
}
catch (Exception)
{
// as expected. Do nothing.
// Note: we're expecting an Error we threw, not just any
// exception. If something else is thrown, then there's
// another problem and the test must fail.
}
}
public void testBond()
{
/* when deeply out-of-the-money, the value of the convertible bond
* should equal that of the underlying plain-vanilla bond. */
// Testing out-of-the-money convertible bonds against vanilla bonds
CommonVars vars = new CommonVars();
vars.conversionRatio = 1.0e-16;
Exercise euExercise = new EuropeanExercise(vars.maturityDate);
Exercise amExercise = new AmericanExercise(vars.issueDate, vars.maturityDate);
int timeSteps = 1001;
IPricingEngine engine = new BinomialConvertibleEngine <CoxRossRubinstein>(vars.process, timeSteps);
Handle <YieldTermStructure> discountCurve = new Handle <YieldTermStructure>(new ForwardSpreadedTermStructure(vars.riskFreeRate, vars.creditSpread));
// zero-coupon
Schedule schedule = new MakeSchedule().from(vars.issueDate)
.to(vars.maturityDate)
.withFrequency(Frequency.Once)
.withCalendar(vars.calendar)
.backwards().value();
ConvertibleZeroCouponBond euZero = new ConvertibleZeroCouponBond(euExercise, vars.conversionRatio,
vars.no_dividends, vars.no_callability,
vars.creditSpread,
vars.issueDate, vars.settlementDays,
vars.dayCounter, schedule,
vars.redemption);
euZero.setPricingEngine(engine);
ConvertibleZeroCouponBond amZero = new ConvertibleZeroCouponBond(amExercise, vars.conversionRatio,
vars.no_dividends, vars.no_callability,
vars.creditSpread,
vars.issueDate, vars.settlementDays,
vars.dayCounter, schedule,
vars.redemption);
amZero.setPricingEngine(engine);
ZeroCouponBond zero = new ZeroCouponBond(vars.settlementDays, vars.calendar,
100.0, vars.maturityDate,
BusinessDayConvention.Following, vars.redemption, vars.issueDate);
IPricingEngine bondEngine = new DiscountingBondEngine(discountCurve);
zero.setPricingEngine(bondEngine);
double tolerance = 1.0e-2 * (vars.faceAmount / 100.0);
double error = Math.Abs(euZero.NPV() - zero.settlementValue());
if (error > tolerance)
{
QAssert.Fail("failed to reproduce zero-coupon bond price:"
+ "\n calculated: " + euZero.NPV()
+ "\n expected: " + zero.settlementValue()
+ "\n error: " + error);
}
error = Math.Abs(amZero.NPV() - zero.settlementValue());
if (error > tolerance)
{
QAssert.Fail("failed to reproduce zero-coupon bond price:"
+ "\n calculated: " + amZero.NPV()
+ "\n expected: " + zero.settlementValue()
+ "\n error: " + error);
}
// coupon
List <double> coupons = new InitializedList <double>(1, 0.05);
schedule = new MakeSchedule().from(vars.issueDate)
.to(vars.maturityDate)
.withFrequency(vars.frequency)
.withCalendar(vars.calendar)
.backwards().value();
ConvertibleFixedCouponBond euFixed = new ConvertibleFixedCouponBond(euExercise, vars.conversionRatio,
vars.no_dividends, vars.no_callability,
vars.creditSpread,
vars.issueDate, vars.settlementDays,
coupons, vars.dayCounter,
schedule, vars.redemption);
euFixed.setPricingEngine(engine);
ConvertibleFixedCouponBond amFixed = new ConvertibleFixedCouponBond(amExercise, vars.conversionRatio,
vars.no_dividends, vars.no_callability,
vars.creditSpread,
vars.issueDate, vars.settlementDays,
coupons, vars.dayCounter,
schedule, vars.redemption);
amFixed.setPricingEngine(engine);
FixedRateBond fixedBond = new FixedRateBond(vars.settlementDays, vars.faceAmount, schedule,
coupons, vars.dayCounter, BusinessDayConvention.Following,
vars.redemption, vars.issueDate);
fixedBond.setPricingEngine(bondEngine);
tolerance = 2.0e-2 * (vars.faceAmount / 100.0);
error = Math.Abs(euFixed.NPV() - fixedBond.settlementValue());
if (error > tolerance)
{
QAssert.Fail("failed to reproduce fixed-coupon bond price:"
+ "\n calculated: " + euFixed.NPV()
+ "\n expected: " + fixedBond.settlementValue()
+ "\n error: " + error);
}
error = Math.Abs(amFixed.NPV() - fixedBond.settlementValue());
if (error > tolerance)
{
QAssert.Fail("failed to reproduce fixed-coupon bond price:"
+ "\n calculated: " + amFixed.NPV()
+ "\n expected: " + fixedBond.settlementValue()
+ "\n error: " + error);
}
// floating-rate
IborIndex index = new Euribor1Y(discountCurve);
int fixingDays = 2;
List <double> gearings = new InitializedList <double>(1, 1.0);
List <double> spreads = new List <double>();
ConvertibleFloatingRateBond euFloating = new ConvertibleFloatingRateBond(euExercise, vars.conversionRatio,
vars.no_dividends, vars.no_callability,
vars.creditSpread,
vars.issueDate, vars.settlementDays,
