public HybridHestonHullWhiteProcess(HestonProcess hestonProcess,
HullWhiteForwardProcess hullWhiteProcess,
double corrEquityShortRate,
Discretization discretization = Discretization.BSMHullWhite)
{
hestonProcess_ = hestonProcess;
hullWhiteProcess_ = hullWhiteProcess;
hullWhiteModel_ = new HullWhite(hestonProcess.riskFreeRate(),
hullWhiteProcess.a(),
hullWhiteProcess.sigma());
corrEquityShortRate_ = corrEquityShortRate;
disc_ = discretization;
maxRho_ = Math.Sqrt(1 - hestonProcess.rho() * hestonProcess.rho())
- Math.Sqrt(Const.QL_EPSILON) /* reserve for rounding errors */;
T_ = hullWhiteProcess.getForwardMeasureTime();
endDiscount_ = hestonProcess.riskFreeRate().link.discount(T_);
Utils.QL_REQUIRE(corrEquityShortRate * corrEquityShortRate
+ hestonProcess.rho() * hestonProcess.rho() <= 1.0, () =>
"correlation matrix is not positive definite");
Utils.QL_REQUIRE(hullWhiteProcess.sigma() > 0.0, () =>
"positive vol of Hull White process is required");
}
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);
}
protected override IPricingEngine controlPricingEngine()
{
HybridHestonHullWhiteProcess process = process_ as HybridHestonHullWhiteProcess;
Utils.QL_REQUIRE(process != null, () => "invalid process");
HestonProcess hestonProcess = process.hestonProcess();
HullWhiteForwardProcess hullWhiteProcess = process.hullWhiteProcess();
HestonModel hestonModel = new HestonModel(hestonProcess);
HullWhite hwModel = new HullWhite(hestonProcess.riskFreeRate(),
hullWhiteProcess.a(),
hullWhiteProcess.sigma());
return(new AnalyticHestonHullWhiteEngine(hestonModel, hwModel, 144));
}
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;
}