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*/
}
public InterpolatedSmileSection(Date d,
List <double> strikes,
List <Handle <Quote> > stdDevHandles,
Handle <Quote> atmLevel,
DayCounter dc = null, //Actual365Fixed(),
Interpolator interpolator = default(Interpolator),
Date referenceDate = null,
double shift = 0.0)
: base(d, dc, referenceDate, VolatilityType.ShiftedLognormal, shift)
{
exerciseTimeSquareRoot_ = Math.Sqrt(exerciseTime());
strikes_ = strikes;
stdDevHandles_ = stdDevHandles;
atmLevel_ = atmLevel;
vols_ = new InitializedList <double>(stdDevHandles.Count);
for (int i = 0; i < stdDevHandles_.Count; ++i)
{
stdDevHandles_[i].registerWith(update);
}
atmLevel_.registerWith(update);
// check strikes!!!!!!!!!!!!!!!!!!!!
interpolation_ = interpolator.interpolate(strikes_, strikes_.Count, vols_);
}
//! fixed reference date, fixed market data
public CapFloorTermVolCurve(Date settlementDate,
Calendar calendar,
BusinessDayConvention bdc,
List <Period> optionTenors,
List <double> vols,
DayCounter dc = null) // Actual365Fixed()
: base(settlementDate, calendar, bdc, dc ?? new Actual365Fixed())
{
nOptionTenors_ = optionTenors.Count;
optionTenors_ = optionTenors;
optionDates_ = new InitializedList <Date>(nOptionTenors_);
optionTimes_ = new InitializedList <double>(nOptionTenors_);
volHandles_ = new InitializedList <Handle <Quote> >(vols.Count);
vols_ = vols; // do not initialize with nOptionTenors_
checkInputs();
initializeOptionDatesAndTimes();
// fill dummy handles to allow generic handle-based computations later
for (int i = 0; i < nOptionTenors_; ++i)
{
volHandles_[i] = new Handle <Quote>(new SimpleQuote(vols_[i]));
}
interpolate();
}
public InterpolatedSmileSection(Date d,
List <double> strikes,
List <double> stdDevs,
double atmLevel,
DayCounter dc = null, // Actual365Fixed(),
Interpolator interpolator = default(Interpolator),
Date referenceDate = null,
double shift = 0.0)
: base(d, dc ?? new Actual365Fixed(), referenceDate, VolatilityType.ShiftedLognormal, shift)
{
strikes_ = strikes;
stdDevHandles_ = new InitializedList <Handle <Quote> >(stdDevs.Count);
vols_ = new InitializedList <double>(stdDevs.Count);
//fill dummy handles to allow generic handle-based
// computations later on
for (int i = 0; i < stdDevs.Count; ++i)
{
stdDevHandles_[i] = new Handle <Quote>(new SimpleQuote(stdDevs[i]));
}
atmLevel_ = new Handle <Quote>(new SimpleQuote(atmLevel));
// check strikes!!!!!!!!!!!!!!!!!!!!
interpolation_ = interpolator.interpolate(strikes_, strikes_.Count, vols_);
}
public InterpolatedSmileSection(double timeToExpiry,
List <double> strikes,
List <double> stdDevs,
double atmLevel,
Interpolator interpolator = default(Interpolator),
DayCounter dc = null, //Actual365Fixed(),
double shift = 0.0)
: base(timeToExpiry, dc, VolatilityType.ShiftedLognormal, shift)
{
exerciseTimeSquareRoot_ = Math.Sqrt(exerciseTime());
strikes_ = strikes;
stdDevHandles_ = new InitializedList <Handle <Quote> >(stdDevs.Count);
vols_ = new InitializedList <double>(stdDevs.Count);
// fill dummy handles to allow generic handle-based
// computations later on
for (int i = 0; i < stdDevs.Count; ++i)
{
stdDevHandles_[i] = new Handle <Quote>(new SimpleQuote(stdDevs[i]));
}
atmLevel_ = new Handle <Quote>(new SimpleQuote(atmLevel));
// check strikes!!!!!!!!!!!!!!!!!!!!
interpolation_ = interpolator.interpolate(strikes_, strikes_.Count, vols_);
}
// Multi leg constructor.
public Swap(List <List <CashFlow> > legs, List <bool> payer)
{
legs_ = (InitializedList <List <CashFlow> >)legs;
payer_ = new InitializedList <double>(legs.Count, 1.0);
legNPV_ = new InitializedList <double?>(legs.Count, 0.0);
legBPS_ = new InitializedList <double?>(legs.Count, 0.0);
startDiscounts_ = new InitializedList <double?>(legs.Count, 0.0);
endDiscounts_ = new InitializedList <double?>(legs.Count, 0.0);
npvDateDiscount_ = 0.0;
Utils.QL_REQUIRE(payer.Count == legs_.Count, () => "size mismatch between payer (" + payer.Count +
") and legs (" + legs_.Count + ")");
for (int i = 0; i < legs_.Count; ++i)
{
if (payer[i])
{
payer_[i] = -1;
}
for (int j = 0; j < legs_[i].Count; j++)
{
legs_[i][j].registerWith(update);
}
}
}
public Fj_Helper(Handle <PiecewiseTimeDependentHestonModel> model, double term, double strike, int j)
{
j_ = j;
term_ = term;
v0_ = model.link.v0();
x_ = Math.Log(model.link.s0());
sx_ = Math.Log(strike);
r_ = new InitializedList <double>(model.link.timeGrid().size() - 1);
q_ = new InitializedList <double>(model.link.timeGrid().size() - 1);
model_ = model;
timeGrid_ = model.link.timeGrid();
for (int i = 0; i < timeGrid_.size() - 1; ++i)
{
double begin = Math.Min(term_, timeGrid_[i]);
double end = Math.Min(term_, timeGrid_[i + 1]);
r_[i] = model.link.riskFreeRate().link.forwardRate(begin, end,
Compounding.Continuous, Frequency.NoFrequency).rate();
q_[i] = model.link.dividendYield().link.forwardRate(begin, end,
Compounding.Continuous, Frequency.NoFrequency).rate();
}
Utils.QL_REQUIRE(term_ < model_.link.timeGrid().Last(), () => "maturity is too large");
}
public override void fetchResults(IPricingEngineResults r)
{
base.fetchResults(r);
Swap.Results results = r as Swap.Results;
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);
}
if (results.legBPS.Count != 0)
{
if (results.legBPS.Count != legBPS_.Count)
{
throw new ArgumentException("wrong number of leg BPS returned");
}
legBPS_ = results.legBPS;
}
else
{
legBPS_ = new InitializedList <double?>(legBPS_.Count);
}
}
public override void calculate()
{
double value = 0.0;
double vega = 0.0;
int optionlets = arguments_.startDates.Count;
List <double> values = new InitializedList <double>(optionlets);
List <double> vegas = new InitializedList <double>(optionlets);
List <double> stdDevs = new InitializedList <double>(optionlets);
CapFloorType type = arguments_.type;
Date today = vol_.link.referenceDate();
Date settlement = discountCurve_.link.referenceDate();
for (int i = 0; i < optionlets; ++i)