index, fixingDays, spreads,
vars.dayCounter, schedule,
vars.redemption);
euFloating.setPricingEngine(engine);
ConvertibleFloatingRateBond amFloating = new ConvertibleFloatingRateBond(amExercise, vars.conversionRatio,
vars.no_dividends, vars.no_callability,
vars.creditSpread,
vars.issueDate, vars.settlementDays,
index, fixingDays, spreads,
vars.dayCounter, schedule,
vars.redemption);
amFloating.setPricingEngine(engine);
IborCouponPricer pricer = new BlackIborCouponPricer(new Handle <OptionletVolatilityStructure>());
Schedule floatSchedule = new Schedule(vars.issueDate, vars.maturityDate,
new Period(vars.frequency),
vars.calendar, BusinessDayConvention.Following, BusinessDayConvention.Following,
DateGeneration.Rule.Backward, false);
FloatingRateBond floating = new FloatingRateBond(vars.settlementDays, vars.faceAmount, floatSchedule,
index, vars.dayCounter, BusinessDayConvention.Following, fixingDays,
gearings, spreads,
new List <double?>(), new List <double?>(),
false,
vars.redemption, vars.issueDate);
floating.setPricingEngine(bondEngine);
Utils.setCouponPricer(floating.cashflows(), pricer);
tolerance = 2.0e-2 * (vars.faceAmount / 100.0);
error = Math.Abs(euFloating.NPV() - floating.settlementValue());
if (error > tolerance)
{
QAssert.Fail("failed to reproduce floating-rate bond price:"
+ "\n calculated: " + euFloating.NPV()
+ "\n expected: " + floating.settlementValue()
+ "\n error: " + error);
}
error = Math.Abs(amFloating.NPV() - floating.settlementValue());
if (error > tolerance)
{
QAssert.Fail("failed to reproduce floating-rate bond price:"
+ "\n calculated: " + amFloating.NPV()
+ "\n expected: " + floating.settlementValue()
+ "\n error: " + error);
}
}
public List<double> discountBond(List<double> rates)
{
List<double> discountFactors = new InitializedList<double>(size_);
discountFactors[0] = 1.0 / (1.0 + rates[0] * accrualPeriod_[0]);
for (int i = 1; i < size_; ++i) {
discountFactors[i] =
discountFactors[i - 1] / (1.0 + rates[i] * accrualPeriod_[i]);
}
return discountFactors;
}
public void testSimpleCovarianceModels()
{
// Testing simple covariance models
const int size = 10;
const double tolerance = 1e-14;
int i;
LmCorrelationModel corrModel = new LmExponentialCorrelationModel(size, 0.1);
Matrix recon = corrModel.correlation(0.0, null)
- corrModel.pseudoSqrt(0.0, null) * Matrix.transpose(corrModel.pseudoSqrt(0.0, null));
for (i = 0; i < size; ++i)
{
for (int j = 0; j < size; ++j)
{
if (Math.Abs(recon[i, j]) > tolerance)
{
QAssert.Fail("Failed to reproduce correlation matrix"
+ "\n calculated: " + recon[i, j]
+ "\n expected: " + 0);
}
}
}
List <double> fixingTimes = new InitializedList <double>(size);
for (i = 0; i < size; ++i)
{
fixingTimes[i] = 0.5 * i;
}
const double a = 0.2;
const double b = 0.1;
const double c = 2.1;
const double d = 0.3;
LmVolatilityModel volaModel = new LmLinearExponentialVolatilityModel(fixingTimes, a, b, c, d);
LfmCovarianceProxy covarProxy = new LfmCovarianceProxy(volaModel, corrModel);
LiborForwardModelProcess process = new LiborForwardModelProcess(size, makeIndex());
LiborForwardModel liborModel = new LiborForwardModel(process, volaModel, corrModel);
for (double t = 0; t < 4.6; t += 0.31)
{
recon = covarProxy.covariance(t, null)
- covarProxy.diffusion(t, null) * Matrix.transpose(covarProxy.diffusion(t, null));
for (int k = 0; k < size; ++k)
{
for (int j = 0; j < size; ++j)
{
if (Math.Abs(recon[k, j]) > tolerance)
{
QAssert.Fail("Failed to reproduce correlation matrix"
+ "\n calculated: " + recon[k, j]
+ "\n expected: " + 0);
}
}
}
Vector volatility = volaModel.volatility(t, null);
for (int k = 0; k < size; ++k)
{
double expected = 0;
if (k > 2 * t)
{
double T = fixingTimes[k];
expected = (a * (T - t) + d) * Math.Exp(-b * (T - t)) + c;
}
if (Math.Abs(expected - volatility[k]) > tolerance)
{
QAssert.Fail("Failed to reproduce volatities"
+ "\n calculated: " + volatility[k]
+ "\n expected: " + expected);
}
}
}
}
public void testSpreadDependency()
{
//"Testing swaption dependency on spread...";
CommonVars vars = new CommonVars();
double[] spreads = { -0.002, -0.001, 0.0, 0.001, 0.002 };
for (int i = 0; i < exercises.Length; i++)
{
for (int j = 0; j < lengths.Length; j++)
{
for (int k = 0; k < type.Length; k++)
{
Date exerciseDate = vars.calendar.advance(vars.today,
exercises[i]);
Date startDate =
vars.calendar.advance(exerciseDate,
vars.settlementDays, TimeUnit.Days);
// store the results for different rates...
