/// <summary>
/// Calculate the Option Adjusted Spread (OAS)
/// <remarks>
/// Calculates the spread that needs to be added to the the
/// reference curve so that the theoretical model value
/// matches the marketPrice.
/// </remarks>
/// </summary>
/// <param name="cleanPrice"></param>
/// <param name="engineTS"></param>
/// <param name="dayCounter"></param>
/// <param name="compounding"></param>
/// <param name="frequency"></param>
/// <param name="settlement"></param>
/// <param name="accuracy"></param>
/// <param name="maxIterations"></param>
/// <param name="guess"></param>
/// <returns></returns>
public double OAS(double cleanPrice,
Handle <YieldTermStructure> engineTS,
DayCounter dayCounter,
Compounding compounding,
Frequency frequency,
Date settlement = null,
double accuracy = 1.0e-10,
int maxIterations = 100,
double guess = 0.0)
{
if (settlement == null)
{
settlement = settlementDate();
}
double dirtyPrice = cleanPrice + accruedAmount(settlement);
var f = new NpvSpreadHelper(this);
OasHelper obj = new OasHelper(f, dirtyPrice);
Brent solver = new Brent();
solver.setMaxEvaluations(maxIterations);
double step = 0.001;
double oas = solver.solve(obj, accuracy, guess, step);
return(continuousToConv(oas,
this,
engineTS,
dayCounter,
compounding,
frequency));
}
//! Tree build-up + numerical fitting to term-structure
public ShortRateTree(TrinomialTree tree,
ShortRateDynamics dynamics,
TermStructureFittingParameter.NumericalImpl theta,
TimeGrid timeGrid)
: base(timeGrid, tree.size(1))
{
tree_ = tree;
dynamics_ = dynamics;
theta.reset();
double value = 1.0;
double vMin = -100.0;
double vMax = 100.0;
for (int i = 0; i < (timeGrid.size() - 1); i++)
{
double discountBond = theta.termStructure().link.discount(t_[i + 1]);
Helper finder = new Helper(i, discountBond, theta, this);
Brent s1d = new Brent();
s1d.setMaxEvaluations(1000);
value = s1d.solve(finder, 1e-7, value, vMin, vMax);
// vMin = value - 1.0;
// vMax = value + 1.0;
theta.change(value);
}
}
private double strikeFromPrice(double price, Option.Type optionType, double referenceStrike)
{
double a, b, min, max, k;
if (optionType == Option.Type.Call)
{
a = swapRateValue_;
min = referenceStrike;
b = max = k = Math.Min(smileSection_.maxStrike(), shiftedUpperBound_);
}
else
{
a = min = k = Math.Max(smileSection_.minStrike(), shiftedLowerBound_);
b = swapRateValue_;
max = referenceStrike;
}
PriceHelper h = new PriceHelper(smileSection_, optionType, price);
Brent solver = new Brent();
try
{
k = solver.solve(h, 1.0E-5, swapRateValue_, a, b);
}
catch (Exception)
{
// use default value set above
}
return(Math.Min(Math.Max(k, min), max));
}
public double value(double x)
{
// first find the right side of the interval
double upper = guess_;
int evaluations = maxEvaluations_;
while (nonCentralDist_.value(upper) < x && evaluations > 0)
{
upper *= 2.0;
--evaluations;
}
// use a brent solver for the rest
Brent solver = new Brent();
solver.setMaxEvaluations(evaluations);
/*return solver.solve(compose(std::bind2nd(std::minus<Real>(),x),
* nonCentralDist_),
* accuracy_, 0.75*upper,
* (evaluations == maxEvaluations_)? 0.0: 0.5*upper,
* upper);*/
return(0d);
}
public override Lattice tree( TimeGrid grid)
{
TermStructureFittingParameter phi= new TermStructureFittingParameter(termStructure());
ShortRateDynamics numericDynamics=
new Dynamics(phi, a(), sigma());
TrinomialTree trinomial=
new TrinomialTree(numericDynamics.process(), grid);
ShortRateTree numericTree =
new ShortRateTree(trinomial, numericDynamics, grid);
TermStructureFittingParameter.NumericalImpl impl =
(TermStructureFittingParameter.NumericalImpl)phi.implementation();
impl.reset();
double value = 1.0;
double vMin = -50.0;
double vMax = 50.0;
for (int i=0; i<(grid.size() - 1); i++) {
double discountBond = termStructure().link.discount(grid[i+1]);
double xMin = trinomial.underlying(i, 0);
double dx = trinomial.dx(i);
Helper finder = new Helper(i, xMin, dx, discountBond, numericTree);
Brent s1d = new Brent();
s1d.setMaxEvaluations(1000);
value = s1d.solve(finder, 1e-7, value, vMin, vMax);
impl.setvalue(grid[i], value);
// vMin = value - 10.0;
// vMax = value + 10.0;
}
return numericTree;
}
public override Lattice tree(TimeGrid grid)
{
TermStructureFittingParameter phi = new TermStructureFittingParameter(termStructure());
ShortRateDynamics numericDynamics =
new Dynamics(phi, a(), sigma());
TrinomialTree trinomial =
new TrinomialTree(numericDynamics.process(), grid);
ShortRateTree numericTree =
new ShortRateTree(trinomial, numericDynamics, grid);
TermStructureFittingParameter.NumericalImpl impl =
(TermStructureFittingParameter.NumericalImpl)phi.implementation();
impl.reset();
double value = 1.0;
double vMin = -50.0;
double vMax = 50.0;