{
Date paymentDate = arguments_.endDates[i];
if (paymentDate > settlement)
{
// discard expired caplets
double d = arguments_.nominals[i] *
arguments_.gearings[i] *
discountCurve_.link.discount(paymentDate) *
arguments_.accrualTimes[i];
double?forward = arguments_.forwards[i];
Date fixingDate = arguments_.fixingDates[i];
double sqrtTime = 0.0;
if (fixingDate > today)
{
sqrtTime = Math.Sqrt(vol_.link.timeFromReference(fixingDate));
}
if (type == CapFloorType.Cap || type == CapFloorType.Collar)
{
double?strike = arguments_.capRates[i];
if (sqrtTime > 0.0)
{
stdDevs[i] = Math.Sqrt(vol_.link.blackVariance(fixingDate, strike.Value));
vegas[i] = Utils.blackFormulaStdDevDerivative(strike.Value, forward.Value, stdDevs[i], d, displacement_) * sqrtTime;
}
// include caplets with past fixing date
values[i] = Utils.blackFormula(Option.Type.Call, strike.Value,
forward.Value, stdDevs[i], d, displacement_);
}
if (type == CapFloorType.Floor || type == CapFloorType.Collar)
{
double?strike = arguments_.floorRates[i];
double floorletVega = 0.0;
if (sqrtTime > 0.0)
{
stdDevs[i] = Math.Sqrt(vol_.link.blackVariance(fixingDate, strike.Value));
floorletVega = Utils.blackFormulaStdDevDerivative(strike.Value, forward.Value, stdDevs[i], d, displacement_) * sqrtTime;
}
double floorlet = Utils.blackFormula(Option.Type.Put, strike.Value,
forward.Value, stdDevs[i], d, displacement_);
if (type == CapFloorType.Floor)
{
values[i] = floorlet;
vegas[i] = floorletVega;
}
else
{
// a collar is long a cap and short a floor
values[i] -= floorlet;
vegas[i] -= floorletVega;
}
}
value += values[i];
vega += vegas[i];
}
}
results_.value = value;
results_.additionalResults["vega"] = vega;
results_.additionalResults["optionletsPrice"] = values;
results_.additionalResults["optionletsVega"] = vegas;
results_.additionalResults["optionletsAtmForward"] = arguments_.forwards;
if (type != CapFloorType.Collar)
{
results_.additionalResults["optionletsStdDev"] = stdDevs;
}
}
public SobolRsg(int dimensionality, ulong seed, DirectionIntegers directionIntegers)
{
dimensionality_ = dimensionality;
sequenceCounter_ = 0;
firstDraw_ = true;
sequence_ = new Sample <List <double> >(new InitializedList <double>(dimensionality), 1.0);
integerSequence_ = new InitializedList <ulong>(dimensionality);
directionIntegers_ = new InitializedList <List <ulong> >(dimensionality);
for (int i = 0; i < dimensionality; i++)
{
directionIntegers_[i] = new InitializedList <ulong>(bits_);
}
if (!(dimensionality > 0))
{
throw new Exception("dimensionality must be greater than 0");
}
if (!(dimensionality <= PPMT_MAX_DIM))
{
throw new Exception("dimensionality " + dimensionality + " exceeds the number of available "
+ "primitive polynomials modulo two (" + PPMT_MAX_DIM + ")");
}
// initializes coefficient array of the k-th primitive polynomial
// and degree of the k-th primitive polynomial
List <uint> degree = new InitializedList <uint>(dimensionality_);
List <long> ppmt = new InitializedList <long>(dimensionality_);
bool useAltPolynomials = false;
if (directionIntegers == DirectionIntegers.Kuo || directionIntegers == DirectionIntegers.Kuo2 ||
directionIntegers == DirectionIntegers.Kuo3 || directionIntegers == DirectionIntegers.SobolLevitan ||
directionIntegers == DirectionIntegers.SobolLevitanLemieux)
{
useAltPolynomials = true;
}
// degree 0 is not used
ppmt[0] = 0;
degree[0] = 0;
int k, index;
uint currentDegree = 1;
k = 1;
index = 0;
uint altDegree = useAltPolynomials ? maxAltDegree : 0;
for ( ; k < Math.Min(dimensionality_, altDegree); k++, index++)
{
ppmt[k] = AltPrimitivePolynomials[currentDegree - 1][index];
if (ppmt[k] == -1)
{
++currentDegree;
index = 0;
ppmt[k] = AltPrimitivePolynomials[currentDegree - 1][index];
}
degree[k] = currentDegree;
}
for ( ; k < dimensionality_; k++, index++)
{
ppmt[k] = PrimitivePolynomials[currentDegree - 1][index];
if (ppmt[k] == -1)
{
++currentDegree;
index = 0;
ppmt[k] = PrimitivePolynomials[currentDegree - 1][index];
}
degree[k] = currentDegree;
}
// initializes bits_ direction integers for each dimension
// and store them into directionIntegers_[dimensionality_][bits_]
//
// In each dimension k with its associated primitive polynomial,
// the first degree_[k] direction integers can be chosen freely
// provided that only the l leftmost bits can be non-zero, and
// that the l-th leftmost bit must be set
// degenerate (no free direction integers) first dimension
int j;
for (j = 0; j < bits_; j++)
{
directionIntegers_[0][j] = (1UL << (bits_ - j - 1));
}
int maxTabulated = 0;
// dimensions from 2 (k=1) to maxTabulated (k=maxTabulated-1) included
// are initialized from tabulated coefficients
switch (directionIntegers)
{
case DirectionIntegers.Unit:
maxTabulated = dimensionality_;
for (k = 1; k < maxTabulated; k++)
{
for (int l = 1; l <= degree[k]; l++)
{
directionIntegers_[k][l - 1] = 1UL;
directionIntegers_[k][l - 1] <<= (bits_ - l);
}
}
break;
case DirectionIntegers.Jaeckel:
// maxTabulated=32
maxTabulated = initializers.Length + 1;
for (k = 1; k < Math.Min(dimensionality_, maxTabulated); k++)
{
j = 0;
// 0UL marks coefficients' end for a given dimension
while (initializers[k - 1][j] != 0UL)
{
directionIntegers_[k][j] = initializers[k - 1][j];
directionIntegers_[k][j] <<= (bits_ - j - 1);
j++;
}
}
break;
case DirectionIntegers.SobolLevitan:
// maxTabulated=40
maxTabulated = SLinitializers.Length + 1;
for (k = 1; k < Math.Min(dimensionality_, maxTabulated); k++)
{
j = 0;
// 0UL marks coefficients' end for a given dimension
while (SLinitializers[k - 1][j] != 0UL)
{
directionIntegers_[k][j] = SLinitializers[k - 1][j];
directionIntegers_[k][j] <<= (bits_ - j - 1);
j++;
}
}
break;
case DirectionIntegers.SobolLevitanLemieux:
// maxTabulated=360
maxTabulated = Linitializers.Length + 1;
for (k = 1; k < Math.Min(dimensionality_, maxTabulated); k++)
{
j = 0;
// 0UL marks coefficients' end for a given dimension
