public SecondDerivativeOp(int direction, FdmMesher mesher)
: base(direction, mesher)
{
FdmLinearOpLayout layout = mesher.layout();
FdmLinearOpIterator endIter = layout.end();
for (FdmLinearOpIterator iter = layout.begin(); iter != endIter; ++iter)
{
int i = iter.index();
double?hm = mesher.dminus(iter, direction_);
double?hp = mesher.dplus(iter, direction_);
double?zetam1 = hm * (hm + hp);
double?zeta0 = hm * hp;
double?zetap1 = hp * (hm + hp);
int co = iter.coordinates()[direction_];
if (co == 0 || co == layout.dim()[direction] - 1)
{
lower_[i] = diag_[i] = upper_[i] = 0.0;
}
else
{
lower_[i] = 2.0 / zetam1.Value;
diag_[i] = -2.0 / zeta0.Value;
upper_[i] = 2.0 / zetap1.Value;
}
}
}
public FdmHestonEquityPart(FdmMesher mesher,
YieldTermStructure rTS,
YieldTermStructure qTS,
FdmQuantoHelper quantoHelper = null,
LocalVolTermStructure leverageFct = null)
{
varianceValues_ = new Vector(0.5 * mesher.locations(1));
dxMap_ = new FirstDerivativeOp(0, mesher);
dxxMap_ = new SecondDerivativeOp(0, mesher).mult(0.5 * mesher.locations(1));
mapT_ = new TripleBandLinearOp(0, mesher);
mesher_ = mesher;
rTS_ = rTS;
qTS_ = qTS;
quantoHelper_ = quantoHelper;
leverageFct_ = leverageFct;
// on the boundary s_min and s_max the second derivative
// d^2V/dS^2 is zero and due to Ito's Lemma the variance term
// in the drift should vanish.
FdmLinearOpLayout layout = mesher_.layout();
FdmLinearOpIterator endIter = layout.end();
for (FdmLinearOpIterator iter = layout.begin(); iter != endIter;
++iter)
{
if (iter.coordinates()[0] == 0 ||
iter.coordinates()[0] == layout.dim()[0] - 1)
{
varianceValues_[iter.index()] = 0.0;
}
}
volatilityValues_ = Vector.Sqrt(2 * varianceValues_);
}
public Fdm1DimSolver(FdmSolverDesc solverDesc,
FdmSchemeDesc schemeDesc,
FdmLinearOpComposite op)
{
solverDesc_ = solverDesc;
schemeDesc_ = schemeDesc;
op_ = op;
thetaCondition_ = new FdmSnapshotCondition(
0.99 * Math.Min(1.0 / 365.0,
solverDesc.condition.stoppingTimes().empty()
? solverDesc.maturity
: solverDesc.condition.stoppingTimes().First()));
conditions_ = FdmStepConditionComposite.joinConditions(thetaCondition_,
solverDesc.condition);
x_ = new InitializedList <double>(solverDesc.mesher.layout().size());
initialValues_ = new InitializedList <double>(solverDesc.mesher.layout().size());
resultValues_ = new Vector(solverDesc.mesher.layout().size());
FdmMesher mesher = solverDesc.mesher;
FdmLinearOpLayout layout = mesher.layout();
FdmLinearOpIterator endIter = layout.end();
for (FdmLinearOpIterator iter = layout.begin(); iter != endIter;
++iter)
{
initialValues_[iter.index()]
= solverDesc_.calculator.avgInnerValue(iter,
solverDesc.maturity);
x_[iter.index()] = mesher.location(iter, 0);
}
}
public FdmDividendHandler(DividendSchedule schedule,
FdmMesher mesher,
Date referenceDate,
DayCounter dayCounter,
int equityDirection)
{
x_ = new Vector(mesher.layout().dim()[equityDirection]);
mesher_ = mesher;
equityDirection_ = equityDirection;
dividends_ = new List <double>();
dividendDates_ = new List <Date>();
dividendTimes_ = new List <double>();
foreach (Dividend iter in schedule)
{
dividends_.Add(iter.amount());
dividendDates_.Add(iter.date());
dividendTimes_.Add(
dayCounter.yearFraction(referenceDate, iter.date()));