List <double> values = new InitializedList <double>(spreads.Length);
List <double> values_cash = new InitializedList <double>(spreads.Length);
for (int l = 0; l < spreads.Length; l++)
{
VanillaSwap swap =
new MakeVanillaSwap(lengths[j], vars.index, 0.06)
.withEffectiveDate(startDate)
.withFloatingLegSpread(spreads[l])
.withType(type[k]);
Swaption swaption =
vars.makeSwaption(swap, exerciseDate, 0.20);
// FLOATING_POINT_EXCEPTION
values[l] = swaption.NPV();
Swaption swaption_cash =
vars.makeSwaption(swap, exerciseDate, 0.20,
Settlement.Type.Cash);
values_cash[l] = swaption_cash.NPV();
}
// and check that they go the right way
if (type[k] == VanillaSwap.Type.Payer)
{
for (int n = 0; n < spreads.Length - 1; n++)
{
if (values[n] > values[n + 1])
{
Assert.Fail("NPV is decreasing with the spread " +
"in a payer swaption (physical delivered):" +
"\nexercise date: " + exerciseDate +
"\nlength: " + lengths[j] +
"\nvalue: " + values[n] + " for spread: " + spreads[n] +
"\nvalue: " + values[n + 1] + " for spread: " + spreads[n + 1]);
}
if (values_cash[n] > values_cash[n + 1])
{
Assert.Fail("NPV is decreasing with the spread " +
"in a payer swaption (cash delivered):" +
"\nexercise date: " + exerciseDate +
"\nlength: " + lengths[j] +
"\nvalue: " + values_cash[n] + " for spread: " + spreads[n] +
"\nvalue: " + values_cash[n + 1] + " for spread: " + spreads[n + 1]);
}
}
}
else
{
for (int n = 0; n < spreads.Length - 1; n++)
{
if (values[n] < values[n + 1])
{
Assert.Fail("NPV is increasing with the spread " +
"in a receiver swaption (physical delivered):" +
"\nexercise date: " + exerciseDate +
"\nlength: " + lengths[j] +
"\nvalue: " + values[n] + " for spread: " + spreads[n] +
"\nvalue: " + values[n + 1] + " for spread: " + spreads[n + 1]);
}
if (values_cash[n] < values_cash[n + 1])
{
Assert.Fail("NPV is increasing with the spread " +
"in a receiver swaption (cash delivered):" +
"\nexercise date: " + exerciseDate +
"\nlength: " + lengths[j] +
"\nvalue: " + values_cash[n] + " for spread: " + spreads[n] +
"\nvalue: " + values_cash[n + 1] + " for spread: " + spreads[n + 1]);
}
}
}
}
}
}
}
public void RiskStatisticsTest()
{
// ("Testing risk measures...");
IncrementalGaussianStatistics igs = new IncrementalGaussianStatistics();
RiskStatistics s = new RiskStatistics();
double[] averages = { -100.0, -1.0, 0.0, 1.0, 100.0 };
double[] sigmas = { 0.1, 1.0, 100.0 };
int i, j, k, N;
N = (int)Math.Pow(2, 16) - 1;
double dataMin, dataMax;
List <double> data = new InitializedList <double>(N), weights = new InitializedList <double>(N);
for (i = 0; i < averages.Length; i++)
{
for (j = 0; j < sigmas.Length; j++)
{
NormalDistribution normal = new NormalDistribution(averages[i], sigmas[j]);
CumulativeNormalDistribution cumulative = new CumulativeNormalDistribution(averages[i], sigmas[j]);
InverseCumulativeNormal inverseCum = new InverseCumulativeNormal(averages[i], sigmas[j]);
SobolRsg rng = new SobolRsg(1);
dataMin = double.MaxValue;
dataMax = double.MinValue;
for (k = 0; k < N; k++)
{
data[k] = inverseCum.value(rng.nextSequence().value[0]);
dataMin = Math.Min(dataMin, data[k]);
dataMax = Math.Max(dataMax, data[k]);
weights[k] = 1.0;
}
igs.addSequence(data, weights);
s.addSequence(data, weights);
// checks
double calculated, expected;
double tolerance;
if (igs.samples() != N)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong number of samples\n"
+ " calculated: " + igs.samples() + "\n"
+ " expected: " + N);
}
if (s.samples() != N)
{
QAssert.Fail("RiskStatistics: wrong number of samples\n"
+ " calculated: " + s.samples() + "\n"
+ " expected: " + N);
}
// weightSum()
tolerance = 1e-10;
expected = weights.Sum();
calculated = igs.weightSum();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong sum of weights\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.weightSum();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong sum of weights\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// min
tolerance = 1e-12;
expected = dataMin;
calculated = igs.min();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong minimum value\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.min();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: "
+ "wrong minimum value\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// max
expected = dataMax;
calculated = igs.max();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong maximum value\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.max();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: "
+ "wrong maximum value\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// mean
expected = averages[i];
tolerance = (expected == 0.0 ? 1.0e-13 :
Math.Abs(expected) * 1.0e-13);
calculated = igs.mean();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong mean value"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.mean();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong mean value"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// variance
expected = sigmas[j] * sigmas[j];
tolerance = expected * 1.0e-1;
calculated = igs.variance();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong variance"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.variance();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong variance"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// standardDeviation
expected = sigmas[j];
tolerance = expected * 1.0e-1;
calculated = igs.standardDeviation();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong standard deviation"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.standardDeviation();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong standard deviation"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// missing errorEstimate() test
// skewness
expected = 0.0;
tolerance = 1.0e-4;
calculated = igs.skewness();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong skewness"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.skewness();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong skewness"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// kurtosis
expected = 0.0;
tolerance = 1.0e-1;
calculated = igs.kurtosis();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong kurtosis"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.kurtosis();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong kurtosis"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// percentile
expected = averages[i];
tolerance = (expected == 0.0 ? 1.0e-3 :
Math.Abs(expected * 1.0e-3));
calculated = igs.gaussianPercentile(0.5);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong Gaussian percentile"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.gaussianPercentile(0.5);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong Gaussian percentile"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.percentile(0.5);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong percentile"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// potential upside
double upper_tail = averages[i] + 2.0 * sigmas[j],
lower_tail = averages[i] - 2.0 * sigmas[j];
double twoSigma = cumulative.value(upper_tail);
expected = Math.Max(upper_tail, 0.0);
tolerance = (expected == 0.0 ? 1.0e-3 :
Math.Abs(expected * 1.0e-3));
calculated = igs.gaussianPotentialUpside(twoSigma);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong Gaussian potential upside"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.gaussianPotentialUpside(twoSigma);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong Gaussian potential upside"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.potentialUpside(twoSigma);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong potential upside"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// just to check that GaussianStatistics<StatsHolder> does work
StatsHolder h = new StatsHolder(s.mean(), s.standardDeviation());
GenericGaussianStatistics <StatsHolder> test = new GenericGaussianStatistics <StatsHolder>(h);
expected = s.gaussianPotentialUpside(twoSigma);
calculated = test.gaussianPotentialUpside(twoSigma);
if (calculated != expected)
{
QAssert.Fail("GenericGaussianStatistics<StatsHolder> fails"
+ "\n calculated: " + calculated
+ "\n expected: " + expected);
}
// value-at-risk
expected = -Math.Min(lower_tail, 0.0);
tolerance = (expected == 0.0 ? 1.0e-3 :
Math.Abs(expected * 1.0e-3));
calculated = igs.gaussianValueAtRisk(twoSigma);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong Gaussian value-at-risk"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.gaussianValueAtRisk(twoSigma);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong Gaussian value-at-risk"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.valueAtRisk(twoSigma);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong value-at-risk"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
if (averages[i] > 0.0 && sigmas[j] < averages[i])
{
// no data will miss the targets:
// skip the rest of this iteration
igs.reset();
s.reset();
continue;
}
// expected shortfall
expected = -Math.Min(averages[i]
- sigmas[j] * sigmas[j]
* normal.value(lower_tail) / (1.0 - twoSigma),
0.0);
tolerance = (expected == 0.0 ? 1.0e-4
: Math.Abs(expected) * 1.0e-2);
calculated = igs.gaussianExpectedShortfall(twoSigma);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong Gaussian expected shortfall"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.gaussianExpectedShortfall(twoSigma);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong Gaussian expected shortfall"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.expectedShortfall(twoSigma);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong expected shortfall"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// shortfall
expected = 0.5;
tolerance = (expected == 0.0 ? 1.0e-3 :
Math.Abs(expected * 1.0e-3));
calculated = igs.gaussianShortfall(averages[i]);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong Gaussian shortfall"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.gaussianShortfall(averages[i]);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong Gaussian shortfall"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.shortfall(averages[i]);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong shortfall"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// average shortfall
expected = sigmas[j] / Math.Sqrt(2.0 * Const.M_PI) * 2.0;
tolerance = expected * 1.0e-3;
calculated = igs.gaussianAverageShortfall(averages[i]);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong Gaussian average shortfall"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.gaussianAverageShortfall(averages[i]);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong Gaussian average shortfall"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.averageShortfall(averages[i]);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong average shortfall"
+ " for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// regret
expected = sigmas[j] * sigmas[j];
tolerance = expected * 1.0e-1;
calculated = igs.gaussianRegret(averages[i]);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong Gaussian regret(" + averages[i] + ") "
+ "for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.gaussianRegret(averages[i]);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: "
+ "wrong Gaussian regret(" + averages[i] + ") "
+ "for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.regret(averages[i]);
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: "
+ "wrong regret(" + averages[i] + ") "
+ "for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// downsideVariance
expected = s.downsideVariance();
tolerance = (expected == 0.0 ? 1.0e-3 :
Math.Abs(expected * 1.0e-3));
calculated = igs.downsideVariance();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong downside variance"
+ "for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = igs.gaussianDownsideVariance();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong Gaussian downside variance"
+ "for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
// downsideVariance
if (averages[i] == 0.0)
{
expected = sigmas[j] * sigmas[j];
tolerance = expected * 1.0e-3;
calculated = igs.downsideVariance();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong downside variance"
+ "for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = igs.gaussianDownsideVariance();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("IncrementalGaussianStatistics: "
+ "wrong Gaussian downside variance"
+ "for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.downsideVariance();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong downside variance"
+ "for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
calculated = s.gaussianDownsideVariance();
if (Math.Abs(calculated - expected) > tolerance)
{
QAssert.Fail("RiskStatistics: wrong Gaussian downside variance"
+ "for N(" + averages[i] + ", "
+ sigmas[j] + ")\n"
+ " calculated: " + calculated + "\n"
+ " expected: " + expected + "\n"
+ " tolerance: " + tolerance);
}
}
igs.reset();
s.reset();
}
}
}
public void testMonteCarloCapletPricing()
{
//"Testing caplet LMM Monte-Carlo caplet pricing..."
//SavedSettings backup;
/* factor loadings are taken from Hull & White article
* plus extra normalisation to get orthogonal eigenvectors
* http://www.rotman.utoronto.ca/~amackay/fin/libormktmodel2.pdf */
double[] compValues = { 0.85549771, 0.46707264, 0.22353259,
0.91915359, 0.37716089, 0.11360610,
0.96438280, 0.26413316, -0.01412414,
0.97939148, 0.13492952, -0.15028753,
0.95970595, -0.00000000, -0.28100621,
0.97939148, -0.13492952, -0.15028753,
0.96438280, -0.26413316, -0.01412414,
0.91915359, -0.37716089, 0.11360610,
0.85549771, -0.46707264, 0.22353259 };
Matrix volaComp = new Matrix(9, 3);
List <double> lcompValues = new InitializedList <double>(27, 0);
List <double> ltemp = new InitializedList <double>(3, 0);
lcompValues = compValues.ToList();
//std::copy(compValues, compValues+9*3, volaComp.begin());
for (int i = 0; i < 9; i++)
{
ltemp = lcompValues.GetRange(3 * i, 3);
for (int j = 0; j < 3; j++)
{
volaComp[i, j] = ltemp[j];
}
}
LiborForwardModelProcess process1 = makeProcess();
LiborForwardModelProcess process2 = makeProcess(volaComp);