for (int i = 0; i < (grid.size() - 1); i++)
{
double discountBond = termStructure().link.discount(grid[i + 1]);
double xMin = trinomial.underlying(i, 0);
double dx = trinomial.dx(i);
Helper finder = new Helper(i, xMin, dx, discountBond, numericTree);
Brent s1d = new Brent();
s1d.setMaxEvaluations(1000);
value = s1d.solve(finder, 1e-7, value, vMin, vMax);
impl.setvalue(grid[i], value);
}
return(numericTree);
}
//! Black volatility implied by the model
public double impliedVolatility(double targetValue, double accuracy, int maxEvaluations, double minVol, double maxVol) {
ImpliedVolatilityHelper f = new ImpliedVolatilityHelper(this, targetValue);
Brent solver = new Brent();
solver.setMaxEvaluations(maxEvaluations);
return solver.solve(f,accuracy,volatility_.link.value(), minVol, maxVol);
}
//! Black volatility implied by the model
public double impliedVolatility(double targetValue, double accuracy, int maxEvaluations, double minVol, double maxVol)
{
ImpliedVolatilityHelper f = new ImpliedVolatilityHelper(this, targetValue);
Brent solver = new Brent();
solver.setMaxEvaluations(maxEvaluations);
return(solver.solve(f, accuracy, volatility_.link.value(), minVol, maxVol));
}
public double yield(DayCounter dc, Compounding comp, Frequency freq, double accuracy, int maxEvaluations)
{
Brent solver = new Brent();
solver.setMaxEvaluations(maxEvaluations);
YieldFinder objective = new YieldFinder(notional(settlementDate()), cashflows_, dirtyPrice(), dc, comp, freq, settlementDate());
return(solver.solve(objective, accuracy, 0.02, 0.0, 1.0));
}
public double MonthlyYield()
{
Brent solver = new Brent();
solver.setMaxEvaluations(100);
List <CashFlow> cf = expectedCashflows();
MonthlyYieldFinder objective = new MonthlyYieldFinder(notional(settlementDate()), cf, settlementDate());
return(solver.solve(objective, 1.0e-10, 0.02, 0.0, 1.0) / 100);
}
public static double calculate(Instrument instrument, IPricingEngine engine, SimpleQuote volQuote, double targetValue, double accuracy, int maxEvaluations, double minVol, double maxVol)
{
instrument.setupArguments(engine.getArguments());
engine.getArguments().validate();
PriceError f = new PriceError(engine, volQuote, targetValue);
Brent solver = new Brent();
solver.setMaxEvaluations(maxEvaluations);
double guess = (minVol + maxVol) / 2.0;
double result = solver.solve(f, accuracy, guess, minVol, maxVol);
return result;
}
public static double calculate(Instrument instrument, IPricingEngine engine, SimpleQuote volQuote, double targetValue, double accuracy, int maxEvaluations, double minVol, double maxVol)
{
instrument.setupArguments(engine.getArguments());
engine.getArguments().validate();
PriceError f = new PriceError(engine, volQuote, targetValue);
Brent solver = new Brent();
solver.setMaxEvaluations(maxEvaluations);
double guess = (minVol + maxVol) / 2.0;
double result = solver.solve(f, accuracy, guess, minVol, maxVol);
return(result);
}
public double value(double x)
{
// first find the right side of the interval
double upper = guess_;
int evaluations = maxEvaluations_;
while (nonCentralDist_.value(upper) < x && evaluations > 0) {
upper*=2.0;
--evaluations;
}
// use a brent solver for the rest
Brent solver = new Brent();
solver.setMaxEvaluations(evaluations);
return 0d;
}
/*! Extrapolation for unknown order of convergence
* \param t first scaling factor for the step size
* \param s second scaling factor for the step size
*/
public double value(double t, double s)
{
Utils.QL_REQUIRE(t > 1 && s > 1, () => "scaling factors must be greater than 1");
Utils.QL_REQUIRE(t > s, () => "t must be greater than s");
double ft = f_(delta_h_ / t);
double fs = f_(delta_h_ / s);
double k = new Brent().solve(new RichardsonEqn(fdelta_h_, ft, fs, t, s),
1e-8, 0.05, 10);
double ts = Math.Pow(s, k);
return((ts * fs - fdelta_h_) / (ts - 1.0));
}
private List <double> spreadsVolImplied()
{
Brent solver = new Brent();
List <double> result = new InitializedList <double>(nOptionExpiries_, 0.0);
double guess = 0.0001, minSpread = -0.1, maxSpread = 0.1;
for (int j = 0; j < nOptionExpiries_; ++j)
{
ObjectiveFunction f = new ObjectiveFunction(stripper1_, caps_[j], atmCapFloorPrices_[j]);
solver.setMaxEvaluations(maxEvaluations_);
double root = solver.solve(f, accuracy_, guess, minSpread, maxSpread);
result[j] = root;
}
return(result);
}
public double yield(double cleanPrice, DayCounter dc, Compounding comp, Frequency freq, Date settlement,
double accuracy, int maxEvaluations)
{
if (settlement == null)
{
settlement = settlementDate();
}
Brent solver = new Brent();
solver.setMaxEvaluations(maxEvaluations);
double dirtyPrice = cleanPrice + accruedAmount(settlement);
YieldFinder objective = new YieldFinder(notional(settlement), cashflows_, dirtyPrice, dc, comp, freq, settlement);