while (Linitializers[k - 1][j] != 0UL)
{
directionIntegers_[k][j] = Linitializers[k - 1][j];
directionIntegers_[k][j] <<= (bits_ - j - 1);
j++;
}
}
break;
case DirectionIntegers.JoeKuoD5:
// maxTabulated=1898
maxTabulated = JoeKuoD5initializers.Length + 1;
for (k = 1; k < Math.Min(dimensionality_, maxTabulated); k++)
{
j = 0;
// 0UL marks coefficients' end for a given dimension
while (JoeKuoD5initializers[k - 1][j] != 0UL)
{
directionIntegers_[k][j] = JoeKuoD5initializers[k - 1][j];
directionIntegers_[k][j] <<= (bits_ - j - 1);
j++;
}
}
break;
case DirectionIntegers.JoeKuoD6:
// maxTabulated=1799
maxTabulated = JoeKuoD6initializers.Length + 1;
for (k = 1; k < Math.Min(dimensionality_, maxTabulated); k++)
{
j = 0;
// 0UL marks coefficients' end for a given dimension
while (JoeKuoD6initializers[k - 1][j] != 0UL)
{
directionIntegers_[k][j] = JoeKuoD6initializers[k - 1][j];
directionIntegers_[k][j] <<= (bits_ - j - 1);
j++;
}
}
break;
case DirectionIntegers.JoeKuoD7:
// maxTabulated=1898
maxTabulated = JoeKuoD7initializers.Length + 1;
for (k = 1; k < Math.Min(dimensionality_, maxTabulated); k++)
{
j = 0;
// 0UL marks coefficients' end for a given dimension
while (JoeKuoD7initializers[k - 1][j] != 0UL)
{
directionIntegers_[k][j] = JoeKuoD7initializers[k - 1][j];
directionIntegers_[k][j] <<= (bits_ - j - 1);
j++;
}
}
break;
case DirectionIntegers.Kuo:
// maxTabulated=4925
maxTabulated = Kuoinitializers.Length + 1;
for (k = 1; k < Math.Min(dimensionality_, maxTabulated); k++)
{
j = 0;
// 0UL marks coefficients' end for a given dimension
while (Kuoinitializers[k - 1][j] != 0UL)
{
directionIntegers_[k][j] = Kuoinitializers[k - 1][j];
directionIntegers_[k][j] <<= (bits_ - j - 1);
j++;
}
}
break;
case DirectionIntegers.Kuo2:
// maxTabulated=3946
maxTabulated = Kuo2initializers.Length + 1;
for (k = 1; k < Math.Min(dimensionality_, maxTabulated); k++)
{
j = 0;
// 0UL marks coefficients' end for a given dimension
while (Kuo2initializers[k - 1][j] != 0UL)
{
directionIntegers_[k][j] = Kuo2initializers[k - 1][j];
directionIntegers_[k][j] <<= (bits_ - j - 1);
j++;
}
}
break;
case DirectionIntegers.Kuo3:
// maxTabulated=4585
maxTabulated = Kuo3initializers.Length + 1;
for (k = 1; k < Math.Min(dimensionality_, maxTabulated); k++)
{
j = 0;
// 0UL marks coefficients' end for a given dimension
while (Kuo3initializers[k - 1][j] != 0UL)
{
directionIntegers_[k][j] = Kuo3initializers[k - 1][j];
directionIntegers_[k][j] <<= (bits_ - j - 1);
j++;
}
}
break;
default:
break;
}
// random initialization for higher dimensions
if (dimensionality_ > maxTabulated)
{
MersenneTwisterUniformRng uniformRng = new MersenneTwisterUniformRng(seed);
for (k = maxTabulated; k < dimensionality_; k++)
{
for (int l = 1; l <= degree[k]; l++)
{
do
{
// u is in (0,1)
double u = uniformRng.next().value;
// the direction integer has at most the
// rightmost l bits non-zero
directionIntegers_[k][l - 1] = (ulong)(u * (1UL << l));
} while (!((directionIntegers_[k][l - 1] & 1UL) != 0));
// iterate until the direction integer is odd
// that is it has the rightmost bit set
// shifting bits_-l bits to the left
// we are guaranteed that the l-th leftmost bit
// is set, and only the first l leftmost bit
// can be non-zero
directionIntegers_[k][l - 1] <<= (bits_ - l);
}
}
}
// computation of directionIntegers_[k][l] for l>=degree_[k]
// by recurrence relation
for (k = 1; k < dimensionality_; k++)
{
uint gk = degree[k];
for (int l = (int)gk; l < bits_; l++)
{
// eq. 8.19 "Monte Carlo Methods in Finance" by P. Jдckel
ulong n = (directionIntegers_[k][(int)(l - gk)] >> (int)gk);
// a[k][j] are the coefficients of the monomials in ppmt[k]
// The highest order coefficient a[k][0] is not actually
// used in the recurrence relation, and the lowest order
// coefficient a[k][gk] is always set: this is the reason
// why the highest and lowest coefficient of
// the polynomial ppmt[k] are not included in its encoding,
// provided that its degree is known.
// That is: a[k][j] = ppmt[k] >> (gk-j-1)
for (uint z = 1; z < gk; z++)
{
// XORed with a selection of (unshifted) direction
// integers controlled by which of the a[k][j] are set
if ((((ulong)ppmt[k] >> (int)(gk - z - 1)) & 1UL) != 0)
{
n ^= directionIntegers_[k][(int)(l - z)];
}
}
// a[k][gk] is always set, so directionIntegers_[k][l-gk]
// will always enter
n ^= directionIntegers_[k][(int)(l - gk)];
directionIntegers_[k][l] = n;
}
}
// in case one needs to check the directionIntegers used
/* bool printDirectionIntegers = false;
* if (printDirectionIntegers) {
* std::ofstream outStream("directionIntegers.txt");
* for (k=0; k<std::min(32UL,dimensionality_); k++) {
* outStream << std::endl << k+1 << "\t"
* << degree[k] << "\t"
* << ppmt[k] << "\t";
* for (j=0; j<10; j++) {
* outStream << io::power_of_two(
* directionIntegers_[k][j]) << "\t";
* }
* }
* outStream.close();
* }
*/
// initialize the Sobol integer/double vectors
// first draw
for (k = 0; k < dimensionality_; k++)
{
integerSequence_[k] = directionIntegers_[k][0];
}
}
public MersenneTwisterUniformRng(ulong seed)
{
mt = new InitializedList <ulong>(N);
seedInitialization(seed);
}
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;
}
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;
}
public void recalibration(double beta, Period swapTenor)
{
List <double> betaVector = new InitializedList <double>(nOptionTenors_, beta);
recalibration(betaVector, swapTenor);
}
public override void update()
{
sectionHelpers_.Clear();
if (size_ == 2) //single period
{
ISectionHelper singleHelper = new EverywhereConstantHelper(yBegin_[1], 0.0, xBegin_[0]);
sectionHelpers_.Add(xBegin_[1], singleHelper);
extrapolationHelper_ = singleHelper;
return;
}
List <double> f = new InitializedList <double>(size_);
sectionHelpers_ = new Dictionary <double, ISectionHelper>(preSectionHelpers_);
int startPoint = sectionHelpers_.Count + 1;
//first derive the boundary forwards.
for (int i = startPoint; i < size_ - 1; ++i)
{
double dxPrev = xBegin_[i] - xBegin_[i - 1];
double dx = xBegin_[i + 1] - xBegin_[i];
f[i] = dxPrev / (dx + dxPrev) * yBegin_[i]
+ dx / (dx + dxPrev) * yBegin_[i + 1];
}
if (startPoint > 1)
{
f[startPoint - 1] = preSectionHelpers_.Last().Value.fNext();
}
if (startPoint == 1)
{
f[0] = 1.5 * yBegin_[1] - 0.5 * f[1];
}
f[size_ - 1] = 1.5 * yBegin_[size_ - 1] - 0.5 * f[size_ - 2];
if (forcePositive_)
{
if (f[0] < 0)
{
f[0] = 0.0;
}
if (f[size_ - 1] < 0.0)
{
f[size_ - 1] = 0.0;
}
}
double primitive = 0.0;
for (int i = 0; i < startPoint - 1; ++i)
{
primitive += yBegin_[i + 1] * (xBegin_[i + 1] - xBegin_[i]);
}
int endPoint = size_;
//constantLastPeriod_ = false;
if (constantLastPeriod_)
{
endPoint = endPoint - 1;
}
for (int i = startPoint; i < endPoint; ++i)
{
double gPrev = f[i - 1] - yBegin_[i];
double gNext = f[i] - yBegin_[i];
//first deal with the zero gradient case
if (Math.Abs(gPrev) < 1.0E-14 && Math.Abs(gNext) < 1.0E-14)
{
ISectionHelper singleHelper = new ConstantGradHelper(f[i - 1], primitive,
xBegin_[i - 1],
xBegin_[i],
f[i]);
sectionHelpers_.Add(xBegin_[i], singleHelper);
}
else
{
double quadraticity = quadraticity_;
ISectionHelper quadraticHelper = null;
ISectionHelper convMonotoneHelper = null;
if (quadraticity_ > 0.0)
{
if (gPrev >= -2.0 * gNext && gPrev > -0.5 * gNext && forcePositive_)
{
quadraticHelper = new QuadraticMinHelper(xBegin_[i - 1],
xBegin_[i],
f[i - 1], f[i],
yBegin_[i],
primitive);
}
else
{
quadraticHelper = new QuadraticHelper(xBegin_[i - 1],
xBegin_[i],
f[i - 1], f[i],
yBegin_[i],
primitive);
}
}
if (quadraticity_ < 1.0)
{
if ((gPrev > 0.0 && -0.5 * gPrev >= gNext && gNext >= -2.0 * gPrev) ||
(gPrev < 0.0 && -0.5 * gPrev <= gNext && gNext <= -2.0 * gPrev))
{
quadraticity = 1.0;
if (quadraticity_ == 0)
{
if (forcePositive_)
{
quadraticHelper = new QuadraticMinHelper(
xBegin_[i - 1],
xBegin_[i],
f[i - 1], f[i],
yBegin_[i],
primitive);
}
else
{
quadraticHelper = new QuadraticHelper(
xBegin_[i - 1],
xBegin_[i],
f[i - 1], f[i],
yBegin_[i],
primitive);
}
}
}
else if ((gPrev < 0.0 && gNext > -2.0 * gPrev) ||
(gPrev > 0.0 && gNext < -2.0 * gPrev))
{
double eta = (gNext + 2.0 * gPrev) / (gNext - gPrev);
double b2 = (1.0 + monotonicity_) / 2.0;
if (eta < b2)
{
convMonotoneHelper = new ConvexMonotone2Helper(
xBegin_[i - 1],
xBegin_[i],
gPrev, gNext,
yBegin_[i],
eta, primitive);
}
else
{
if (forcePositive_)
{
convMonotoneHelper = new ConvexMonotone4MinHelper(
xBegin_[i - 1],
xBegin_[i],
gPrev, gNext,
yBegin_[i],
b2, primitive);
}
else
{
convMonotoneHelper = new ConvexMonotone4Helper(
xBegin_[i - 1],
xBegin_[i],
gPrev, gNext,
yBegin_[i],
b2, primitive);
}
}
}
else if ((gPrev > 0.0 && gNext < 0.0 && gNext > -0.5 * gPrev) ||
(gPrev < 0.0 && gNext > 0.0 && gNext < -0.5 * gPrev))
{
double eta = gNext / (gNext - gPrev) * 3.0;
double b3 = (1.0 - monotonicity_) / 2.0;
if (eta > b3)
{
convMonotoneHelper = new ConvexMonotone3Helper(
xBegin_[i - 1],
xBegin_[i],
gPrev, gNext,
yBegin_[i],
eta, primitive);
}
else
{
if (forcePositive_)
{
convMonotoneHelper = new ConvexMonotone4MinHelper(
xBegin_[i - 1],
xBegin_[i],
gPrev, gNext,
yBegin_[i],
b3, primitive);
}
else
{
convMonotoneHelper = new ConvexMonotone4Helper(
xBegin_[i - 1],
xBegin_[i],
gPrev, gNext,
yBegin_[i],
b3, primitive);
}
}
}
else
{
double eta = gNext / (gPrev + gNext);
double b2 = (1.0 + monotonicity_) / 2.0;
double b3 = (1.0 - monotonicity_) / 2.0;
if (eta > b2)
{
eta = b2;
}
if (eta < b3)
{
eta = b3;
}
if (forcePositive_)
{
convMonotoneHelper = new ConvexMonotone4MinHelper(
xBegin_[i - 1],
xBegin_[i],
gPrev, gNext,
yBegin_[i],
eta, primitive);
}
else
{
convMonotoneHelper = new ConvexMonotone4Helper(
xBegin_[i - 1],
xBegin_[i],
gPrev, gNext,
yBegin_[i],
eta, primitive);
}
}
}
if (quadraticity == 1.0)
{
sectionHelpers_.Add(xBegin_[i], quadraticHelper);
}
else if (quadraticity == 0.0)
{
sectionHelpers_.Add(xBegin_[i], convMonotoneHelper);
}
else
{
sectionHelpers_.Add(xBegin_[i], new ComboHelper(quadraticHelper, convMonotoneHelper, quadraticity));
}
}
primitive += yBegin_[i] * (xBegin_[i] - xBegin_[i - 1]);
}
if (constantLastPeriod_)
{
sectionHelpers_.Add(xBegin_[size_ - 1], new EverywhereConstantHelper(yBegin_[size_ - 1], primitive, xBegin_[size_ - 2]));
extrapolationHelper_ = sectionHelpers_[xBegin_[size_ - 1]];
}
else
{
extrapolationHelper_ = new EverywhereConstantHelper((sectionHelpers_.Last()).Value.value(xBegin_.Last()),
primitive, xBegin_.Last());
}
}
public FdmLinearOpIterator(List <int> dim)
{
index_ = 0;
dim_ = dim;
coordinates_ = new InitializedList <int>(dim.Count, 0);
}
public override EndCriteria.Type minimize(Problem P, EndCriteria endCriteria)
{
// set up of the problem
//double ftol = endCriteria.functionEpsilon(); // end criteria on f(x) (see Numerical Recipes in C++, p.410)
double xtol = endCriteria.rootEpsilon(); // end criteria on x (see GSL v. 1.9, http://www.gnu.org/software/gsl/)
int maxStationaryStateIterations_ = endCriteria.maxStationaryStateIterations();
EndCriteria.Type ecType = EndCriteria.Type.None;
P.reset();
Vector x_ = P.currentValue();
int iterationNumber_ = 0;
// Initialize vertices of the simplex
bool end = false;
int n = x_.Count;
vertices_ = new InitializedList <Vector>(n + 1, x_);
for (int i = 0; i < n; i++)
{
Vector direction = new Vector(n, 0.0);
Vector vertice = vertices_[i + 1];
direction[i] = 1.0;
P.constraint().update(ref vertice, direction, lambda_);
vertices_[i + 1] = vertice;
}
// Initialize function values at the vertices of the simplex
values_ = new Vector(n + 1, 0.0);
for (int i = 0; i <= n; i++)
{
values_[i] = P.value(vertices_[i]);
}
// Loop looking for minimum
do
{
sum_ = new Vector(n, 0.0);
for (int i = 0; i <= n; i++)
{
sum_ += vertices_[i];
}
// Determine the best (iLowest), worst (iHighest)
// and 2nd worst (iNextHighest) vertices
int iLowest = 0;
int iHighest;
int iNextHighest;
if (values_[0] < values_[1])
{
iHighest = 1;
iNextHighest = 0;
}
else
{
iHighest = 0;
iNextHighest = 1;
}
for (int i = 1; i <= n; i++)
{
if (values_[i] > values_[iHighest])
{
iNextHighest = iHighest;
iHighest = i;
}
else
{
if ((values_[i] > values_[iNextHighest]) && i != iHighest)
{
iNextHighest = i;
}
}
if (values_[i] < values_[iLowest])
{
iLowest = i;
}
}
