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 FdmHestonLocalVolatilityVarianceMesher(int size,
HestonProcess process,
LocalVolTermStructure leverageFct,
double maturity,
int tAvgSteps = 10,
double epsilon = 0.0001)
: base(size)
{
leverageFct_ = leverageFct;
FdmHestonVarianceMesher mesher = new FdmHestonVarianceMesher(size, process, maturity, tAvgSteps, epsilon);
for (int i = 0; i < size; ++i)
{
dplus_[i] = mesher.dplus(i);
dminus_[i] = mesher.dminus(i);
locations_[i] = mesher.location(i);
}
volaEstimate_ = mesher.volaEstimate();
if (leverageFct != null)
{
double s0 = process.s0().currentLink().value();
List <double> acc = new List <double>();
acc.Add(leverageFct.localVol(0.0, s0, true));
Handle <YieldTermStructure> rTS = process.riskFreeRate();
Handle <YieldTermStructure> qTS = process.dividendYield();
for (int l = 1; l <= tAvgSteps; ++l)
{
double t = (maturity * l) / tAvgSteps;
double vol = volaEstimate_ * acc.Average();
double fwd = s0 * qTS.currentLink().discount(t) / rTS.currentLink().discount(t);
int sAvgSteps = 50;
Vector u = new Vector(sAvgSteps), sig = new Vector(sAvgSteps);
for (int i = 0; i < sAvgSteps; ++i)
{
u[i] = epsilon + ((1.0 - 2.0 * epsilon) / (sAvgSteps - 1.0)) * i;
double x = new InverseCumulativeNormal().value(u[i]);
double gf = x * vol * Math.Sqrt(t);
double f = fwd * Math.Exp(gf);
sig[i] = Math.Pow(leverageFct.localVol(t, f, true), 2.0);
}
double leverageAvg = new GaussLobattoIntegral(10000, 1E-4).value(new interpolated_volatility(u, sig).value,
u.First(),
u.Last())
/ (1.0 - 2.0 * epsilon);
acc.Add(leverageAvg);
}
volaEstimate_ *= acc.Average();
}
}
public FdmHestonSolver(
Handle <HestonProcess> process,
FdmSolverDesc solverDesc,
FdmSchemeDesc schemeDesc = null,
Handle <FdmQuantoHelper> quantoHelper = null,
LocalVolTermStructure leverageFct = null)
{
process_ = process;
solverDesc_ = solverDesc;
schemeDesc_ = schemeDesc ?? new FdmSchemeDesc().Douglas();
quantoHelper_ = quantoHelper == null ? new Handle <FdmQuantoHelper>() : quantoHelper;
leverageFct_ = leverageFct;
}
// Constructor
public FdHestonRebateEngine(
HestonModel model,
int tGrid = 100, int xGrid = 100,
int vGrid = 50, int dampingSteps = 0,
FdmSchemeDesc schemeDesc = null,
LocalVolTermStructure leverageFct = null)
: base(model)
{
tGrid_ = tGrid;
xGrid_ = xGrid;
vGrid_ = vGrid;
dampingSteps_ = dampingSteps;
schemeDesc_ = schemeDesc == null ? new FdmSchemeDesc().Hundsdorfer() : schemeDesc;
leverageFct_ = leverageFct;
model_.registerWith(update);
}
public FdHestonVanillaEngine(
HestonModel model,
FdmQuantoHelper quantoHelper,
int tGrid, int xGrid, int vGrid, int dampingSteps,
FdmSchemeDesc schemeDesc,
LocalVolTermStructure leverageFct)
: base(model)
{
tGrid_ = tGrid;
xGrid_ = xGrid;
vGrid_ = vGrid;
dampingSteps_ = dampingSteps;
schemeDesc_ = schemeDesc;
leverageFct_ = leverageFct;
strikes_ = new List <double>();
cachedArgs2results_ = new List <Pair <DividendVanillaOption.Arguments, OneAssetOption.Results> >();
quantoHelper_ = quantoHelper;
}
public FdHestonVanillaEngine(
HestonModel model,
int tGrid = 100, int xGrid = 100,
int vGrid = 50, int dampingSteps = 0,
FdmSchemeDesc schemeDesc = null,
LocalVolTermStructure leverageFct = null)
: base(model)
{
tGrid_ = tGrid;
xGrid_ = xGrid;
vGrid_ = vGrid;
dampingSteps_ = dampingSteps;
schemeDesc_ = schemeDesc == null ? new FdmSchemeDesc().Hundsdorfer() : schemeDesc;
leverageFct_ = leverageFct;
strikes_ = new List <double>();
cachedArgs2results_ = new List <Pair <DividendVanillaOption.Arguments, OneAssetOption.Results> >();
quantoHelper_ = null;
model_.registerWith(update);
}
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 MakeFdHestonVanillaEngine withLeverageFunction(
LocalVolTermStructure leverageFct)
{
leverageFct_ = leverageFct;
return(this);
}