return(solver.solve(objective, accuracy, 0.02, 0.0, 1.0));
}
protected override double blackVolImpl(double t, double strike)
{
HestonProcess process = hestonModel_.link.process();
double df = process.riskFreeRate().link.discount(t, true);
double div = process.dividendYield().link.discount(t, true);
double spotPrice = process.s0().link.value();
double fwd = spotPrice
* process.dividendYield().link.discount(t, true)
/ process.riskFreeRate().link.discount(t, true);
var payoff = new PlainVanillaPayoff(fwd > strike ? Option.Type.Put : Option.Type.Call, strike);
double kappa = hestonModel_.link.kappa();
double theta = hestonModel_.link.theta();
double rho = hestonModel_.link.rho();
double sigma = hestonModel_.link.sigma();
double v0 = hestonModel_.link.v0();
AnalyticHestonEngine.ComplexLogFormula cpxLogFormula = AnalyticHestonEngine.ComplexLogFormula.Gatheral;
AnalyticHestonEngine hestonEnginePtr = null;
double?npv = null;
int evaluations = 0;
AnalyticHestonEngine.doCalculation(
df, div, spotPrice, strike, t,
kappa, theta, sigma, v0, rho,
payoff, integration_, cpxLogFormula,
hestonEnginePtr, ref npv, ref evaluations);
if (npv <= 0.0)
{
return(Math.Sqrt(theta));
}
Brent solver = new Brent();
solver.setMaxEvaluations(10000);
double guess = Math.Sqrt(theta);
double accuracy = Const.QL_EPSILON;
var f = new ImpliedVolHelper(payoff.optionType(), strike, fwd, t, df, npv.Value);
return(solver.solve(f, accuracy, guess, 0.01));
}
//@}
//! \name Calculations
//@{
//! returns the Black implied forward yield volatility
/*! the forward yield volatility, see Hull, Fourth Edition,
* Chapter 20, pg 536). Relevant only to European put/call
* schedules
*/
public double impliedVolatility(double targetValue,
Handle <YieldTermStructure> discountCurve,
double accuracy,
int maxEvaluations,
double minVol,
double maxVol)
{
calculate();
Utils.QL_REQUIRE(!isExpired(), () => "instrument expired");
double guess = 0.5 * (minVol + maxVol);
blackDiscountCurve_.linkTo(discountCurve, false);
ImpliedVolHelper f = new ImpliedVolHelper(this, targetValue);
Brent solver = new Brent();
solver.setMaxEvaluations(maxEvaluations);
return(solver.solve(f, accuracy, guess, minVol, maxVol));
}
public double value(double x)
{
CumulativeNormalDistribution phi = new CumulativeNormalDistribution();
double temp = (x - mux_) / sigmax_;
double txy = Math.Sqrt(1.0 - rhoxy_ * rhoxy_);
Vector lambda = new Vector(size_);
int i;
for (i = 0; i < size_; i++)
{
double tau = (i == 0 ? t_[0] - T_ : t_[i] - t_[i - 1]);
double c = (i == size_ - 1 ? (1.0 + rate_ * tau) : rate_ * tau);
lambda[i] = c * A_[i] * Math.Exp(-Ba_[i] * x);
}
//SolvingFunction function = new SolvingFunction(lambda, Bb_);
//verifier le polymorphisme
SolvingFunction function = new SolvingFunction(lambda, Bb_);
Brent s1d = new Brent();
s1d.setMaxEvaluations(1000);
double yb = s1d.solve(function, 1e-6, 0.00, -100.0, 100.0);
double h1 = (yb - muy_) / (sigmay_ * txy) -
rhoxy_ * (x - mux_) / (sigmax_ * txy);
double value = phi.value(-w_ * h1);
for (i = 0; i < size_; i++)
{
double h2 = h1 +
Bb_[i] * sigmay_ *Math.Sqrt(1.0 - rhoxy_ *rhoxy_);
double kappa = -Bb_[i] *
(muy_ - 0.5 * txy * txy * sigmay_ * sigmay_ * Bb_[i] +
rhoxy_ * sigmay_ * (x - mux_) / sigmax_);
value -= lambda[i] * Math.Exp(kappa) * phi.value(-w_ * h2);
}
return(Math.Exp(-0.5 * temp * temp) * value /
(sigmax_ * Math.Sqrt(2.0 * QLNet.Const.M_PI)));
}
public double value(double x)
{
// first find the right side of the interval
double upper = guess_;
int evaluations = maxEvaluations_;
while (nonCentralDist_.value(upper) < x && evaluations > 0)
{
upper *= 2.0;
--evaluations;
}
// use a brent solver for the rest
Brent solver = new Brent();
solver.setMaxEvaluations(evaluations);
return(solver.solve(new IncChiQuareFinder(x, nonCentralDist_.value),
accuracy_, 0.75 * upper, (evaluations == maxEvaluations_) ? 0.0 : 0.5 * upper,
upper));
}
//! implied Z-spread.
public static double zSpread(Leg leg, double npv, YieldTermStructure discount, DayCounter dayCounter, Compounding compounding,
Frequency frequency, bool includeSettlementDateFlows, Date settlementDate = null,
Date npvDate = null, double accuracy = 1.0e-10, int maxIterations = 100, double guess = 0.0)
{
if (settlementDate == null)
{
settlementDate = Settings.evaluationDate();
}
if (npvDate == null)
{
npvDate = settlementDate;
}
Brent solver = new Brent();
solver.setMaxEvaluations(maxIterations);
ZSpreadFinder objFunction = new ZSpreadFinder(leg, discount, npv, dayCounter, compounding, frequency,
includeSettlementDateFlows, settlementDate, npvDate);
double step = 0.01;
return(solver.solve(objFunction, accuracy, guess, step));
}
public Concentrating1dMesher(double start, double end, int size,
