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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2009 Klaus Spanderen
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it
under the terms of the QuantLib license. You should have received a
copy of the license along with this program; if not, please email
<quantlib-dev@lists.sf.net>. The license is also available online at
<https://www.quantlib.org/license.shtml>.
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the license for more details.
*/
#include <ql/methods/finitedifferences/meshers/fdmblackscholesmesher.hpp>
#include <ql/methods/finitedifferences/meshers/fdmblackscholesmultistrikemesher.hpp>
#include <ql/methods/finitedifferences/meshers/fdmhestonvariancemesher.hpp>
#include <ql/methods/finitedifferences/meshers/fdmmeshercomposite.hpp>
#include <ql/methods/finitedifferences/meshers/fdmsimpleprocess1dmesher.hpp>
#include <ql/methods/finitedifferences/meshers/uniform1dmesher.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/methods/finitedifferences/stepconditions/fdmstepconditioncomposite.hpp>
#include <ql/methods/finitedifferences/utilities/fdminnervaluecalculator.hpp>
#include <ql/pricingengines/vanilla/analytichestonengine.hpp>
#include <ql/pricingengines/vanilla/fdhestonhullwhitevanillaengine.hpp>
#include <ql/pricingengines/vanilla/fdhestonvanillaengine.hpp>
#include <utility>
namespace QuantLib {
FdHestonHullWhiteVanillaEngine::FdHestonHullWhiteVanillaEngine(
const ext::shared_ptr<HestonModel>& hestonModel,
ext::shared_ptr<HullWhiteProcess> hwProcess,
Real corrEquityShortRate,
Size tGrid,
Size xGrid,
Size vGrid,
Size rGrid,
Size dampingSteps,
bool controlVariate,
const FdmSchemeDesc& schemeDesc)
: GenericModelEngine<HestonModel,
VanillaOption::arguments,
VanillaOption::results>(hestonModel),
hwProcess_(std::move(hwProcess)),
corrEquityShortRate_(corrEquityShortRate), tGrid_(tGrid),
xGrid_(xGrid), vGrid_(vGrid), rGrid_(rGrid), dampingSteps_(dampingSteps),
schemeDesc_(schemeDesc), controlVariate_(controlVariate) {}
FdHestonHullWhiteVanillaEngine::FdHestonHullWhiteVanillaEngine(
const ext::shared_ptr<HestonModel>& hestonModel,
ext::shared_ptr<HullWhiteProcess> hwProcess,
DividendSchedule dividends,
Real corrEquityShortRate,
Size tGrid,
Size xGrid,
Size vGrid,
Size rGrid,
Size dampingSteps,
bool controlVariate,
const FdmSchemeDesc& schemeDesc)
: GenericModelEngine<HestonModel,
VanillaOption::arguments,
VanillaOption::results>(hestonModel),
hwProcess_(std::move(hwProcess)), dividends_(std::move(dividends)),
corrEquityShortRate_(corrEquityShortRate), tGrid_(tGrid),
xGrid_(xGrid), vGrid_(vGrid), rGrid_(rGrid), dampingSteps_(dampingSteps),
schemeDesc_(schemeDesc), controlVariate_(controlVariate) {}
void FdHestonHullWhiteVanillaEngine::calculate() const {
// 1. cache lookup for precalculated results
for (auto& cachedArgs2result : cachedArgs2results_) {
if (cachedArgs2result.first.exercise->type() == arguments_.exercise->type() &&
cachedArgs2result.first.exercise->dates() == arguments_.exercise->dates()) {
ext::shared_ptr<PlainVanillaPayoff> p1 =
ext::dynamic_pointer_cast<PlainVanillaPayoff>(
arguments_.payoff);
ext::shared_ptr<PlainVanillaPayoff> p2 =
ext::dynamic_pointer_cast<PlainVanillaPayoff>(cachedArgs2result.first.payoff);
if ((p1 != nullptr) && p1->strike() == p2->strike() &&
p1->optionType() == p2->optionType()) {
QL_REQUIRE(dividends_.empty(),
"multiple strikes engine does not work with discrete dividends");
results_ = cachedArgs2result.second;
return;
}
}
}
// 2. