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 SecondDerivativeOp(SecondDerivativeOp rhs)
: base(rhs.direction_, rhs.mesher_)
{
lower_ = rhs.lower_;
diag_ = rhs.diag_;
upper_ = rhs.upper_;
}
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 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;
}