}
Vector tmp = mesher_.locations(equityDirection);
int spacing = mesher_.layout().spacing()[equityDirection];
for (int i = 0; i < x_.size(); ++i)
{
x_[i] = Math.Exp(tmp[i * spacing]);
}
}
public FdmLogInnerValue(Payoff payoff,
FdmMesher mesher,
int direction)
{
payoff_ = payoff;
mesher_ = mesher;
direction_ = direction;
avgInnerValues_ = new List <double>();
}
public FdmHestonVariancePart(
FdmMesher mesher,
YieldTermStructure rTS,
double sigma, double kappa, double theta)
{
dyMap_ = new SecondDerivativeOp(1, mesher)
.mult(0.5 * sigma * sigma * mesher.locations(1))
.add(new FirstDerivativeOp(1, mesher)
.mult(kappa * (theta - mesher.locations(1))));
mapT_ = new TripleBandLinearOp(1, mesher);
rTS_ = rTS;
}
public FdmHullWhiteOp(FdmMesher mesher,
HullWhite model,
int direction)
{
x_ = mesher.locations(direction);
dzMap_ = new TripleBandLinearOp(new FirstDerivativeOp(direction, mesher).mult(-1.0 * x_ * model.a()).add(
new SecondDerivativeOp(direction, mesher).mult(0.5 * model.sigma() * model.sigma()
* new Vector(mesher.layout().size(), 1.0))));
mapT_ = new TripleBandLinearOp(direction, mesher);
direction_ = direction;
model_ = model;
}
public FdmBermudanStepCondition(List <Date> exerciseDates,
Date referenceDate,
DayCounter dayCounter,
FdmMesher mesher,
FdmInnerValueCalculator calculator)
{
mesher_ = mesher;
calculator_ = calculator;
exerciseTimes_ = new List <double>();
foreach (Date iter in exerciseDates)
{
exerciseTimes_.Add(
dayCounter.yearFraction(referenceDate, iter));
}
}
public NinePointLinearOp(int d0, int d1, FdmMesher mesher)
{
d0_ = d0;
d1_ = d1;
i00_ = new InitializedList <int>(mesher.layout().size());
i10_ = new InitializedList <int>(mesher.layout().size());
i20_ = new InitializedList <int>(mesher.layout().size());
i01_ = new InitializedList <int>(mesher.layout().size());
i21_ = new InitializedList <int>(mesher.layout().size());
i02_ = new InitializedList <int>(mesher.layout().size());
i12_ = new InitializedList <int>(mesher.layout().size());
i22_ = new InitializedList <int>(mesher.layout().size());
a00_ = new InitializedList <double>(mesher.layout().size());
a10_ = new InitializedList <double>(mesher.layout().size());
a20_ = new InitializedList <double>(mesher.layout().size());
a01_ = new InitializedList <double>(mesher.layout().size());
a11_ = new InitializedList <double>(mesher.layout().size());
a21_ = new InitializedList <double>(mesher.layout().size());
a02_ = new InitializedList <double>(mesher.layout().size());
a12_ = new InitializedList <double>(mesher.layout().size());
a22_ = new InitializedList <double>(mesher.layout().size());
mesher_ = mesher;
Utils.QL_REQUIRE(d0_ != d1_ &&
d0_ < mesher.layout().dim().Count &&
d1_ < mesher.layout().dim().Count,
() => "inconsistent derivative directions");
FdmLinearOpLayout layout = mesher.layout();
FdmLinearOpIterator endIter = layout.end();
for (FdmLinearOpIterator iter = layout.begin(); iter != endIter; ++iter)
{
int i = iter.index();
i10_[i] = layout.neighbourhood(iter, d1_, -1);
i01_[i] = layout.neighbourhood(iter, d0_, -1);
i21_[i] = layout.neighbourhood(iter, d0_, 1);
i12_[i] = layout.neighbourhood(iter, d1_, 1);
i00_[i] = layout.neighbourhood(iter, d0_, -1, d1_, -1);
i20_[i] = layout.neighbourhood(iter, d0_, 1, d1_, -1);