List <Tuple <double?, double?, bool> > cPoints,
double tol = 1e-8)
: base(size)
{
Utils.QL_REQUIRE(end > start, () => "end must be larger than start");
List <double?> points = new List <double?>(), betas = new List <double?>();
foreach (Tuple <double?, double?, bool> iter in cPoints)
{
points.Add(iter.Item1);
betas.Add((iter.Item2 * (end - start)) * (iter.Item2 * (end - start)));
}
// get scaling factor a so that y(1) = end
double aInit = 0.0;
for (int i = 0; i < points.Count; ++i)
{
double c1 = Utils.Asinh((start - points[i].GetValueOrDefault()) / betas[i].GetValueOrDefault());
double c2 = Utils.Asinh((end - points[i].GetValueOrDefault()) / betas[i].GetValueOrDefault());
aInit += (c2 - c1) / points.Count;
}
OdeIntegrationFct fct = new OdeIntegrationFct(points, betas, tol);
double a = new Brent().solve(
new OdeSolver(fct, start, 0.0, 1.0, end),
tol, aInit, 0.1 * aInit);
// solve ODE for all grid points
Vector x = new Vector(size), y = new Vector(size);
x[0] = 0.0;
y[0] = start;
double dx = 1.0 / (size - 1);
for (int i = 1; i < size; ++i)
{
x[i] = i * dx;
y[i] = fct.solve(a, y[i - 1], x[i - 1], x[i]);
}
// eliminate numerical noise and ensure y(1) = end
double dy = y[y.Count - 1] - end;
for (int i = 1; i < size; ++i)
{
y[i] -= i * dx * dy;
}
LinearInterpolation odeSolution = new LinearInterpolation(x, x.Count, y);
// ensure required points are part of the grid
List <Pair <double?, double?> > w =
new InitializedList <Pair <double?, double?> >(1, new Pair <double?, double?>(0.0, 0.0));
for (int i = 0; i < points.Count; ++i)
{
if (cPoints[i].Item3 && points[i] > start && points[i] < end)
{
int j = y.distance(y[0], y.BinarySearch(points[i].Value));
double e = new Brent().solve(
new OdeSolver2(odeSolution.value, points[i].Value),
Const.QL_EPSILON, x[j], 0.5 / size);
w.Add(new Pair <double?, double?>(Math.Min(x[size - 2], x[j]), e));
}
}
w.Add(new Pair <double?, double?>(1.0, 1.0));
w = w.OrderBy(xx => xx.first).Distinct(new equal_on_first()).ToList();
List <double> u = new List <double>(w.Count), z = new List <double>(w.Count);
for (int i = 0; i < w.Count; ++i)
{
u[i] = w[i].first.GetValueOrDefault();
z[i] = w[i].second.GetValueOrDefault();
}
LinearInterpolation transform = new LinearInterpolation(u, u.Count, z);
for (int i = 0; i < size; ++i)
{
locations_[i] = odeSolution.value(transform.value(i * dx));
}
for (int i = 0; i < size - 1; ++i)
{
dplus_[i] = dminus_[i + 1] = locations_[i + 1] - locations_[i];
}
dplus_[dplus_.Count] = null;
dminus_[0] = null;
}
// alternative delta type
private double strikeFromDelta(double delta, DeltaVolQuote.DeltaType dt)
{
double res = 0.0;
double arg = 0.0;
InverseCumulativeNormal f = new InverseCumulativeNormal();
Utils.QL_REQUIRE(delta * phi_ >= 0.0, () => "Option type and delta are incoherent.");
switch (dt)
{
case DeltaVolQuote.DeltaType.Spot:
Utils.QL_REQUIRE(Math.Abs(delta) <= fDiscount_, () => "Spot delta out of range.");
arg = -phi_ *f.value(phi_ *delta / fDiscount_) * stdDev_ + 0.5 * stdDev_ * stdDev_;
res = forward_ * Math.Exp(arg);
break;
case DeltaVolQuote.DeltaType.Fwd:
Utils.QL_REQUIRE(Math.Abs(delta) <= 1.0, () => "Forward delta out of range.");
arg = -phi_ *f.value(phi_ *delta) * stdDev_ + 0.5 * stdDev_ * stdDev_;
res = forward_ * Math.Exp(arg);
break;
case DeltaVolQuote.DeltaType.PaSpot:
case DeltaVolQuote.DeltaType.PaFwd:
// This has to be solved numerically. One of the
// problems is that the premium adjusted call delta is
// not monotonic in strike, such that two solutions
// might occur. The one right to the max of the delta is
// considered to be the correct strike. Some proper
// interval bounds for the strike need to be chosen, the
// numerics can otherwise be very unreliable and
// unstable. I've chosen Brent over Newton, since the
// interval can be specified explicitly and we can not
// run into the area on the left of the maximum. The
// put delta doesn't have this property and can be
// solved without any problems, but also numerically.
BlackDeltaPremiumAdjustedSolverClass f1 = new BlackDeltaPremiumAdjustedSolverClass(
ot_, dt, spot_, dDiscount_, fDiscount_, stdDev_, delta);
Brent solver = new Brent();
solver.setMaxEvaluations(1000);
double accuracy = 1.0e-10;
double rightLimit = 0.0;
double leftLimit = 0.0;
// Strike of not premium adjusted is always to the right of premium adjusted
if (dt == DeltaVolQuote.DeltaType.PaSpot)
{
rightLimit = strikeFromDelta(delta, DeltaVolQuote.DeltaType.Spot);
}
else
{
rightLimit = strikeFromDelta(delta, DeltaVolQuote.DeltaType.Fwd);
}
if (phi_ < 0)
{
// if put
res = solver.solve(f1, accuracy, rightLimit, 0.0, spot_ * 100.0);
break;
}
else
{
// find out the left limit which is the strike
// corresponding to the value where premium adjusted
// deltas have their maximum.