List <double> tmp = process1.fixingTimes();
TimeGrid grid = new TimeGrid(tmp, 12);
List <int> location = new List <int>();
for (int i = 0; i < tmp.Count; ++i)
{
location.Add(grid.index(tmp[i]));
}
// set-up a small Monte-Carlo simulation to price caplets
// and ratchet caps using a one- and a three factor libor market model
ulong seed = 42;
LowDiscrepancy.icInstance = new InverseCumulativeNormal();
IRNG rsg1 = (IRNG) new LowDiscrepancy().make_sequence_generator(
process1.factors() * (grid.size() - 1), seed);
IRNG rsg2 = (IRNG) new LowDiscrepancy().make_sequence_generator(
process2.factors() * (grid.size() - 1), seed);
MultiPathGenerator <IRNG> generator1 = new MultiPathGenerator <IRNG> (process1, grid, rsg1, false);
MultiPathGenerator <IRNG> generator2 = new MultiPathGenerator <IRNG> (process2, grid, rsg2, false);
const int nrTrails = 250000;
List <GeneralStatistics> stat1 = new InitializedList <GeneralStatistics>(process1.size());
List <GeneralStatistics> stat2 = new InitializedList <GeneralStatistics>(process2.size());
List <GeneralStatistics> stat3 = new InitializedList <GeneralStatistics>(process2.size() - 1);
for (int i = 0; i < nrTrails; ++i)
{
Sample <MultiPath> path1 = generator1.next();
Sample <MultiPath> path2 = generator2.next();
List <double> rates1 = new InitializedList <double>(len);
List <double> rates2 = new InitializedList <double>(len);
for (int j = 0; j < process1.size(); ++j)
{
rates1[j] = path1.value[j][location[j]];
rates2[j] = path2.value[j][location[j]];
}
List <double> dis1 = process1.discountBond(rates1);
List <double> dis2 = process2.discountBond(rates2);
for (int k = 0; k < process1.size(); ++k)
{
double accrualPeriod = process1.accrualEndTimes()[k]
- process1.accrualStartTimes()[k];
// caplet payoff function, cap rate at 4%
double payoff1 = Math.Max(rates1[k] - 0.04, 0.0) * accrualPeriod;
double payoff2 = Math.Max(rates2[k] - 0.04, 0.0) * accrualPeriod;
stat1[k].add(dis1[k] * payoff1);
stat2[k].add(dis2[k] * payoff2);
if (k != 0)
{
// ratchet cap payoff function
double payoff3 = Math.Max(rates2[k] - (rates2[k - 1] + 0.0025), 0.0)
* accrualPeriod;
stat3[k - 1].add(dis2[k] * payoff3);
}
}
}
double[] capletNpv = { 0.000000000000, 0.000002841629, 0.002533279333,
0.009577143571, 0.017746502618, 0.025216116835,
0.031608230268, 0.036645683881, 0.039792254012,
0.041829864365 };
double[] ratchetNpv = { 0.0082644895, 0.0082754754, 0.0082159966,
0.0082982822, 0.0083803357, 0.0084366961,
0.0084173270, 0.0081803406, 0.0079533814 };
for (int k = 0; k < process1.size(); ++k)
{
double calculated1 = stat1[k].mean();
double tolerance1 = stat1[k].errorEstimate();
double expected = capletNpv[k];
if (Math.Abs(calculated1 - expected) > tolerance1)
{
Assert.Fail("Failed to reproduce expected caplet NPV"
+ "\n calculated: " + calculated1
+ "\n error int: " + tolerance1
+ "\n expected: " + expected);
}
double calculated2 = stat2[k].mean();
double tolerance2 = stat2[k].errorEstimate();
if (Math.Abs(calculated2 - expected) > tolerance2)
{
Assert.Fail("Failed to reproduce expected caplet NPV"
+ "\n calculated: " + calculated2
+ "\n error int: " + tolerance2
+ "\n expected: " + expected);
}
if (k != 0)
{
double calculated3 = stat3[k - 1].mean();
double tolerance3 = stat3[k - 1].errorEstimate();
expected = ratchetNpv[k - 1];
double refError = 1e-5; // 1e-5. error bars of the reference values
if (Math.Abs(calculated3 - expected) > tolerance3 + refError)
{
Assert.Fail("Failed to reproduce expected caplet NPV"
+ "\n calculated: " + calculated3
+ "\n error int: " + tolerance3 + refError
+ "\n expected: " + expected);
}
}
}
}
static void Main(string[] args) {
DateTime timer = DateTime.Now;
/*********************
*** MARKET DATA ***
*********************/
Calendar calendar = new TARGET();
Date settlementDate = new Date(18, Month.September, 2008);
// must be a business day
settlementDate = calendar.adjust(settlementDate);
int fixingDays = 3;
int settlementDays = 3;
Date todaysDate = calendar.advance(settlementDate, -fixingDays, TimeUnit.Days);
// nothing to do with Date::todaysDate
Settings.setEvaluationDate(todaysDate);
Console.WriteLine("Today: {0}, {1}", todaysDate.DayOfWeek, todaysDate);
Console.WriteLine("Settlement date: {0}, {1}", settlementDate.DayOfWeek, settlementDate);
// Building of the bonds discounting yield curve
/*********************
*** RATE HELPERS ***
*********************/
// RateHelpers are built from the above quotes together with
// other instrument dependant infos. Quotes are passed in
// relinkable handles which could be relinked to some other
// data source later.
// Common data
// ZC rates for the short end
double zc3mQuote=0.0096;
double zc6mQuote=0.0145;
double zc1yQuote=0.0194;
Quote zc3mRate = new SimpleQuote(zc3mQuote);
Quote zc6mRate = new SimpleQuote(zc6mQuote);
Quote zc1yRate = new SimpleQuote(zc1yQuote);
DayCounter zcBondsDayCounter = new Actual365Fixed();
RateHelper zc3m = new DepositRateHelper(new Handle<Quote>(zc3mRate),
new Period(3, TimeUnit.Months), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, zcBondsDayCounter);
RateHelper zc6m = new DepositRateHelper(new Handle<Quote>(zc6mRate),
new Period(6, TimeUnit.Months), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, zcBondsDayCounter);
RateHelper zc1y = new DepositRateHelper(new Handle<Quote>(zc1yRate),
new Period(1, TimeUnit.Years), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, zcBondsDayCounter);
// setup bonds
double redemption = 100.0;
const int numberOfBonds = 5;
Date[] issueDates = {
new Date (15, Month.March, 2005),
new Date (15, Month.June, 2005),
new Date (30, Month.June, 2006),
new Date (15, Month.November, 2002),
new Date (15, Month.May, 1987)
};
Date[] maturities = {
new Date (31, Month.August, 2010),
new Date (31, Month.August, 2011),
new Date (31, Month.August, 2013),
new Date (15, Month.August, 2018),
new Date (15, Month.May, 2038)
};
double[] couponRates = {
0.02375,
0.04625,
0.03125,
0.04000,
0.04500
};
double[] marketQuotes = {
100.390625,
106.21875,
100.59375,
101.6875,
102.140625
};
List<SimpleQuote> quote = new List<SimpleQuote>();
for (int i=0; i<numberOfBonds; i++) {
SimpleQuote cp = new SimpleQuote(marketQuotes[i]);
quote.Add(cp);
}
List<RelinkableHandle<Quote>> quoteHandle = new InitializedList<RelinkableHandle<Quote>>(numberOfBonds);
for (int i=0; i<numberOfBonds; i++) {
quoteHandle[i].linkTo(quote[i]);
}
// Definition of the rate helpers
List<FixedRateBondHelper> bondsHelpers = new List<FixedRateBondHelper>();
for (int i=0; i<numberOfBonds; i++) {
Schedule schedule = new Schedule(issueDates[i], maturities[i], new Period(Frequency.Semiannual),
new UnitedStates(UnitedStates.Market.GovernmentBond),
BusinessDayConvention.Unadjusted, BusinessDayConvention.Unadjusted,
DateGeneration.Rule.Backward, false);
FixedRateBondHelper bondHelper = new FixedRateBondHelper(quoteHandle[i],
settlementDays,
100.0,
schedule,
new List<double>() { couponRates[i] },
new ActualActual(ActualActual.Convention.Bond),
BusinessDayConvention.Unadjusted,
redemption,
issueDates[i]);
bondsHelpers.Add(bondHelper);
}
/*********************
** CURVE BUILDING **
*********************/
// Any DayCounter would be fine.