i02_[i] = layout.neighbourhood(iter, d0_, -1, d1_, 1);
i22_[i] = layout.neighbourhood(iter, d0_, 1, d1_, 1);
}
}
public FdmHestonOp(FdmMesher mesher,
HestonProcess hestonProcess,
FdmQuantoHelper quantoHelper = null,
LocalVolTermStructure leverageFct = null)
{
correlationMap_ = new SecondOrderMixedDerivativeOp(0, 1, mesher)
.mult(hestonProcess.rho() * hestonProcess.sigma()
* mesher.locations(1));
dyMap_ = new FdmHestonVariancePart(mesher,
hestonProcess.riskFreeRate().currentLink(),
hestonProcess.sigma(),
hestonProcess.kappa(),
hestonProcess.theta());
dxMap_ = new FdmHestonEquityPart(mesher,
hestonProcess.riskFreeRate().currentLink(),
hestonProcess.dividendYield().currentLink(),
quantoHelper,
leverageFct);
}
public FdmDirichletBoundary(FdmMesher mesher,
double valueOnBoundary, int direction, Side side)
{
side_ = side;
valueOnBoundary_ = valueOnBoundary;
indices_ = new FdmIndicesOnBoundary(mesher.layout(),
direction, side).getIndices();
if (side_ == Side.Lower)
{
xExtreme_ = mesher.locations(direction)[0];
}
else if (side_ == Side.Upper)
{
xExtreme_ = mesher
.locations(direction)[mesher.layout().dim()[direction] - 1];
}
else
{
Utils.QL_FAIL("internal error");
}
}
public static FdmStepConditionComposite vanillaComposite(DividendSchedule cashFlow,
Exercise exercise,
FdmMesher mesher,
FdmInnerValueCalculator calculator,
Date refDate,
DayCounter dayCounter)
{
List <List <double> > stoppingTimes = new List <List <double> >();
List <IStepCondition <Vector> > stepConditions = new List <IStepCondition <Vector> >();
if (!cashFlow.empty())
{
FdmDividendHandler dividendCondition =
new FdmDividendHandler(cashFlow, mesher,
refDate, dayCounter, 0);
stepConditions.Add(dividendCondition);
stoppingTimes.Add(dividendCondition.dividendTimes());
}
Utils.QL_REQUIRE(exercise.type() == Exercise.Type.American ||
exercise.type() == Exercise.Type.European ||
exercise.type() == Exercise.Type.Bermudan,
() => "exercise type is not supported");
if (exercise.type() == Exercise.Type.American)
{
stepConditions.Add(new FdmAmericanStepCondition(mesher, calculator));
}
else if (exercise.type() == Exercise.Type.Bermudan)
{
FdmBermudanStepCondition bermudanCondition =
new FdmBermudanStepCondition(exercise.dates(),
refDate, dayCounter,
mesher, calculator);
stepConditions.Add(bermudanCondition);
stoppingTimes.Add(bermudanCondition.exerciseTimes());
}
return(new FdmStepConditionComposite(stoppingTimes, stepConditions));
}
public TripleBandLinearOp(int direction, FdmMesher mesher)
{
direction_ = direction;
i0_ = new InitializedList <int>(mesher.layout().size());
i2_ = new InitializedList <int>(mesher.layout().size());
reverseIndex_ = new InitializedList <int>(mesher.layout().size());
lower_ = new InitializedList <double>(mesher.layout().size());
diag_ = new InitializedList <double>(mesher.layout().size());
upper_ = new InitializedList <double>(mesher.layout().size());
mesher_ = mesher;
FdmLinearOpLayout layout = mesher.layout();
FdmLinearOpIterator endIter = layout.end();
int tmp;
List <int> newDim = new List <int>(layout.dim());
tmp = newDim[direction_];
newDim[direction_] = newDim[0];
newDim[0] = tmp;
List <int> newSpacing = new FdmLinearOpLayout(newDim).spacing();
