public override void calculate()
{
// 1. Mesher
HestonProcess process = model_.currentLink().process();
double maturity = process.time(arguments_.exercise.lastDate());
// 1.1 The variance mesher
int tGridMin = 5;
int tGridAvgSteps = Math.Max(tGridMin, tGrid_ / 50);
FdmHestonLocalVolatilityVarianceMesher varianceMesher
= new FdmHestonLocalVolatilityVarianceMesher(vGrid_, process, leverageFct_, maturity, tGridAvgSteps);
// 1.2 the equity mesher
StrikedTypePayoff payoff = arguments_.payoff as StrikedTypePayoff;
double?xMin = null;
double?xMax = null;
if (arguments_.barrierType == Barrier.Type.DownIn ||
arguments_.barrierType == Barrier.Type.DownOut)
{
xMin = Math.Log(arguments_.barrier.Value);
}
if (arguments_.barrierType == Barrier.Type.UpIn ||
arguments_.barrierType == Barrier.Type.UpOut)
{
xMax = Math.Log(arguments_.barrier.Value);
}
Fdm1dMesher equityMesher =
new FdmBlackScholesMesher(xGrid_,
FdmBlackScholesMesher.processHelper(process.s0(),
process.dividendYield(),
process.riskFreeRate(),
varianceMesher.volaEstimate()),
maturity,
payoff.strike(),
xMin,
xMax,
0.0001,
1.5,
new Pair <double?, double?>(),
arguments_.cashFlow);
FdmMesher mesher =
new FdmMesherComposite(equityMesher, varianceMesher);
// 2. Calculator
StrikedTypePayoff rebatePayoff =
new CashOrNothingPayoff(Option.Type.Call, 0.0, arguments_.rebate.Value);
FdmInnerValueCalculator calculator =
new FdmLogInnerValue(rebatePayoff, mesher, 0);
// 3. Step conditions
Utils.QL_REQUIRE(arguments_.exercise.type() == Exercise.Type.European,
() => "only european style option are supported");
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();
if (arguments_.barrierType == Barrier.Type.DownIn ||
arguments_.barrierType == Barrier.Type.DownOut)
{
boundaries.Add(new FdmDirichletBoundary(mesher, arguments_.rebate.Value, 0,
FdmDirichletBoundary.Side.Lower));
}
if (arguments_.barrierType == Barrier.Type.UpIn ||
arguments_.barrierType == Barrier.Type.UpOut)
{
boundaries.Add(new FdmDirichletBoundary(mesher, arguments_.rebate.Value, 0,
FdmDirichletBoundary.Side.Upper));
}
// 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_;
FdmHestonSolver solver =
new FdmHestonSolver(
new Handle <HestonProcess>(process),
solverDesc, schemeDesc_,
new Handle <FdmQuantoHelper>(),
leverageFct_);
double spot = process.s0().currentLink().value();
results_.value = solver.valueAt(spot, process.v0());
results_.delta = solver.deltaAt(spot, process.v0());
results_.gamma = solver.gammaAt(spot, process.v0());
results_.theta = solver.thetaAt(spot, process.v0());
}
public override void calculate()
{
// 1. Mesher
HestonProcess process = model_.currentLink().process();
double maturity = process.time(arguments_.exercise.lastDate());
// 1.1 Variance Mesher
int tGridMin = 5;
int tGridAvgSteps = Math.Max(tGridMin, tGrid_ / 50);
FdmHestonLocalVolatilityVarianceMesher varianceMesher = new FdmHestonLocalVolatilityVarianceMesher(vGrid_,
process,
leverageFct_,
maturity,
tGridAvgSteps);
// 1.2 Equity Mesher
StrikedTypePayoff payoff = arguments_.payoff as StrikedTypePayoff;
double?xMin = null;
double?xMax = null;
if (arguments_.barrierType == Barrier.Type.DownIn ||
arguments_.barrierType == Barrier.Type.DownOut)
{
xMin = Math.Log(arguments_.barrier.Value);
}
if (arguments_.barrierType == Barrier.Type.UpIn ||
arguments_.barrierType == Barrier.Type.UpOut)
{
xMax = Math.Log(arguments_.barrier.Value);
}
Fdm1dMesher equityMesher =
new FdmBlackScholesMesher(xGrid_,
FdmBlackScholesMesher.processHelper(process.s0(),
process.dividendYield(),
process.riskFreeRate(),