// Now compute accuracy, update iteration number and check end criteria
//// Numerical Recipes exit strategy on fx (see NR in C++, p.410)
//double low = values_[iLowest];
//double high = values_[iHighest];
//double rtol = 2.0*std::fabs(high - low)/
// (std::fabs(high) + std::fabs(low) + QL_EPSILON);
//++iterationNumber_;
//if (rtol < ftol ||
// endCriteria.checkMaxIterations(iterationNumber_, ecType)) {
// GSL exit strategy on x (see GSL v. 1.9, http://www.gnu.org/software/gsl
double simplexSize = Utils.computeSimplexSize(vertices_);
++iterationNumber_;
if (simplexSize < xtol || endCriteria.checkMaxIterations(iterationNumber_, ref ecType))
{
endCriteria.checkStationaryPoint(0.0, 0.0, ref maxStationaryStateIterations_, ref ecType);
endCriteria.checkMaxIterations(iterationNumber_, ref ecType);
x_ = vertices_[iLowest];
double low = values_[iLowest];
P.setFunctionValue(low);
P.setCurrentValue(x_);
return(ecType);
}
// If end criteria is not met, continue
double factor = -1.0;
double vTry = extrapolate(ref P, iHighest, ref factor);
if ((vTry <= values_[iLowest]) && (factor == -1.0))
{
factor = 2.0;
extrapolate(ref P, iHighest, ref factor);
}
else if (Math.Abs(factor) > Const.QL_EPSILON)
{
if (vTry >= values_[iNextHighest])
{
double vSave = values_[iHighest];
factor = 0.5;
vTry = extrapolate(ref P, iHighest, ref factor);
if (vTry >= vSave && Math.Abs(factor) > Const.QL_EPSILON)
{
for (int i = 0; i <= n; i++)
{
if (i != iLowest)
{
#if QL_ARRAY_EXPRESSIONS
vertices_[i] = 0.5 * (vertices_[i] + vertices_[iLowest]);
#else
vertices_[i] += vertices_[iLowest];
vertices_[i] *= 0.5;
#endif
values_[i] = P.value(vertices_[i]);
}
}
}
}
}
// If can't extrapolate given the constraints, exit
if (Math.Abs(factor) <= Const.QL_EPSILON)
{
x_ = vertices_[iLowest];
double low = values_[iLowest];
P.setFunctionValue(low);
P.setCurrentValue(x_);
return(EndCriteria.Type.StationaryFunctionValue);
}
} while (end == false);
throw new Exception("optimization failed: unexpected behaviour");
}
public override void calculate()
{
// copy black version then adapt to others
double value = 0.0;
int optionlets = arguments_.startDates.Count;
List <double> values = new InitializedList <double>(optionlets, 0.0);
List <double> stdDevs = new InitializedList <double>(optionlets, 0.0);
List <double> forwards = new InitializedList <double> (optionlets, 0.0);
CapFloorType type = arguments_.type;
Handle <YoYInflationTermStructure> yoyTS
= index().yoyInflationTermStructure();
Handle <YieldTermStructure> nominalTS
= yoyTS.link.nominalTermStructure();
Date settlement = nominalTS.link.referenceDate();
for (int i = 0; i < optionlets; ++i)
{
Date paymentDate = arguments_.payDates[i];
if (paymentDate > settlement)
{
// discard expired caplets
double d = arguments_.nominals[i] *
arguments_.gearings[i] *
nominalTS.link.discount(paymentDate) *
arguments_.accrualTimes[i];
// We explicitly have the index and assume that
// the fixing is natural, i.e. no convexity adjustment.
// If that was required then we would also need
// nominal vols in the pricing engine, i.e. a different engine.
// This also means that we do not need the coupon to have
// a pricing engine to return the swaplet rate and then
// the adjusted fixing in the instrument.
forwards[i] = yoyTS.link.yoyRate(arguments_.fixingDates[i], new Period(0, TimeUnit.Days));
double forward = forwards[i];
Date fixingDate = arguments_.fixingDates[i];
double sqrtTime = 0.0;
if (fixingDate > volatility_.link.baseDate())
{
sqrtTime = Math.Sqrt(volatility_.link.timeFromBase(fixingDate));
}
if (type == CapFloorType.Cap || type == CapFloorType.Collar)
{
double strike = arguments_.capRates[i].Value;
if (sqrtTime > 0.0)
{
stdDevs[i] = Math.Sqrt(volatility_.link.totalVariance(fixingDate, strike, new Period(0, TimeUnit.Days)));
}
// sttDev=0 for already-fixed dates so everything on forward
values[i] = optionletImpl(Option.Type.Call, strike, forward, stdDevs[i], d);
}
if (type == CapFloorType.Floor || type == CapFloorType.Collar)
{
double strike = arguments_.floorRates[i].Value;
if (sqrtTime > 0.0)
{
stdDevs[i] = Math.Sqrt(volatility_.link.totalVariance(fixingDate, strike, new Period(0, TimeUnit.Days)));
}
double floorlet = optionletImpl(Option.Type.Put, strike, forward, stdDevs[i], d);
if (type == CapFloorType.Floor)
{
values[i] = floorlet;
}
else
{
// a collar is long a cap and short a floor
values[i] -= floorlet;
}
}
value += values[i];
}
}
results_.value = value;
results_.additionalResults["optionletsPrice"] = values;
results_.additionalResults["optionletsAtmForward"] = forwards;
if (type != CapFloorType.Collar)
{
results_.additionalResults["optionletsStdDev"] = stdDevs;
}
}
protected List <double> spreadVolInterpolation(Date atmOptionDate, Period atmSwapTenor)
{
double atmOptionTime = timeFromReference(atmOptionDate);
double atmTimeLength = swapLength(atmSwapTenor);
List <double> result = new List <double>();
List <double> optionTimes = sparseParameters_.optionTimes();
List <double> swapLengths = sparseParameters_.swapLengths();
List <Date> optionDates = sparseParameters_.optionDates();
List <Period> swapTenors = sparseParameters_.swapTenors();
double optionTimesPreviousNode, swapLengthsPreviousNode;
optionTimesPreviousNode = optionTimes_.First(x => x >= atmOptionTime);
int optionTimesPreviousIndex = optionTimes_.IndexOf(optionTimesPreviousNode);
swapLengthsPreviousNode = swapLengths_.First(x => x >= atmTimeLength);
int swapLengthsPreviousIndex = swapLengths_.IndexOf(swapLengthsPreviousNode);
if (optionTimesPreviousIndex > 0)
{
optionTimesPreviousIndex--;
}
if (swapLengthsPreviousIndex > 0)
{
swapLengthsPreviousIndex--;
}
List <List <SmileSection> > smiles = new List <List <SmileSection> >();
List <SmileSection> smilesOnPreviousExpiry = new List <SmileSection>();
List <SmileSection> smilesOnNextExpiry = new List <SmileSection>();
Utils.QL_REQUIRE(optionTimesPreviousIndex + 1 < sparseSmiles_.Count, () =>
"optionTimesPreviousIndex+1 >= sparseSmiles_.size()");
Utils.QL_REQUIRE(swapLengthsPreviousIndex + 1 < sparseSmiles_[0].Count, () =>
"swapLengthsPreviousIndex+1 >= sparseSmiles_[0].size()");
smilesOnPreviousExpiry.Add(sparseSmiles_[optionTimesPreviousIndex][swapLengthsPreviousIndex]);
smilesOnPreviousExpiry.Add(sparseSmiles_[optionTimesPreviousIndex][swapLengthsPreviousIndex + 1]);
smilesOnNextExpiry.Add(sparseSmiles_[optionTimesPreviousIndex + 1][swapLengthsPreviousIndex]);
smilesOnNextExpiry.Add(sparseSmiles_[optionTimesPreviousIndex + 1][swapLengthsPreviousIndex + 1]);
smiles.Add(smilesOnPreviousExpiry);
smiles.Add(smilesOnNextExpiry);
List <double> optionsNodes = new InitializedList <double>(2);
optionsNodes[0] = optionTimes[optionTimesPreviousIndex];
optionsNodes[1] = optionTimes[optionTimesPreviousIndex + 1];
List <Date> optionsDateNodes = new InitializedList <Date>(2);
optionsDateNodes[0] = optionDates[optionTimesPreviousIndex];
optionsDateNodes[1] = optionDates[optionTimesPreviousIndex + 1];
List <double> swapLengthsNodes = new InitializedList <double>(2);
swapLengthsNodes[0] = swapLengths[swapLengthsPreviousIndex];
swapLengthsNodes[1] = swapLengths[swapLengthsPreviousIndex + 1];
List <Period> swapTenorNodes = new InitializedList <Period>(2);
swapTenorNodes[0] = swapTenors[swapLengthsPreviousIndex];
swapTenorNodes[1] = swapTenors[swapLengthsPreviousIndex + 1];
double atmForward = atmStrike(atmOptionDate, atmSwapTenor);
double shift = atmVol_.link.shift(atmOptionTime, atmTimeLength);
Matrix atmForwards = new Matrix(2, 2, 0.0);
Matrix atmShifts = new Matrix(2, 2, 0.0);
Matrix atmVols = new Matrix(2, 2, 0.0);
for (int i = 0; i < 2; i++)
{
for (int j = 0; j < 2; j++)
{
atmForwards[i, j] = atmStrike(optionsDateNodes[i], swapTenorNodes[j]);
atmShifts[i, j] = atmVol_.link.shift(optionsNodes[i], swapLengthsNodes[j]);
atmVols[i, j] = atmVol_.link.volatility(optionsDateNodes[i], swapTenorNodes[j], atmForwards[i, j]);
/* With the old implementation the interpolated spreads on ATM
* volatilities were null even if the spreads on ATM volatilities to be
* interpolated were non-zero. The new implementation removes
* this behaviour, but introduces a small ERROR in the cube:
* even if no spreads are applied on any cube ATM volatility corresponding
* to quoted smile sections (that is ATM volatilities in sparse cube), the
* cube ATM volatilities corresponding to not quoted smile sections (that
* is ATM volatilities in dense cube) are no more exactly the quoted values,
* but that ones PLUS the linear interpolation of the fit errors on the ATM
* volatilities in sparse cube whose spreads are used in the calculation.
* A similar imprecision is introduced to the volatilities in dense cube
* whith moneyness near to 1.
* (See below how spreadVols are calculated).
* The extent of this error depends on the quality of the fit: in case of
* good fits it is negligibile.
*/
}
}
for (int k = 0; k < nStrikes_; k++)
{
double strike = Math.Max(atmForward + strikeSpreads_[k], cutoffStrike_ - shift);
double moneyness = (atmForward + shift) / (strike + shift);
Matrix strikes = new Matrix(2, 2, 0.0);
Matrix spreadVols = new Matrix(2, 2, 0.0);
for (int i = 0; i < 2; i++)
{
for (int j = 0; j < 2; j++)
{
strikes[i, j] = (atmForwards[i, j] + atmShifts[i, j]) / moneyness - atmShifts[i, j];
spreadVols[i, j] = smiles[i][j].volatility(strikes[i, j]) - atmVols[i, j];
}
}
Cube localInterpolator = new Cube(optionsDateNodes, swapTenorNodes, optionsNodes, swapLengthsNodes, 1);
localInterpolator.setLayer(0, spreadVols);
localInterpolator.updateInterpolators();
result.Add(localInterpolator.value(atmOptionTime, atmTimeLength)[0]);
}
return(result);
}
protected Cube sabrCalibration(Cube marketVolCube)
{
List <double> optionTimes = marketVolCube.optionTimes();
List <double> swapLengths = marketVolCube.swapLengths();
List <Date> optionDates = marketVolCube.optionDates();
List <Period> swapTenors = marketVolCube.swapTenors();
Matrix alphas = new Matrix(optionTimes.Count, swapLengths.Count, 0.0);
Matrix betas = new Matrix(alphas);
Matrix nus = new Matrix(alphas);
Matrix rhos = new Matrix(alphas);
Matrix forwards = new Matrix(alphas);
Matrix errors = new Matrix(alphas);
Matrix maxErrors = new Matrix(alphas);
Matrix endCriteria = new Matrix(alphas);
List <Matrix> tmpMarketVolCube = marketVolCube.points();
List <double> strikes = new InitializedList <double>(strikeSpreads_.Count);
List <double> volatilities = new InitializedList <double>(strikeSpreads_.Count);
for (int j = 0; j < optionTimes.Count; j++)
{
for (int k = 0; k < swapLengths.Count; k++)
{
double atmForward = atmStrike(optionDates[j], swapTenors[k]);
double shiftTmp = atmVol_.link.shift(optionTimes[j], swapLengths[k]);
strikes.Clear();
volatilities.Clear();
for (int i = 0; i < nStrikes_; i++)
{
double strike = atmForward + strikeSpreads_[i];
if (strike + shiftTmp >= cutoffStrike_)
{
strikes.Add(strike);
Matrix matrix = tmpMarketVolCube[i];
volatilities.Add(matrix[j, k]);
}
}
List <double> guess = parametersGuess_.value(optionTimes[j], swapLengths[k]);
SABRInterpolation sabrInterpolation = new SABRInterpolation(strikes, strikes.Count,
volatilities,
optionTimes[j], atmForward,
guess[0], guess[1],
guess[2], guess[3],
isParameterFixed_[0],
isParameterFixed_[1],
isParameterFixed_[2],
isParameterFixed_[3],
vegaWeightedSmileFit_,
endCriteria_,
optMethod_,
errorAccept_,
useMaxError_,
maxGuesses_
);// shiftTmp
sabrInterpolation.update();
double rmsError = sabrInterpolation.rmsError();
double maxError = sabrInterpolation.maxError();
alphas [j, k] = sabrInterpolation.alpha();
betas [j, k] = sabrInterpolation.beta();
nus [j, k] = sabrInterpolation.nu();
rhos [j, k] = sabrInterpolation.rho();
forwards [j, k] = atmForward;
errors [j, k] = rmsError;
maxErrors [j, k] = maxError;
endCriteria[j, k] = (double)sabrInterpolation.endCriteria();
Utils.QL_REQUIRE(endCriteria[j, k].IsNotEqual((double)EndCriteria.Type.MaxIterations), () =>
"global swaptions calibration failed: " +
"MaxIterations reached: " + "\n" +
"option maturity = " + optionDates[j] + ", \n" +
"swap tenor = " + swapTenors[k] + ", \n" +
"error = " + (errors[j, k]) + ", \n" +
"max error = " + (maxErrors[j, k]) + ", \n" +
" alpha = " + alphas[j, k] + "n" +
" beta = " + betas[j, k] + "\n" +
" nu = " + nus[j, k] + "\n" +
" rho = " + rhos[j, k] + "\n"
);
Utils.QL_REQUIRE(useMaxError_ ? maxError > 0 : rmsError < maxErrorTolerance_, () =>
"global swaptions calibration failed: " +
"option tenor " + optionDates[j] +
", swap tenor " + swapTenors[k] +