tmp = newSpacing[direction_];
newSpacing[direction_] = newSpacing[0];
newSpacing[0] = tmp;
for (FdmLinearOpIterator iter = layout.begin(); iter != endIter; ++iter)
{
int i = iter.index();
i0_[i] = layout.neighbourhood(iter, direction, -1);
i2_[i] = layout.neighbourhood(iter, direction, 1);
List <int> coordinates = iter.coordinates();
int newIndex = coordinates.inner_product(0, coordinates.Count, 0, newSpacing, 0);
reverseIndex_[newIndex] = i;
}
}
public FdmBlackScholesOp(FdmMesher mesher,
GeneralizedBlackScholesProcess bsProcess,
double strike,
bool localVol = false,
double?illegalLocalVolOverwrite = null,
int direction = 0,
FdmQuantoHelper quantoHelper = null)
{
mesher_ = mesher;
rTS_ = bsProcess.riskFreeRate().currentLink();
qTS_ = bsProcess.dividendYield().currentLink();
volTS_ = bsProcess.blackVolatility().currentLink();
localVol_ = (localVol) ? bsProcess.localVolatility().currentLink()
: null;
x_ = (localVol) ? new Vector(Vector.Exp(mesher.locations(direction))) : null;
dxMap_ = new FirstDerivativeOp(direction, mesher);
dxxMap_ = new SecondDerivativeOp(direction, mesher);
mapT_ = new TripleBandLinearOp(direction, mesher);
strike_ = strike;
illegalLocalVolOverwrite_ = illegalLocalVolOverwrite;
direction_ = direction;
quantoHelper_ = quantoHelper;
}
public FirstDerivativeOp(int direction, FdmMesher mesher)
: base(direction, mesher)
{
FdmLinearOpLayout layout = mesher.layout();
FdmLinearOpIterator endIter = layout.end();
for (FdmLinearOpIterator iter = layout.begin(); iter != endIter; ++iter)
{
int i = iter.index();
double?hm = mesher.dminus(iter, direction_);
double?hp = mesher.dplus(iter, direction_);
double?zetam1 = hm * (hm + hp);
double?zeta0 = hm * hp;
double?zetap1 = hp * (hm + hp);
if (iter.coordinates()[direction_] == 0)
{
//upwinding scheme
lower_[i] = 0.0;
diag_[i] = -(upper_[i] = 1 / hp.Value);
}
else if (iter.coordinates()[direction_]
== layout.dim()[direction] - 1)
{
// downwinding scheme
lower_[i] = -(diag_[i] = 1 / hm.Value);
upper_[i] = 0.0;
}
else
{
lower_[i] = -hp.Value / zetam1.Value;
diag_[i] = (hp.Value - hm.Value) / zeta0.Value;
upper_[i] = hm.Value / zetap1.Value;
}
}
}
public FdmAffineModelSwapInnerValue(
ModelType disModel,
ModelType fwdModel,
VanillaSwap swap,
Dictionary <double, Date> exerciseDates,
FdmMesher mesher,
int direction)
{
disModel_ = disModel;
fwdModel_ = fwdModel;
mesher_ = mesher;
direction_ = direction;
swap_ = new VanillaSwap(swap.swapType,
swap.nominal,
swap.fixedSchedule(),
swap.fixedRate,
swap.fixedDayCount(),
swap.floatingSchedule(),
swap.iborIndex().clone(fwdTs_),
swap.spread,
swap.floatingDayCount(),
null);
exerciseDates_ = exerciseDates;
}
public FdmAmericanStepCondition(FdmMesher mesher, FdmInnerValueCalculator calculator)
{
mesher_ = mesher;
calculator_ = calculator;
}
public SecondOrderMixedDerivativeOp(int d0, int d1, FdmMesher mesher)
: base(d0, d1, mesher)
{
FdmLinearOpLayout layout = mesher.layout();
FdmLinearOpIterator endIter = layout.end();
for (FdmLinearOpIterator iter = layout.begin(); iter != endIter; ++iter)
{
int i = iter.index();
double?hm_d0 = mesher.dminus(iter, d0_);
double?hp_d0 = mesher.dplus(iter, d0_);
double?hm_d1 = mesher.dminus(iter, d1_);
double?hp_d1 = mesher.dplus(iter, d1_);