// ActualActual::ISDA ensures that 30 years is 30.0
DayCounter termStructureDayCounter = new ActualActual(ActualActual.Convention.ISDA);
double tolerance = 1.0e-15;
// A depo-bond curve
List<RateHelper> bondInstruments = new List<RateHelper>();
// Adding the ZC bonds to the curve for the short end
bondInstruments.Add(zc3m);
bondInstruments.Add(zc6m);
bondInstruments.Add(zc1y);
// Adding the Fixed rate bonds to the curve for the long end
for (int i=0; i<numberOfBonds; i++) {
bondInstruments.Add(bondsHelpers[i]);
}
YieldTermStructure bondDiscountingTermStructure = new PiecewiseYieldCurve<Discount,LogLinear>(
settlementDate, bondInstruments,
termStructureDayCounter,
new List<Handle<Quote>>(),
new List<Date>(),
tolerance);
// Building of the Libor forecasting curve
// deposits
double d1wQuote=0.043375;
double d1mQuote=0.031875;
double d3mQuote=0.0320375;
double d6mQuote=0.03385;
double d9mQuote=0.0338125;
double d1yQuote=0.0335125;
// swaps
double s2yQuote=0.0295;
double s3yQuote=0.0323;
double s5yQuote=0.0359;
double s10yQuote=0.0412;
double s15yQuote=0.0433;
/********************
*** QUOTES ***
********************/
// SimpleQuote stores a value which can be manually changed;
// other Quote subclasses could read the value from a database
// or some kind of data feed.
// deposits
Quote d1wRate = new SimpleQuote(d1wQuote);
Quote d1mRate = new SimpleQuote(d1mQuote);
Quote d3mRate = new SimpleQuote(d3mQuote);
Quote d6mRate = new SimpleQuote(d6mQuote);
Quote d9mRate = new SimpleQuote(d9mQuote);
Quote d1yRate = new SimpleQuote(d1yQuote);
// swaps
Quote s2yRate = new SimpleQuote(s2yQuote);
Quote s3yRate = new SimpleQuote(s3yQuote);
Quote s5yRate = new SimpleQuote(s5yQuote);
Quote s10yRate = new SimpleQuote(s10yQuote);
Quote s15yRate = new SimpleQuote(s15yQuote);
/*********************
*** RATE HELPERS ***
*********************/
// RateHelpers are built from the above quotes together with
// other instrument dependant infos. Quotes are passed in
// relinkable handles which could be relinked to some other
// data source later.
// deposits
DayCounter depositDayCounter = new Actual360();
RateHelper d1w = new DepositRateHelper(
new Handle<Quote>(d1wRate),
new Period(1, TimeUnit.Weeks), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, depositDayCounter);
RateHelper d1m = new DepositRateHelper(
new Handle<Quote>(d1mRate),
new Period(1, TimeUnit.Months), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, depositDayCounter);
RateHelper d3m = new DepositRateHelper(
new Handle<Quote>(d3mRate),
new Period(3, TimeUnit.Months), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, depositDayCounter);
RateHelper d6m = new DepositRateHelper(
new Handle<Quote>(d6mRate),
new Period(6, TimeUnit.Months), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, depositDayCounter);
RateHelper d9m = new DepositRateHelper(
new Handle<Quote>(d9mRate),
new Period(9, TimeUnit.Months), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, depositDayCounter);
RateHelper d1y = new DepositRateHelper(
new Handle<Quote>(d1yRate),
new Period(1, TimeUnit.Years), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, depositDayCounter);
// setup swaps
Frequency swFixedLegFrequency =Frequency.Annual;
BusinessDayConvention swFixedLegConvention = BusinessDayConvention.Unadjusted;
DayCounter swFixedLegDayCounter = new Thirty360(Thirty360.Thirty360Convention.European);
IborIndex swFloatingLegIndex = new Euribor6M();
Period forwardStart = new Period(1, TimeUnit.Days);
RateHelper s2y = new SwapRateHelper(
new Handle<Quote>(s2yRate), new Period(2, TimeUnit.Years),
calendar, swFixedLegFrequency,
swFixedLegConvention, swFixedLegDayCounter,
swFloatingLegIndex, new Handle<Quote>(),forwardStart);
RateHelper s3y = new SwapRateHelper(
new Handle<Quote>(s3yRate), new Period(3, TimeUnit.Years),
calendar, swFixedLegFrequency,
swFixedLegConvention, swFixedLegDayCounter,
swFloatingLegIndex, new Handle<Quote>(),forwardStart);
RateHelper s5y = new SwapRateHelper(
new Handle<Quote>(s5yRate), new Period(5, TimeUnit.Years),
calendar, swFixedLegFrequency,
swFixedLegConvention, swFixedLegDayCounter,
swFloatingLegIndex, new Handle<Quote>(),forwardStart);
RateHelper s10y = new SwapRateHelper(
new Handle<Quote>(s10yRate), new Period(10, TimeUnit.Years),
calendar, swFixedLegFrequency,
swFixedLegConvention, swFixedLegDayCounter,
swFloatingLegIndex, new Handle<Quote>(),forwardStart);
RateHelper s15y = new SwapRateHelper(
new Handle<Quote>(s15yRate), new Period(15, TimeUnit.Years),
calendar, swFixedLegFrequency,
swFixedLegConvention, swFixedLegDayCounter,
swFloatingLegIndex, new Handle<Quote>(),forwardStart);
/*********************
** CURVE BUILDING **
*********************/
// Any DayCounter would be fine.