(useMaxError_ ? ": max error " : ": error") +
(useMaxError_ ? maxError : rmsError) +
" alpha = " + alphas[j, k] + "\n" +
" beta = " + betas[j, k] + "\n" +
" nu = " + nus[j, k] + "\n" +
" rho = " + rhos[j, k] + "\n" +
(useMaxError_ ? ": error" : ": max error ") +
(useMaxError_ ? rmsError :maxError)
);
}
}
Cube sabrParametersCube = new Cube(optionDates, swapTenors, optionTimes, swapLengths, 8, true, backwardFlat_);
sabrParametersCube.setLayer(0, alphas);
sabrParametersCube.setLayer(1, betas);
sabrParametersCube.setLayer(2, nus);
sabrParametersCube.setLayer(3, rhos);
sabrParametersCube.setLayer(4, forwards);
sabrParametersCube.setLayer(5, errors);
sabrParametersCube.setLayer(6, maxErrors);
sabrParametersCube.setLayer(7, endCriteria);
return(sabrParametersCube);
}
public EuropeanExercise(Date date) : base(Type.European)
{
dates_ = new InitializedList <Date>(1, date);
}
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 latest, bool payoffAtExpiry = false) : base(Type.American, payoffAtExpiry)
{
dates_ = new InitializedList <Date>(2);
dates_[0] = Date.minDate();
dates_[1] = latest;
}
//@}
public override void calculate()
{
if (!(base.arguments_.settlementType == Settlement.Type.Physical))
{
throw new ArgumentException("cash-settled swaptions not priced with tree engine");
}
if (base.model_ == null)
{
throw new ArgumentException("no model specified");
}
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();
}
DiscretizedSwaption swaption = new DiscretizedSwaption(arguments_, referenceDate, dayCounter);
Lattice lattice;
if (lattice_ != null)
{
lattice = lattice_;
}
else
{
List <double> times = swaption.mandatoryTimes();
TimeGrid timeGrid = new TimeGrid(times, times.Count, timeSteps_);
lattice = model_.link.tree(timeGrid);
}
List <double> stoppingTimes = new InitializedList <double>(arguments_.exercise.dates().Count);
for (int i = 0; i < stoppingTimes.Count; ++i)
{
stoppingTimes[i] =
dayCounter.yearFraction(referenceDate,
arguments_.exercise.date(i));
}
swaption.initialize(lattice, stoppingTimes.Last());
double nextExercise;
/*std::find_if(stoppingTimes.begin(),
* stoppingTimes.end(),
* std::bind2nd(std::greater_equal<Time>(), 0.0));*/
List <double> listExercise = new List <double>();
listExercise.AddRange(stoppingTimes.FindAll(x => x >= 0));
nextExercise = listExercise[0];
swaption.rollback(nextExercise);
results_.value = swaption.presentValue();
}
// calculating swaption volatility matrix using
// Rebonatos approx. formula. Be aware that this
// matrix is valid only for regular fixings and
// assumes that the fix and floating leg have the
// same frequency
public SwaptionVolatilityMatrix getSwaptionVolatilityMatrix()
{
if (swaptionVola != null)
{
return(swaptionVola);
}
IborIndex index = process_.index();
Date today = process_.fixingDates()[0];
int size = process_.size() / 2;
Matrix volatilities = new Matrix(size, size);
List <Date> exercises = new InitializedList <Date>(size);
for (int i = 0; i < size; ++i)
{
exercises[i] = process_.fixingDates()[i + 1];
}
List <Period> lengths = new InitializedList <Period>(size);
for (int i = 0; i < size; ++i)
{
lengths[i] = (i + 1) * index.tenor();
}
Vector f = process_.initialValues();
for (int k = 0; k < size; ++k)
{
int alpha = k;
double t_alpha = process_.fixingTimes()[alpha + 1];
Matrix var = new Matrix(size, size);
for (int i = alpha + 1; i <= k + size; ++i)
{
for (int j = i; j <= k + size; ++j)
{
var[i - alpha - 1, j - alpha - 1] = var[j - alpha - 1, i - alpha - 1] =
covarProxy_.integratedCovariance(i, j, t_alpha, null);
}
}
for (int l = 1; l <= size; ++l)
{
int beta = l + k;
Vector w = w_0(alpha, beta);
double sum = 0.0;
for (int i = alpha + 1; i <= beta; ++i)
{
for (int j = alpha + 1; j <= beta; ++j)
{
sum += w[i] * w[j] * f[i] * f[j] * var[i - alpha - 1, j - alpha - 1];
}
}
volatilities[k, l - 1] =
Math.Sqrt(sum / t_alpha) / S_0(alpha, beta);
}
}
return(swaptionVola = new SwaptionVolatilityMatrix(today, exercises, lengths,
volatilities, index.dayCounter()));
}
public void sabrCalibrationSection(Cube marketVolCube, Cube parametersCube, Period swapTenor)
{
List <double> optionTimes = marketVolCube.optionTimes();
List <double> swapLengths = marketVolCube.swapLengths();
List <Date> optionDates = marketVolCube.optionDates();
List <Period> swapTenors = marketVolCube.swapTenors();
int k = swapTenors.IndexOf(swapTenors.First(x => x == swapTenor));
Utils.QL_REQUIRE(k != swapTenors.Count, () => "swap tenor not found");
List <double> calibrationResult = new InitializedList <double>(8, 0.0);
List <Matrix> tmpMarketVolCube = marketVolCube.points();
List <double> strikes = new List <double>(strikeSpreads_.Count);
List <double> volatilities = new List <double>(strikeSpreads_.Count);
for (int j = 0; j < optionTimes.Count; j++)
{
double atmForward = atmStrike(optionDates[j], swapTenors[k]);
double shiftTmp = atmVol_.link.shift(optionTimes[j], swapLengths[k]);
strikes.Clear();
volatilities.Clear();
for (int i = 0; i < nStrikes_; i++)
{
double strike = atmForward + strikeSpreads_[i];
if (strike + shiftTmp >= cutoffStrike_)
{
strikes.Add(strike);
volatilities.Add(tmpMarketVolCube[i][j, k]);
}
}
List <double> guess = parametersGuess_.value(optionTimes[j], swapLengths[k]);
var sabrInterpolation = new SABRInterpolation(strikes,
strikes.Count,
volatilities,
optionTimes[j], atmForward,
guess[0], guess[1],
guess[2], guess[3],
isParameterFixed_[0],
isParameterFixed_[1],
isParameterFixed_[2],
isParameterFixed_[3],
vegaWeightedSmileFit_,
endCriteria_,
optMethod_,
errorAccept_,
useMaxError_,
maxGuesses_
);//shiftTmp
sabrInterpolation.update();
double interpolationError = sabrInterpolation.rmsError();
calibrationResult[0] = sabrInterpolation.alpha();
calibrationResult[1] = sabrInterpolation.beta();
calibrationResult[2] = sabrInterpolation.nu();
calibrationResult[3] = sabrInterpolation.rho();
calibrationResult[4] = atmForward;
calibrationResult[5] = interpolationError;
calibrationResult[6] = sabrInterpolation.maxError();
calibrationResult[7] = (double)sabrInterpolation.endCriteria();
Utils.QL_REQUIRE(calibrationResult[7].IsNotEqual((double)EndCriteria.Type.MaxIterations), () =>
"section calibration failed: " +
"option tenor " + optionDates[j] +
", swap tenor " + swapTenors[k] +
": max iteration (" +