BlackDeltaPremiumAdjustedMaxStrikeClass g = new BlackDeltaPremiumAdjustedMaxStrikeClass(
ot_, dt, spot_, dDiscount_, fDiscount_, stdDev_);
leftLimit = solver.solve(g, accuracy, rightLimit * 0.5, 0.0, rightLimit);
double guess = leftLimit + (rightLimit - leftLimit) * 0.5;
res = solver.solve(f1, accuracy, guess, leftLimit, rightLimit);
} // end if phi<0 else
break;
default:
Utils.QL_FAIL("invalid delta type");
break;
}
return(res);
}
public void calculate()
{
//prepare instruments
int n = ts_.instruments_.Count, i;
// ensure rate helpers are sorted
ts_.instruments_.Sort((x, y) => x.latestDate().CompareTo(y.latestDate()));
// check that there is no instruments with the same maturity
for (i = 1; i < n; ++i)
{
Date m1 = ts_.instruments_[i - 1].latestDate(),
m2 = ts_.instruments_[i].latestDate();
if (m1 == m2)
{
throw new ArgumentException("two instruments have the same maturity (" + m1 + ")");
}
}
// check that there is no instruments with invalid quote
if ((i = ts_.instruments_.FindIndex(x => !x.quoteIsValid())) != -1)
{
throw new ArgumentException("instrument " + i + " (maturity: " + ts_.instruments_[i].latestDate() +
") has an invalid quote");
}
// setup instruments and register with them
ts_.instruments_.ForEach(x => x.setTermStructure(ts_));
// calculate dates and times
ts_.dates_ = new InitializedList <Date>(n + 1);
ts_.times_ = new InitializedList <double>(n + 1);
ts_.dates_[0] = ts_.initialDate(ts_);
ts_.times_[0] = ts_.timeFromReference(ts_.dates_[0]);
for (i = 0; i < n; ++i)
{
ts_.dates_[i + 1] = ts_.instruments_[i].latestDate();
ts_.times_[i + 1] = ts_.timeFromReference(ts_.dates_[i + 1]);
}
// set initial guess only if the current curve cannot be used as guess
if (validCurve_)
{
if (ts_.data_.Count != n + 1)
{
throw new ArgumentException("dimension mismatch: expected " + n + 1 + ", actual " + ts_.data_.Count);
}
}
else
{
ts_.data_ = new InitializedList <double>(n + 1);
ts_.data_[0] = ts_.initialValue(ts_);
for (i = 0; i < n; ++i)
{
ts_.data_[i + 1] = ts_.initialGuess();
}
}
Brent solver = new Brent();
int maxIterations = ts_.maxIterations();
for (int iteration = 0; ; ++iteration)
{
List <double> previousData = ts_.data();
// restart from the previous interpolation
if (validCurve_)
{
ts_.interpolation_ = ts_.interpolator_.interpolate(ts_.times_, ts_.times_.Count, ts_.data_);
}
for (i = 1; i < n + 1; ++i)
{
// calculate guess before extending interpolation to ensure that any extrapolation is performed
// using the curve bootstrapped so far and no more
RateHelper instrument = ts_.instruments_[i - 1];
double guess = 0;
if (validCurve_ || iteration > 0)
{
guess = ts_.data_[i];
}
else if (i == 1)
{
guess = ts_.initialGuess();
}
else
{
// most traits extrapolate
guess = ts_.guess(ts_, ts_.dates_[i]);
}
// bracket
double min = ts_.minValueAfter(i, ts_.data_);
double max = ts_.maxValueAfter(i, ts_.data_);
if (guess <= min || guess >= max)
{
guess = (min + max) / 2.0;
}
if (!validCurve_ && iteration == 0)
{
// extend interpolation a point at a time
try {
ts_.interpolation_ = ts_.interpolator_.interpolate(ts_.times_, i + 1, ts_.data_);
} catch {
if (!ts_.interpolator_.global)
{
throw; // no chance to fix it in a later iteration
}
// otherwise, if the target interpolation is not usable yet
ts_.interpolation_ = new Linear().interpolate(ts_.times_, i + 1, ts_.data_);
}
}
// required because we just changed the data
// is it really required?
ts_.interpolation_.update();
try {
var error = new BootstrapError(ts_, instrument, i);
double r = solver.solve(error, ts_.accuracy_, guess, min, max);
// redundant assignment (as it has been already performed by BootstrapError in solve procedure), but safe
ts_.data_[i] = r;
} catch (Exception e) {
validCurve_ = false;
throw new ArgumentException(" iteration: " + iteration + 1 +
"could not bootstrap the " + i + " instrument, maturity " + ts_.dates_[i] +
": " + e.Message);
}
}
if (!ts_.interpolator_.global)
{
break; // no need for convergence loop
}
else if (!validCurve_ && iteration == 0)
{
// ensure the target interpolation is used
ts_.interpolation_ = ts_.interpolator_.interpolate(ts_.times_, ts_.times_.Count, ts_.data_);
// at least one more iteration is needed to check convergence
continue;
}
// exit conditions
double improvement = 0.0;
for (i = 1; i < n + 1; ++i)
{
improvement = Math.Max(improvement, Math.Abs(ts_.data_[i] - previousData[i]));
}
if (improvement <= ts_.accuracy_) // convergence reached
{
break;
}
if (!(iteration + 1 < maxIterations))
{
throw new ArgumentException("convergence not reached after " + iteration + 1 + " iterations; last improvement " +
improvement + ", required accuracy " + ts_.accuracy_);
}
}
validCurve_ = true;
}
public void calculate()
{
//prepare instruments
int n = ts_.instruments_.Count, i;
// ensure rate helpers are sorted
ts_.instruments_.Sort((x, y) => x.latestDate().CompareTo(y.latestDate()));
// check that there is no instruments with the same maturity
for (i = 1; i < n; ++i) {
Date m1 = ts_.instruments_[i - 1].latestDate(),
m2 = ts_.instruments_[i].latestDate();
if (m1 == m2) throw new ArgumentException("two instruments have the same maturity (" + m1 + ")");
}
// check that there is no instruments with invalid quote
if ((i = ts_.instruments_.FindIndex(x => !x.quoteIsValid())) != -1)
throw new ArgumentException("instrument " + i + " (maturity: " + ts_.instruments_[i].latestDate() +
") has an invalid quote");
// setup instruments and register with them
ts_.instruments_.ForEach(x => x.setTermStructure(ts_));
// calculate dates and times
ts_.dates_ = new InitializedList<Date>(n + 1);
ts_.times_ = new InitializedList<double>(n + 1);
ts_.dates_[0] = ts_.initialDate(ts_);
ts_.times_[0] = ts_.timeFromReference(ts_.dates_[0]);
for (i = 0; i < n; ++i) {
ts_.dates_[i + 1] = ts_.instruments_[i].latestDate();
ts_.times_[i + 1] = ts_.timeFromReference(ts_.dates_[i + 1]);
}
// set initial guess only if the current curve cannot be used as guess
if (validCurve_) {
if (ts_.data_.Count != n + 1)
throw new ArgumentException("dimension mismatch: expected " + n + 1 + ", actual " + ts_.data_.Count);
} else {
ts_.data_ = new InitializedList<double>(n + 1);
ts_.data_[0] = ts_.initialValue(ts_);
for (i=0; i<n; ++i)
ts_.data_[i+1] = ts_.initialGuess();
}
Brent solver = new Brent();
int maxIterations = ts_.maxIterations();
for (int iteration=0; ; ++iteration) {
List<double> previousData = ts_.data();
// restart from the previous interpolation
if (validCurve_) {
ts_.interpolation_ = ts_.interpolator_.interpolate(ts_.times_, ts_.times_.Count, ts_.data_);
}
for (i=1; i<n+1; ++i) {
// calculate guess before extending interpolation to ensure that any extrapolation is performed
// using the curve bootstrapped so far and no more
RateHelper instrument = ts_.instruments_[i-1];
double guess = 0;
if (validCurve_ || iteration>0) {
guess = ts_.data_[i];
} else if (i==1) {
guess = ts_.initialGuess();
} else {
// most traits extrapolate
guess = ts_.guess(ts_, ts_.dates_[i]);
}
// bracket
double min = ts_.minValueAfter(i, ts_.data_);
double max = ts_.maxValueAfter(i, ts_.data_);
if (guess <= min || guess >= max)
guess = (min + max) / 2.0;
if (!validCurve_ && iteration == 0) {
// extend interpolation a point at a time
try {
ts_.interpolation_ = ts_.interpolator_.interpolate(ts_.times_, i + 1, ts_.data_);
} catch {
if (!ts_.interpolator_.global)
throw; // no chance to fix it in a later iteration
// otherwise, if the target interpolation is not usable yet
ts_.interpolation_ = new Linear().interpolate(ts_.times_, i + 1, ts_.data_);
}
}
// required because we just changed the data
// is it really required?