// ActualActual::ISDA ensures that 30 years is 30.0
// A depo-swap curve
List<RateHelper> depoSwapInstruments = new List<RateHelper>();
depoSwapInstruments.Add(d1w);
depoSwapInstruments.Add(d1m);
depoSwapInstruments.Add(d3m);
depoSwapInstruments.Add(d6m);
depoSwapInstruments.Add(d9m);
depoSwapInstruments.Add(d1y);
depoSwapInstruments.Add(s2y);
depoSwapInstruments.Add(s3y);
depoSwapInstruments.Add(s5y);
depoSwapInstruments.Add(s10y);
depoSwapInstruments.Add(s15y);
YieldTermStructure depoSwapTermStructure = new PiecewiseYieldCurve<Discount,LogLinear>(
settlementDate, depoSwapInstruments,
termStructureDayCounter,
new List<Handle<Quote> >(),
new List<Date>(),
tolerance);
// Term structures that will be used for pricing:
// the one used for discounting cash flows
RelinkableHandle<YieldTermStructure> discountingTermStructure = new RelinkableHandle<YieldTermStructure>();
// the one used for forward rate forecasting
RelinkableHandle<YieldTermStructure> forecastingTermStructure = new RelinkableHandle<YieldTermStructure>();
/*********************
* BONDS TO BE PRICED *
**********************/
// Common data
double faceAmount = 100;
// Pricing engine
IPricingEngine bondEngine = new DiscountingBondEngine(discountingTermStructure);
// Zero coupon bond
ZeroCouponBond zeroCouponBond = new ZeroCouponBond(
settlementDays,
new UnitedStates(UnitedStates.Market.GovernmentBond),
faceAmount,
new Date(15, Month.August,2013),
BusinessDayConvention.Following,
116.92,
new Date(15, Month.August,2003));
zeroCouponBond.setPricingEngine(bondEngine);
// Fixed 4.5% US Treasury Note
Schedule fixedBondSchedule = new Schedule(new Date(15, Month.May, 2007),
new Date(15,Month.May,2017), new Period(Frequency.Semiannual),
new UnitedStates(UnitedStates.Market.GovernmentBond),
BusinessDayConvention.Unadjusted, BusinessDayConvention.Unadjusted, DateGeneration.Rule.Backward, false);
FixedRateBond fixedRateBond = new FixedRateBond(
settlementDays,
faceAmount,
fixedBondSchedule,
new List<double>() { 0.045 },
new ActualActual(ActualActual.Convention.Bond),
BusinessDayConvention.ModifiedFollowing,
100.0, new Date(15, Month.May, 2007));
fixedRateBond.setPricingEngine(bondEngine);
// Floating rate bond (3M USD Libor + 0.1%)
// Should and will be priced on another curve later...
RelinkableHandle<YieldTermStructure> liborTermStructure = new RelinkableHandle<YieldTermStructure>();
IborIndex libor3m = new USDLibor(new Period(3, TimeUnit.Months), liborTermStructure);
libor3m.addFixing(new Date(17, Month.July, 2008),0.0278625);
Schedule floatingBondSchedule = new Schedule(new Date(21, Month.October, 2005),
new Date(21, Month.October, 2010), new Period(Frequency.Quarterly),
new UnitedStates(UnitedStates.Market.NYSE),
BusinessDayConvention.Unadjusted, BusinessDayConvention.Unadjusted, DateGeneration.Rule.Backward, true);
FloatingRateBond floatingRateBond = new FloatingRateBond(
settlementDays,
faceAmount,
floatingBondSchedule,
libor3m,
new Actual360(),
BusinessDayConvention.ModifiedFollowing,
2,
// Gearings
new List<double>() { 1.0 },
// Spreads
new List<double>() { 0.001 },
// Caps
new List<double>(),
// Floors
new List<double>(),
// Fixing in arrears
true,
100.0,
new Date(21, Month.October, 2005));
floatingRateBond.setPricingEngine(bondEngine);
// Coupon pricers
IborCouponPricer pricer = new BlackIborCouponPricer();
// optionLet volatilities
double volatility = 0.0;
Handle<OptionletVolatilityStructure> vol;
vol = new Handle<OptionletVolatilityStructure>(
new ConstantOptionletVolatility(
settlementDays,
calendar,
BusinessDayConvention.ModifiedFollowing,
volatility,
new Actual365Fixed()));
pricer.setCapletVolatility(vol);
Utils.setCouponPricer(floatingRateBond.cashflows(),pricer);
// Yield curve bootstrapping
forecastingTermStructure.linkTo(depoSwapTermStructure);
discountingTermStructure.linkTo(bondDiscountingTermStructure);
// We are using the depo & swap curve to estimate the future Libor rates
liborTermStructure.linkTo(depoSwapTermStructure);
/***************
* BOND PRICING *
****************/
// write column headings
int[] widths = { 18, 10, 10, 10 };
Console.WriteLine("{0,18}{1,10}{2,10}{3,10}", "", "ZC", "Fixed", "Floating");
string separator = " | ";
int width = widths[0]
+ widths[1]
+ widths[2]
+ widths[3];
string rule = "".PadLeft(width, '-'), dblrule = "".PadLeft(width, '=');
string tab = "".PadLeft(8, ' ');
Console.WriteLine(rule);
Console.WriteLine("Net present value".PadLeft(widths[0]) + "{0,10:n2}{1,10:n2}{2,10:n2}",
zeroCouponBond.NPV(),
fixedRateBond.NPV(),
