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 override void calculate()
{
// cache lookup for precalculated results
for (int i = 0; i < cachedArgs2results_.Count; ++i)
{
if (cachedArgs2results_[i].first.exercise.type()
== arguments_.exercise.type() &&
cachedArgs2results_[i].first.exercise.dates()
== arguments_.exercise.dates())
{
PlainVanillaPayoff p1 = arguments_.payoff as PlainVanillaPayoff;
PlainVanillaPayoff p2 = cachedArgs2results_[i].first.payoff as PlainVanillaPayoff;
if (p1 != null && p1.strike() == p2.strike() &&
p1.optionType() == p2.optionType())
{
Utils.QL_REQUIRE(arguments_.cashFlow.empty(),
() => "multiple strikes engine does "
+ "not work with discrete dividends");
results_ = cachedArgs2results_[i].second;
return;
}
}
}
HestonProcess process = model_.currentLink().process();
FdmHestonSolver solver = new FdmHestonSolver(
new Handle <HestonProcess>(process),
getSolverDesc(1.5), schemeDesc_,
new Handle <FdmQuantoHelper>(), leverageFct_);
double v0 = process.v0();
double spot = process.s0().currentLink().value();
results_.value = solver.valueAt(spot, v0);
results_.delta = solver.deltaAt(spot, v0);
results_.gamma = solver.gammaAt(spot, v0);
results_.theta = solver.thetaAt(spot, v0);
cachedArgs2results_ = new InitializedList <Pair <DividendVanillaOption.Arguments, DividendVanillaOption.Results> >(strikes_.Count);
StrikedTypePayoff payoff = arguments_.payoff as StrikedTypePayoff;
for (int i = 0; i < strikes_.Count; ++i)
{
cachedArgs2results_[i] = new Pair <DividendVanillaOption.Arguments, OneAssetOption.Results>(new DividendVanillaOption.Arguments(), new OneAssetOption.Results());
cachedArgs2results_[i].first.exercise = arguments_.exercise;
cachedArgs2results_[i].first.payoff = new PlainVanillaPayoff(payoff.optionType(), strikes_[i]);
double d = payoff.strike() / strikes_[i];
cachedArgs2results_[i].second.value = solver.valueAt(spot * d, v0) / d;
cachedArgs2results_[i].second.delta = solver.deltaAt(spot * d, v0);
cachedArgs2results_[i].second.gamma = solver.gammaAt(spot * d, v0) * d;
cachedArgs2results_[i].second.theta = solver.thetaAt(spot * d, v0) / d;
}
}
protected override double blackVolImpl(double t, double strike)
{
HestonProcess process = hestonModel_.link.process();
double df = process.riskFreeRate().link.discount(t, true);
double div = process.dividendYield().link.discount(t, true);
double spotPrice = process.s0().link.value();
double fwd = spotPrice
* process.dividendYield().link.discount(t, true)
/ process.riskFreeRate().link.discount(t, true);
var payoff = new PlainVanillaPayoff(fwd > strike ? Option.Type.Put : Option.Type.Call, strike);
double kappa = hestonModel_.link.kappa();
double theta = hestonModel_.link.theta();
double rho = hestonModel_.link.rho();
double sigma = hestonModel_.link.sigma();
double v0 = hestonModel_.link.v0();
AnalyticHestonEngine.ComplexLogFormula cpxLogFormula = AnalyticHestonEngine.ComplexLogFormula.Gatheral;
AnalyticHestonEngine hestonEnginePtr = null;
double?npv = null;
int evaluations = 0;
AnalyticHestonEngine.doCalculation(
df, div, spotPrice, strike, t,
kappa, theta, sigma, v0, rho,
payoff, integration_, cpxLogFormula,
hestonEnginePtr, ref npv, ref evaluations);
if (npv <= 0.0)
{
return(Math.Sqrt(theta));
}
Brent solver = new Brent();
solver.setMaxEvaluations(10000);
double guess = Math.Sqrt(theta);
double accuracy = Const.QL_EPSILON;
var f = new ImpliedVolHelper(payoff.optionType(), strike, fwd, t, df, npv.Value);
return(solver.solve(f, accuracy, guess, 0.01));
}
public HestonModel(HestonProcess process)
: base(5)
{
process_ = process;
arguments_[0] = new ConstantParameter(process.theta(), new PositiveConstraint());
arguments_[1] = new ConstantParameter(process.kappa(), new PositiveConstraint());
arguments_[2] = new ConstantParameter(process.sigma(), new PositiveConstraint());
arguments_[3] = new ConstantParameter(process.rho(), new BoundaryConstraint(-1.0, 1.0));
arguments_[4] = new ConstantParameter(process.v0(), new PositiveConstraint());
generateArguments();
process_.riskFreeRate().registerWith(update);
process_.dividendYield().registerWith(update);
process_.s0().registerWith(update);
}
public override void calculate()
{
// this is a european option pricer
Utils.QL_REQUIRE(arguments_.exercise.type() == Exercise.Type.European, () => "not an European option");
// plain vanilla
PlainVanillaPayoff payoff = arguments_.payoff as PlainVanillaPayoff;
Utils.QL_REQUIRE(payoff != null, () => "non plain vanilla payoff given");
HestonProcess process = model_.link.process();
double riskFreeDiscount = process.riskFreeRate().link.discount(arguments_.exercise.lastDate());
double dividendDiscount = process.dividendYield().link.discount(arguments_.exercise.lastDate());
double spotPrice = process.s0().link.value();
Utils.QL_REQUIRE(spotPrice > 0.0, () => "negative or null underlying given");
double strikePrice = payoff.strike();
double term = process.time(arguments_.exercise.lastDate());
double?resultsValue = null;
doCalculation(riskFreeDiscount,
dividendDiscount,
spotPrice,
strikePrice,
term,
model_.link.kappa(),
model_.link.theta(),
model_.link.sigma(),
model_.link.v0(),
model_.link.rho(),
payoff,
integration_,
cpxLog_,
this,
ref resultsValue,
ref evaluations_);
results_.value = resultsValue;
}
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;
}
}
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);
}