varianceMesher.volaEstimate()),
maturity,
payoff.strike(),
xMin,
xMax,
0.0001,
1.5,
new Pair <double?, double?>(),
arguments_.cashFlow);
FdmMesher mesher =
new FdmMesherComposite(equityMesher, varianceMesher);
// 2. Calculator
FdmInnerValueCalculator calculator =
new FdmLogInnerValue(payoff, mesher, 0);
// 3. Step conditions
List <IStepCondition <Vector> > stepConditions = new List <IStepCondition <Vector> >();
List <List <double> > stoppingTimes = new List <List <double> >();
// 3.1 Step condition if discrete dividends
FdmDividendHandler dividendCondition =
new FdmDividendHandler(arguments_.cashFlow, mesher,
process.riskFreeRate().currentLink().referenceDate(),
process.riskFreeRate().currentLink().dayCounter(), 0);
if (!arguments_.cashFlow.empty())
{
stepConditions.Add(dividendCondition);
stoppingTimes.Add(dividendCondition.dividendTimes());
}
Utils.QL_REQUIRE(arguments_.exercise.type() == Exercise.Type.European,
() => "only european style option are supported");
FdmStepConditionComposite conditions =
new FdmStepConditionComposite(stoppingTimes, stepConditions);
// 4. Boundary conditions
FdmBoundaryConditionSet boundaries = new FdmBoundaryConditionSet();
if (arguments_.barrierType == Barrier.Type.DownIn ||
arguments_.barrierType == Barrier.Type.DownOut)
{
boundaries.Add(
new FdmDirichletBoundary(mesher, arguments_.rebate.Value, 0,
FdmDirichletBoundary.Side.Lower));
}
if (arguments_.barrierType == Barrier.Type.UpIn ||
arguments_.barrierType == Barrier.Type.UpOut)
{
boundaries.Add(
new FdmDirichletBoundary(mesher, arguments_.rebate.Value, 0,
FdmDirichletBoundary.Side.Upper));
}
// 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_;
FdmHestonSolver solver =
new FdmHestonSolver(
new Handle <HestonProcess>(process),
solverDesc, schemeDesc_,
new Handle <FdmQuantoHelper>(), leverageFct_);
double spot = process.s0().currentLink().value();
results_.value = solver.valueAt(spot, process.v0());
results_.delta = solver.deltaAt(spot, process.v0());
results_.gamma = solver.gammaAt(spot, process.v0());
results_.theta = solver.thetaAt(spot, process.v0());
// 6. Calculate vanilla option and rebate for in-barriers
if (arguments_.barrierType == Barrier.Type.DownIn ||
arguments_.barrierType == Barrier.Type.UpIn)
{
// Cast the payoff
StrikedTypePayoff castedPayoff = arguments_.payoff as StrikedTypePayoff;
// Calculate the vanilla option
DividendVanillaOption vanillaOption =
new DividendVanillaOption(castedPayoff, arguments_.exercise,
dividendCondition.dividendDates(),
dividendCondition.dividends());
vanillaOption.setPricingEngine(
new FdHestonVanillaEngine(
model_, tGrid_, xGrid_,
vGrid_, dampingSteps_,
schemeDesc_));
// Calculate the rebate value
DividendBarrierOption rebateOption =
new DividendBarrierOption(arguments_.barrierType,
arguments_.barrier.Value,
arguments_.rebate.Value,
castedPayoff, arguments_.exercise,
dividendCondition.dividendDates(),
dividendCondition.dividends());
int xGridMin = 20;
int vGridMin = 10;
int rebateDampingSteps
= (dampingSteps_ > 0) ? Math.Min(1, dampingSteps_ / 2) : 0;
rebateOption.setPricingEngine(new FdHestonRebateEngine(
model_, tGrid_, Math.Max(xGridMin, xGrid_ / 4),
Math.Max(vGridMin, vGrid_ / 4),
rebateDampingSteps, schemeDesc_));
results_.value = vanillaOption.NPV() + rebateOption.NPV()
- results_.value;
results_.delta = vanillaOption.delta() + rebateOption.delta()
- results_.delta;
results_.gamma = vanillaOption.gamma() + rebateOption.gamma()
- results_.gamma;
results_.theta = vanillaOption.theta() + rebateOption.theta()
- results_.theta;
}
}