floatingRateBond.NPV());
Console.WriteLine("Clean price".PadLeft(widths[0]) + "{0,10:n2}{1,10:n2}{2,10:n2}",
zeroCouponBond.cleanPrice(),
fixedRateBond.cleanPrice(),
floatingRateBond.cleanPrice());
Console.WriteLine("Dirty price".PadLeft(widths[0]) + "{0,10:n2}{1,10:n2}{2,10:n2}",
zeroCouponBond.dirtyPrice(),
fixedRateBond.dirtyPrice(),
floatingRateBond.dirtyPrice());
Console.WriteLine("Accrued coupon".PadLeft(widths[0]) + "{0,10:n2}{1,10:n2}{2,10:n2}",
zeroCouponBond.accruedAmount(),
fixedRateBond.accruedAmount(),
floatingRateBond.accruedAmount());
Console.WriteLine("Previous coupon".PadLeft(widths[0]) + "{0,10:0.00%}{1,10:0.00%}{2,10:0.00%}",
"N/A",
fixedRateBond.previousCoupon(),
floatingRateBond.previousCoupon());
Console.WriteLine("Next coupon".PadLeft(widths[0]) + "{0,10:0.00%}{1,10:0.00%}{2,10:0.00%}",
"N/A",
fixedRateBond.nextCoupon(),
floatingRateBond.nextCoupon());
Console.WriteLine("Yield".PadLeft(widths[0]) + "{0,10:0.00%}{1,10:0.00%}{2,10:0.00%}",
zeroCouponBond.yield(new Actual360(), Compounding.Compounded, Frequency.Annual),
fixedRateBond.yield(new Actual360(), Compounding.Compounded, Frequency.Annual),
floatingRateBond.yield(new Actual360(), Compounding.Compounded, Frequency.Annual));
Console.WriteLine();
// Other computations
Console.WriteLine("Sample indirect computations (for the floating rate bond): ");
Console.WriteLine(rule);
Console.WriteLine("Yield to Clean Price: {0:n2}",
floatingRateBond.cleanPrice(floatingRateBond.yield(new Actual360(), Compounding.Compounded, Frequency.Annual),
new Actual360(), Compounding.Compounded, Frequency.Annual,
settlementDate));
Console.WriteLine("Clean Price to Yield: {0:0.00%}",
floatingRateBond.yield(floatingRateBond.cleanPrice(),new Actual360(), Compounding.Compounded, Frequency.Annual,
settlementDate));
/* "Yield to Price"
"Price to Yield" */
Console.WriteLine(" \nRun completed in {0}", DateTime.Now - timer);
Console.WriteLine();
Console.Write("Press any key to continue ...");
Console.ReadKey();
}
public void testLiborFixing()
{
// "Testing use of today's LIBOR fixings in swap curve...");
CommonVars vars = new CommonVars();
var swapHelpers = new InitializedList <RateHelper>();
IborIndex euribor6m = new Euribor6M();
for (int i = 0; i < vars.swaps; i++)
{
Handle <Quote> r = new Handle <Quote>(vars.rates[i + vars.deposits]);
swapHelpers.Add(new SwapRateHelper(r, new Period(vars.swapData[i].n, vars.swapData[i].units),
vars.calendar,
vars.fixedLegFrequency, vars.fixedLegConvention,
vars.fixedLegDayCounter, euribor6m));
}
vars.termStructure = new PiecewiseYieldCurve <Discount, LogLinear>(vars.settlement, swapHelpers, new Actual360());
Handle <YieldTermStructure> curveHandle = new Handle <YieldTermStructure>(vars.termStructure);
IborIndex index = new Euribor6M(curveHandle);
for (int i = 0; i < vars.swaps; i++)
{
Period tenor = new Period(vars.swapData[i].n, vars.swapData[i].units);
VanillaSwap swap = new MakeVanillaSwap(tenor, index, 0.0)
.withEffectiveDate(vars.settlement)
.withFixedLegDayCount(vars.fixedLegDayCounter)
.withFixedLegTenor(new Period(vars.fixedLegFrequency))
.withFixedLegConvention(vars.fixedLegConvention)
.withFixedLegTerminationDateConvention(vars.fixedLegConvention)
.value();
double expectedRate = vars.swapData[i].rate / 100,
estimatedRate = swap.fairRate();
double tolerance = 1.0e-9;
if (Math.Abs(expectedRate - estimatedRate) > tolerance)
{
QAssert.Fail("before LIBOR fixing:\n"
+ vars.swapData[i].n + " year(s) swap:\n"
+ " estimated rate: "
+ (estimatedRate) + "\n"
+ " expected rate: "
+ (expectedRate));
}
}
Flag f = new Flag();
vars.termStructure.registerWith(f.update);
f.lower();
index.addFixing(vars.today, 0.0425);
if (!f.isUp())
{
QAssert.Fail("Observer was not notified of rate fixing");
}
for (int i = 0; i < vars.swaps; i++)
{
Period tenor = new Period(vars.swapData[i].n, vars.swapData[i].units);
VanillaSwap swap = new MakeVanillaSwap(tenor, index, 0.0)
.withEffectiveDate(vars.settlement)
.withFixedLegDayCount(vars.fixedLegDayCounter)
.withFixedLegTenor(new Period(vars.fixedLegFrequency))
.withFixedLegConvention(vars.fixedLegConvention)
.withFixedLegTerminationDateConvention(vars.fixedLegConvention)
.value();
double expectedRate = vars.swapData[i].rate / 100,
estimatedRate = swap.fairRate();
double tolerance = 1.0e-9;
if (Math.Abs(expectedRate - estimatedRate) > tolerance)
{
QAssert.Fail("after LIBOR fixing:\n"
+ vars.swapData[i].n + " year(s) swap:\n"
+ " estimated rate: "
+ (estimatedRate) + "\n"
+ " expected rate: "
+ (expectedRate));
}
}
}