ts_.interpolation_.update();
try {
var error = new BootstrapError(ts_, instrument, i);
double r = solver.solve(error, ts_.accuracy_, guess, min, max);
// redundant assignment (as it has been already performed by BootstrapError in solve procedure), but safe
ts_.data_[i] = r;
} catch (Exception e) {
validCurve_ = false;
throw new ArgumentException(" iteration: " + iteration + 1 +
"could not bootstrap the " + i + " instrument, maturity " + ts_.dates_[i] +
": " + e.Message);
}
}
if (!ts_.interpolator_.global)
break; // no need for convergence loop
else if (!validCurve_ && iteration == 0) {
// ensure the target interpolation is used
ts_.interpolation_ = ts_.interpolator_.interpolate(ts_.times_, ts_.times_.Count, ts_.data_);
// at least one more iteration is needed to check convergence
continue;
}
// exit conditions
double improvement = 0.0;
for (i=1; i<n+1; ++i)
improvement = Math.Max(improvement, Math.Abs(ts_.data_[i]-previousData[i]));
if (improvement<=ts_.accuracy_) // convergence reached
break;
if (!(iteration+1 < maxIterations))
throw new ArgumentException("convergence not reached after " + iteration+1 + " iterations; last improvement " +
improvement + ", required accuracy " + ts_.accuracy_);
}
validCurve_ = true;
}
/*! Extrapolation for unknown order of convergence
\param t first scaling factor for the step size
\param s second scaling factor for the step size
*/
public double value( double t, double s )
{
Utils.QL_REQUIRE(t > 1 && s > 1, ()=>"scaling factors must be greater than 1");
Utils.QL_REQUIRE(t > s, ()=> "t must be greater than s");
double ft = f_(delta_h_/t);
double fs = f_(delta_h_/s);
double k = new Brent().solve(new RichardsonEqn(fdelta_h_, ft, fs, t, s),
1e-8, 0.05, 10);
double ts = Math.Pow(s, k);
return (ts*fs-fdelta_h_)/(ts-1.0);
}
public double value(double x)
{
CumulativeNormalDistribution phi = new CumulativeNormalDistribution();
double temp = (x - mux_)/sigmax_;
double txy = Math.Sqrt(1.0 - rhoxy_*rhoxy_);
Vector lambda = new Vector(size_);
int i;
for (i=0; i<size_; i++) {
double tau = (i==0 ? t_[0] - T_ : t_[i] - t_[i-1]);
double c = (i==size_-1 ? (1.0+rate_*tau) : rate_*tau);
lambda[i] = c*A_[i]*Math.Exp(-Ba_[i]*x);
}
//SolvingFunction function = new SolvingFunction(lambda, Bb_);
//verifier le polymorphisme
SolvingFunction function = new SolvingFunction(lambda, Bb_);
Brent s1d = new Brent();
s1d.setMaxEvaluations(1000);
double yb = s1d.solve(function, 1e-6, 0.00, -100.0, 100.0);
double h1 = (yb - muy_)/(sigmay_*txy) -
rhoxy_*(x - mux_)/(sigmax_*txy);
double value = phi.value(-w_*h1);
for (i=0; i<size_; i++) {
double h2 = h1 +
Bb_[i]*sigmay_*Math.Sqrt(1.0-rhoxy_*rhoxy_);
double kappa = - Bb_[i] *
(muy_ - 0.5*txy*txy*sigmay_*sigmay_*Bb_[i] +
rhoxy_*sigmay_*(x-mux_)/sigmax_);
value -= lambda[i] *Math.Exp(kappa)*phi.value(-w_*h2);
}
return Math.Exp(-0.5*temp*temp)*value/
(sigmax_*Math.Sqrt(2.0*QLNet.Const.M_PI));
}
public override Vector evolve(double t0, Vector x0, double dt, Vector dw)
{
Vector retVal = new Vector(2);
double vol, vol2, mu, nu, dy;
double sdt = Math.Sqrt(dt);
double sqrhov = Math.Sqrt(1.0 - rho_ * rho_);
switch (discretization_)
{
// For the definition of PartialTruncation, FullTruncation
// and Reflection see Lord, R., R. Koekkoek and D. van Dijk (2006),
// "A Comparison of biased simulation schemes for
// stochastic volatility models",
// Working Paper, Tinbergen Institute
case Discretization.PartialTruncation:
vol = (x0[1] > 0.0) ? Math.Sqrt(x0[1]) : 0.0;
vol2 = sigma_ * vol;
mu = riskFreeRate_.link.forwardRate(t0, t0 + dt, Compounding.Continuous).value()
- dividendYield_.link.forwardRate(t0, t0 + dt, Compounding.Continuous).value()
- 0.5 * vol * vol;
nu = kappa_ * (theta_ - x0[1]);
retVal[0] = x0[0] * Math.Exp(mu * dt + vol * dw[0] * sdt);
retVal[1] = x0[1] + nu * dt + vol2 * sdt * (rho_ * dw[0] + sqrhov * dw[1]);
break;
case Discretization.FullTruncation:
vol = (x0[1] > 0.0) ? Math.Sqrt(x0[1]) : 0.0;
vol2 = sigma_ * vol;
mu = riskFreeRate_.link.forwardRate(t0, t0 + dt, Compounding.Continuous).value()
- dividendYield_.link.forwardRate(t0, t0 + dt, Compounding.Continuous).value()
- 0.5 * vol * vol;
nu = kappa_ * (theta_ - vol * vol);