endCriteria_.maxIterations() + ")" +
", alpha " + calibrationResult[0] +
", beta " + calibrationResult[1] +
", nu " + calibrationResult[2] +
", rho " + calibrationResult[3] +
", max error " + calibrationResult[6] +
", error " + calibrationResult[5]
);
Utils.QL_REQUIRE(useMaxError_ ? calibrationResult[6] > 0 : calibrationResult[5] < maxErrorTolerance_, () =>
"section calibration failed: " +
"option tenor " + optionDates[j] +
", swap tenor " + swapTenors[k] +
(useMaxError_ ? ": max error " : ": error ") +
(useMaxError_ ? calibrationResult[6] : calibrationResult[5]) +
", alpha " + calibrationResult[0] +
", beta " + calibrationResult[1] +
", nu " + calibrationResult[2] +
", rho " + calibrationResult[3] +
(useMaxError_ ? ": error" : ": max error ") +
(useMaxError_ ? calibrationResult[5] : calibrationResult[6])
);
parametersCube.setPoint(optionDates[j], swapTenors[k], optionTimes[j], swapLengths[k], calibrationResult);
parametersCube.updateInterpolators();
}
}
protected override void setupExpired()
{
base.setupExpired();
legNPV_ = new InitializedList <double?>(legNPV_.Count);
}
public override List <SparseMatrix> toMatrixDecomp()
{
List <SparseMatrix> retVal = new InitializedList <SparseMatrix>(1, mapT_.toMatrix());
return(retVal);
}
public LinearInterpolationImpl(List <double> xBegin, int size, List <double> yBegin)
: base(xBegin, size, yBegin)
{
primitiveConst_ = new InitializedList <double>(size_);
s_ = new InitializedList <double>(size_);
}
public override void calculate()
{
/* this engine cannot really check for the averageType==Geometric
* since it can be used as control variate for the Arithmetic version
* QL_REQUIRE(arguments_.averageType == Average::Geometric,
* "not a geometric average option");
*/
if (!(arguments_.exercise.type() == Exercise.Type.European))
{
throw new ApplicationException("not an European Option");
}
double runningLog;
int pastFixings;
if (arguments_.averageType == Average.Type.Geometric)
{
if (!(arguments_.runningAccumulator > 0.0))
{
throw new ApplicationException("positive running product required: "
+ arguments_.runningAccumulator + " not allowed");
}
runningLog =
Math.Log(arguments_.runningAccumulator.GetValueOrDefault());
pastFixings = arguments_.pastFixings.GetValueOrDefault();
}
else // it is being used as control variate
{
runningLog = 1.0;
pastFixings = 0;
}
PlainVanillaPayoff payoff = (PlainVanillaPayoff)(arguments_.payoff);
if (payoff == null)
{
throw new ApplicationException("non-plain payoff given");
}
Date referenceDate = process_.riskFreeRate().link.referenceDate();
DayCounter rfdc = process_.riskFreeRate().link.dayCounter();
DayCounter divdc = process_.dividendYield().link.dayCounter();
DayCounter voldc = process_.blackVolatility().link.dayCounter();
List <double> fixingTimes = new InitializedList <double>(arguments_.fixingDates.Count());
int i;
for (i = 0; i < arguments_.fixingDates.Count(); i++)
{
if (arguments_.fixingDates[i] >= referenceDate)
{
double t = voldc.yearFraction(referenceDate,
arguments_.fixingDates[i]);
fixingTimes.Add(t);
}
}
int remainingFixings = fixingTimes.Count();
int numberOfFixings = pastFixings + remainingFixings;
double N = numberOfFixings;
double pastWeight = pastFixings / N;
double futureWeight = 1.0 - pastWeight;
/*double timeSum = std::accumulate(fixingTimes.begin(),
* fixingTimes.end(), 0.0);*/
double timeSum = 0;
fixingTimes.ForEach((ii, vv) => timeSum += fixingTimes[ii]);
double vola = process_.blackVolatility().link.blackVol(
arguments_.exercise.lastDate(),
payoff.strike());
double temp = 0.0;
for (i = pastFixings + 1; i < numberOfFixings; i++)
{
temp += fixingTimes[i - pastFixings - 1] * (N - i);
}
double variance = vola * vola / N / N * (timeSum + 2.0 * temp);
double dsigG_dsig = Math.Sqrt((timeSum + 2.0 * temp)) / N;
double sigG = vola * dsigG_dsig;
double dmuG_dsig = -(vola * timeSum) / N;
Date exDate = arguments_.exercise.lastDate();
double dividendRate = process_.dividendYield().link.
zeroRate(exDate, divdc, Compounding.Continuous, Frequency.NoFrequency).rate();
double riskFreeRate = process_.riskFreeRate().link.
zeroRate(exDate, rfdc, Compounding.Continuous, Frequency.NoFrequency).rate();
double nu = riskFreeRate - dividendRate - 0.5 * vola * vola;
double s = process_.stateVariable().link.value();
if (!(s > 0.0))
{
throw new ApplicationException("positive underlying value required");
}
int M = (pastFixings == 0 ? 1 : pastFixings);
double muG = pastWeight * runningLog / M +
futureWeight * Math.Log(s) + nu * timeSum / N;
double forwardPrice = Math.Exp(muG + variance / 2.0);
double riskFreeDiscount = process_.riskFreeRate().link.discount(
arguments_.exercise.lastDate());
BlackCalculator black = new BlackCalculator(payoff, forwardPrice, Math.Sqrt(variance),
riskFreeDiscount);
results_.value = black.value();
results_.delta = futureWeight * black.delta(forwardPrice) * forwardPrice / s;
results_.gamma = forwardPrice * futureWeight / (s * s)
* (black.gamma(forwardPrice) * futureWeight * forwardPrice
- pastWeight * black.delta(forwardPrice));
double Nx_1, nx_1;
CumulativeNormalDistribution CND = new CumulativeNormalDistribution();
NormalDistribution ND = new NormalDistribution();
if (sigG > Const.QL_Epsilon)
{
double x_1 = (muG - Math.Log(payoff.strike()) + variance) / sigG;
Nx_1 = CND.value(x_1);
nx_1 = ND.value(x_1);
}
else
{
Nx_1 = (muG > Math.Log(payoff.strike()) ? 1.0 : 0.0);
nx_1 = 0.0;
}
results_.vega = forwardPrice * riskFreeDiscount *
((dmuG_dsig + sigG * dsigG_dsig) * Nx_1 + nx_1 * dsigG_dsig);
if (payoff.optionType() == Option.Type.Put)
{
results_.vega -= riskFreeDiscount * forwardPrice *
(dmuG_dsig + sigG * dsigG_dsig);
}
double tRho = rfdc.yearFraction(process_.riskFreeRate().link.referenceDate(),
arguments_.exercise.lastDate());
results_.rho = black.rho(tRho) * timeSum / (N * tRho)
- (tRho - timeSum / N) * results_.value;
double tDiv = divdc.yearFraction(
process_.dividendYield().link.referenceDate(),
arguments_.exercise.lastDate());
results_.dividendRho = black.dividendRho(tDiv) * timeSum / (N * tDiv);
results_.strikeSensitivity = black.strikeSensitivity();
results_.theta = Utils.blackScholesTheta(process_,
results_.value.GetValueOrDefault(),
results_.delta.GetValueOrDefault(),
results_.gamma.GetValueOrDefault());
}