double?zetam1 = hm_d0 * (hm_d0 + hp_d0);
double?zeta0 = hm_d0 * hp_d0;
double?zetap1 = hp_d0 * (hm_d0 + hp_d0);
double?phim1 = hm_d1 * (hm_d1 + hp_d1);
double?phi0 = hm_d1 * hp_d1;
double?phip1 = hp_d1 * (hm_d1 + hp_d1);
int c0 = iter.coordinates()[d0_];
int c1 = iter.coordinates()[d1_];
if (c0 == 0 && c1 == 0)
{
// lower left corner
a00_[i] = a01_[i] = a02_[i] = a10_[i] = a20_[i] = 0.0;
a11_[i] = a22_[i] = 1.0 / (hp_d0.Value * hp_d1.Value);
a21_[i] = a12_[i] = -a11_[i];
}
else if (c0 == layout.dim()[d0_] - 1 && c1 == 0)
{
// upper left corner
a22_[i] = a21_[i] = a20_[i] = a10_[i] = a00_[i] = 0.0;
a01_[i] = a12_[i] = 1.0 / (hm_d0.Value * hp_d1.Value);
a11_[i] = a02_[i] = -a01_[i];
}
else if (c0 == 0 && c1 == layout.dim()[d1_] - 1)
{
// lower right corner
a00_[i] = a01_[i] = a02_[i] = a12_[i] = a22_[i] = 0.0;
a10_[i] = a21_[i] = 1.0 / (hp_d0.Value * hm_d1.Value);
a20_[i] = a11_[i] = -a10_[i];
}
else if (c0 == layout.dim()[d0_] - 1 && c1 == layout.dim()[d1_] - 1)
{
// upper right corner
a20_[i] = a21_[i] = a22_[i] = a12_[i] = a02_[i] = 0.0;
a00_[i] = a11_[i] = 1.0 / (hm_d0.Value * hm_d1.Value);
a10_[i] = a01_[i] = -a00_[i];
}
else if (c0 == 0)
{
// lower side
a00_[i] = a01_[i] = a02_[i] = 0.0;
a10_[i] = hp_d1.Value / (hp_d0.Value * phim1.Value);
a20_[i] = -a10_[i];
a21_[i] = (hp_d1.Value - hm_d1.Value) / (hp_d0.Value * phi0.Value);
a11_[i] = -a21_[i];
a22_[i] = hm_d1.Value / (hp_d0.Value * phip1.Value);
a12_[i] = -a22_[i];
}
else if (c0 == layout.dim()[d0_] - 1)
{
// upper side
a20_[i] = a21_[i] = a22_[i] = 0.0;
a00_[i] = hp_d1.Value / (hm_d0.Value * phim1.Value);
a10_[i] = -a00_[i];
a11_[i] = (hp_d1.Value - hm_d1.Value) / (hm_d0.Value * phi0.Value);
a01_[i] = -a11_[i];
a12_[i] = hm_d1.Value / (hm_d0.Value * phip1.Value);
a02_[i] = -a12_[i];
}
else if (c1 == 0)
{
// left side
a00_[i] = a10_[i] = a20_[i] = 0.0;
a01_[i] = hp_d0.Value / (zetam1.Value * hp_d1.Value);
a02_[i] = -a01_[i];
a12_[i] = (hp_d0.Value - hm_d0.Value) / (zeta0.Value * hp_d1.Value);
a11_[i] = -a12_[i];
a22_[i] = hm_d0.Value / (zetap1.Value * hp_d1.Value);
a21_[i] = -a22_[i];
}
else if (c1 == layout.dim()[d1_] - 1)
{
// right side
a22_[i] = a12_[i] = a02_[i] = 0.0;
a00_[i] = hp_d0.Value / (zetam1.Value * hm_d1.Value);
a01_[i] = -a00_[i];
a11_[i] = (hp_d0.Value - hm_d0.Value) / (zeta0.Value * hm_d1.Value);
a10_[i] = -a11_[i];
a21_[i] = hm_d0.Value / (zetap1.Value * hm_d1.Value);
a20_[i] = -a21_[i];
}
else
{
a00_[i] = hp_d0.Value * hp_d1.Value / (zetam1.Value * phim1.Value);
a10_[i] = -(hp_d0.Value - hm_d0.Value) * hp_d1.Value / (zeta0.Value * phim1.Value);
a20_[i] = -hm_d0.Value * hp_d1.Value / (zetap1.Value * phim1.Value);
a01_[i] = -hp_d0.Value * (hp_d1.Value - hm_d1.Value) / (zetam1.Value * phi0.Value);
a11_[i] = (hp_d0.Value - hm_d0.Value) * (hp_d1.Value - hm_d1.Value) / (zeta0.Value * phi0.Value);
a21_[i] = hm_d0.Value * (hp_d1.Value - hm_d1.Value) / (zetap1.Value * phi0.Value);
a02_[i] = -hp_d0.Value * hm_d1.Value / (zetam1.Value * phip1.Value);
a12_[i] = hm_d1.Value * (hp_d0.Value - hm_d0.Value) / (zeta0.Value * phip1.Value);
a22_[i] = hm_d0.Value * hm_d1.Value / (zetap1.Value * phip1.Value);
}
}
}
public FdmLogBasketInnerValue(BasketPayoff payoff,
FdmMesher mesher)
{
payoff_ = payoff;
mesher_ = mesher;
}