retVal[0] = x0[0] * Math.Exp(mu * dt + vol * dw[0] * sdt);
retVal[1] = x0[1] + nu * dt + vol2 * sdt * (rho_ * dw[0] + sqrhov * dw[1]);
break;
case Discretization.Reflection:
vol = Math.Sqrt(Math.Abs(x0[1]));
vol2 = sigma_ * vol;
mu = riskFreeRate_.link.forwardRate(t0, t0 + dt, Compounding.Continuous).value()
- dividendYield_.link.forwardRate(t0, t0 + dt, Compounding.Continuous).value()
- 0.5 * vol * vol;
nu = kappa_ * (theta_ - vol * vol);
retVal[0] = x0[0] * Math.Exp(mu * dt + vol * dw[0] * sdt);
retVal[1] = vol * vol
+ nu * dt + vol2 * sdt * (rho_ * dw[0] + sqrhov * dw[1]);
break;
case Discretization.NonCentralChiSquareVariance:
// use Alan Lewis trick to decorrelate the equity and the variance
// process by using y(t)=x(t)-\frac{rho}{sigma}\nu(t)
// and Ito's Lemma. Then use exact sampling for the variance
// process. For further details please read the Wilmott thread
// "QuantLib code is very high quality"
vol = (x0[1] > 0.0) ? Math.Sqrt(x0[1]) : 0.0;
mu = riskFreeRate_.link.forwardRate(t0, t0 + dt, Compounding.Continuous).value()
- dividendYield_.link.forwardRate(t0, t0 + dt, Compounding.Continuous).value()
- 0.5 * vol * vol;
retVal[1] = varianceDistribution(x0[1], dw[1], dt);
dy = (mu - rho_ / sigma_ * kappa_
* (theta_ - vol * vol)) * dt + vol * sqrhov * dw[0] * sdt;
retVal[0] = x0[0] * Math.Exp(dy + rho_ / sigma_ * (retVal[1] - x0[1]));
break;
case Discretization.QuadraticExponential:
case Discretization.QuadraticExponentialMartingale:
{
// for details of the quadratic exponential discretization scheme
// see Leif Andersen,
// Efficient Simulation of the Heston Stochastic Volatility Model
double ex = Math.Exp(-kappa_ * dt);
double m = theta_ + (x0[1] - theta_) * ex;
double s2 = x0[1] * sigma_ * sigma_ * ex / kappa_ * (1 - ex)
+ theta_ * sigma_ * sigma_ / (2 * kappa_) * (1 - ex) * (1 - ex);
double psi = s2 / (m * m);
double g1 = 0.5;
double g2 = 0.5;
double k0 = -rho_ * kappa_ * theta_ * dt / sigma_;
double k1 = g1 * dt * (kappa_ * rho_ / sigma_ - 0.5) - rho_ / sigma_;
double k2 = g2 * dt * (kappa_ * rho_ / sigma_ - 0.5) + rho_ / sigma_;
double k3 = g1 * dt * (1 - rho_ * rho_);
double k4 = g2 * dt * (1 - rho_ * rho_);
double A = k2 + 0.5 * k4;
if (psi < 1.5)
{
double b2 = 2 / psi - 1 + Math.Sqrt(2 / psi * (2 / psi - 1));
double b = Math.Sqrt(b2);
double a = m / (1 + b2);
if (discretization_ == Discretization.QuadraticExponentialMartingale)
{
// martingale correction
Utils.QL_REQUIRE(A < 1 / (2 * a), () => "illegal value");
k0 = -A * b2 * a / (1 - 2 * A * a) + 0.5 * Math.Log(1 - 2 * A * a)
- (k1 + 0.5 * k3) * x0[1];
}
retVal[1] = a * (b + dw[1]) * (b + dw[1]);
}
else
{
double p = (psi - 1) / (psi + 1);
double beta = (1 - p) / m;
double u = new CumulativeNormalDistribution().value(dw[1]);
if (discretization_ == Discretization.QuadraticExponentialMartingale)
{
// martingale correction
Utils.QL_REQUIRE(A < beta, () => "illegal value");
k0 = -Math.Log(p + beta * (1 - p) / (beta - A)) - (k1 + 0.5 * k3) * x0[1];
}
retVal[1] = ((u <= p) ? 0.0 : Math.Log((1 - p) / (1 - u)) / beta);
}
mu = riskFreeRate_.link.forwardRate(t0, t0 + dt, Compounding.Continuous).value()
- dividendYield_.link.forwardRate(t0, t0 + dt, Compounding.Continuous).value();
retVal[0] = x0[0] * Math.Exp(mu * dt + k0 + k1 * x0[1] + k2 * retVal[1]
+ Math.Sqrt(k3 * x0[1] + k4 * retVal[1]) * dw[0]);
}
break;
case Discretization.BroadieKayaExactSchemeLobatto:
case Discretization.BroadieKayaExactSchemeLaguerre:
case Discretization.BroadieKayaExactSchemeTrapezoidal:
{
double nu_0 = x0[1];
double nu_t = varianceDistribution(nu_0, dw[1], dt);
double x = Math.Min(1.0 - Const.QL_EPSILON,
Math.Max(0.0, new CumulativeNormalDistribution().value(dw[2])));
cdf_nu_ds f = new cdf_nu_ds(this, nu_0, nu_t, dt, discretization_);
double vds = new Brent().solve(f, 1e-5, -x, theta_ * dt, 0.1 * theta_ * dt);
//double vds = new Brent().solve( boost::lambda::bind(&cdf_nu_ds, *this, boost::lambda::_1,
// nu_0, nu_t, dt, discretization_)-x,
// 1e-5, theta_*dt, 0.1*theta_*dt);
double vdw = (nu_t - nu_0 - kappa_ * theta_ * dt + kappa_ * vds) / sigma_;
mu = (riskFreeRate_.link.forwardRate(t0, t0 + dt, Compounding.Continuous).value()
- dividendYield_.link.forwardRate(t0, t0 + dt, Compounding.Continuous).value()) * dt
