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 FdmSolverDesc getSolverDesc(double x)
{
// 1. Mesher
HestonProcess process = model_.currentLink().process();
double maturity = process.time(arguments_.exercise.lastDate());
// 1.1 The variance mesher
int tGridMin = 5;
FdmHestonVarianceMesher varianceMesher =
new FdmHestonVarianceMesher(vGrid_, process,
maturity, Math.Max(tGridMin, tGrid_ / 50));
// 1.2 The equity mesher
StrikedTypePayoff payoff = arguments_.payoff as StrikedTypePayoff;
Fdm1dMesher equityMesher;
if (strikes_.empty())
{
equityMesher = new FdmBlackScholesMesher(
xGrid_,
FdmBlackScholesMesher.processHelper(
process.s0(), process.dividendYield(),
process.riskFreeRate(), varianceMesher.volaEstimate()),
maturity, payoff.strike(),
null, null, 0.0001, x,
new Pair <double?, double?>(payoff.strike(), 0.1),
arguments_.cashFlow);
}
else
{
Utils.QL_REQUIRE(arguments_.cashFlow.empty(), () => "multiple strikes engine "
+ "does not work with discrete dividends");
equityMesher = new FdmBlackScholesMultiStrikeMesher(
xGrid_,
FdmBlackScholesMesher.processHelper(
process.s0(), process.dividendYield(),
process.riskFreeRate(), varianceMesher.volaEstimate()),
maturity, strikes_, 0.0001, x,
new Pair <double?, double?>(payoff.strike(), 0.075));
}
FdmMesher mesher = new FdmMesherComposite(equityMesher, varianceMesher);
// 2. Calculator
FdmInnerValueCalculator calculator = new FdmLogInnerValue(arguments_.payoff, mesher, 0);
// 3. Step conditions
FdmStepConditionComposite conditions =
FdmStepConditionComposite.vanillaComposite(
arguments_.cashFlow, arguments_.exercise,
mesher, calculator,
process.riskFreeRate().currentLink().referenceDate(),
process.riskFreeRate().currentLink().dayCounter());
// 4. Boundary conditions
FdmBoundaryConditionSet boundaries = new FdmBoundaryConditionSet();
// 5. Solver
FdmSolverDesc solverDesc = new FdmSolverDesc();
solverDesc.mesher = mesher;
solverDesc.bcSet = boundaries;
solverDesc.condition = conditions;
solverDesc.calculator = calculator;
solverDesc.maturity = maturity;
solverDesc.dampingSteps = dampingSteps_;
solverDesc.timeSteps = tGrid_;
return(solverDesc);
}