- 0.5 * vds + rho_ * vdw;
double sig = Math.Sqrt((1 - rho_ * rho_) * vds);
double s = x0[0] * Math.Exp(mu + sig * dw[0]);
retVal[0] = s;
retVal[1] = nu_t;
}
break;
default:
Utils.QL_FAIL("unknown discretization schema");
break;
}
return(retVal);
}
public double MonthlyYield()
{
Brent solver = new Brent();
solver.setMaxEvaluations(100);
List<CashFlow> cf = expectedCashflows();
MonthlyYieldFinder objective = new MonthlyYieldFinder(notional(settlementDate()), cf, settlementDate());
return solver.solve(objective, 1.0e-10, 0.02, 0.0, 1.0) /100 ;
}
public override void calculate()
{
Utils.QL_REQUIRE(arguments_.settlementType == Settlement.Type.Physical, () =>
"cash-settled swaptions not priced by Jamshidian engine");
Utils.QL_REQUIRE(arguments_.exercise.type() == Exercise.Type.European, () =>
"cannot use the Jamshidian decomposition on exotic swaptions");
Utils.QL_REQUIRE(arguments_.swap.spread.IsEqual(0.0), () =>
"non zero spread (" + arguments_.swap.spread + ") not allowed");
Date referenceDate;
DayCounter dayCounter;
ITermStructureConsistentModel tsmodel = (ITermStructureConsistentModel)base.model_.link;
try
{
if (tsmodel != null)
{
referenceDate = tsmodel.termStructure().link.referenceDate();
dayCounter = tsmodel.termStructure().link.dayCounter();
}
else
{
referenceDate = termStructure_.link.referenceDate();
dayCounter = termStructure_.link.dayCounter();
}
}
catch
{
referenceDate = termStructure_.link.referenceDate();
dayCounter = termStructure_.link.dayCounter();
}
List <double> amounts = new InitializedList <double>(arguments_.fixedCoupons.Count);
for (int i = 0; i < amounts.Count; i++)
{
amounts[i] = arguments_.fixedCoupons[i];
}
amounts[amounts.Count - 1] = amounts.Last() + arguments_.nominal;
double maturity = dayCounter.yearFraction(referenceDate,
arguments_.exercise.date(0));
List <double> fixedPayTimes = new InitializedList <double>(arguments_.fixedPayDates.Count);
for (int i = 0; i < fixedPayTimes.Count; i++)
{
fixedPayTimes[i] =
dayCounter.yearFraction(referenceDate,
arguments_.fixedPayDates[i]);
}
rStarFinder finder = new rStarFinder(model_, arguments_.nominal, maturity,
fixedPayTimes, amounts);
Brent s1d = new Brent();
double minStrike = -10.0;
double maxStrike = 10.0;
s1d.setMaxEvaluations(10000);
s1d.setLowerBound(minStrike);
s1d.setUpperBound(maxStrike);
double rStar = s1d.solve(finder, 1e-8, 0.05, minStrike, maxStrike);
Option.Type w = arguments_.type == VanillaSwap.Type.Payer ?
Option.Type.Put : Option.Type.Call;
int size = arguments_.fixedCoupons.Count;
double value = 0.0;
for (int i = 0; i < size; i++)
{
double fixedPayTime =
dayCounter.yearFraction(referenceDate,
arguments_.fixedPayDates[i]);
double strike = model_.link.discountBond(maturity,
fixedPayTime,
rStar);
double dboValue = model_.link.discountBondOption(
w, strike, maturity,
fixedPayTime);
value += amounts[i] * dboValue;
}
results_.value = value;
}
//! implied Z-spread.
public static double zSpread(Leg leg, double npv, YieldTermStructure discount, DayCounter dayCounter, Compounding compounding,
Frequency frequency, bool includeSettlementDateFlows, Date settlementDate = null,
Date npvDate = null, double accuracy = 1.0e-10, int maxIterations = 100, double guess = 0.0)
{
if (settlementDate == null)
settlementDate = Settings.evaluationDate();
if (npvDate == null)
npvDate = settlementDate;
Brent solver = new Brent();
solver.setMaxEvaluations(maxIterations);
ZSpreadFinder objFunction = new ZSpreadFinder(leg,discount,npv,dayCounter, compounding, frequency,
includeSettlementDateFlows, settlementDate, npvDate);
double step = 0.01;
return solver.solve(objFunction, accuracy, guess, step);
}
public double value(double x)
{
// first find the right side of the interval
double upper = guess_;
int evaluations = maxEvaluations_;
while (nonCentralDist_.value(upper) < x && evaluations > 0) {
upper*=2.0;
--evaluations;
}
// use a brent solver for the rest
Brent solver = new Brent();
solver.setMaxEvaluations(evaluations);
/*return solver.solve(compose(std::bind2nd(std::minus<Real>(),x),
nonCentralDist_),
accuracy_, 0.75*upper,
(evaluations == maxEvaluations_)? 0.0: 0.5*upper,
upper);*/
return 0d;
}
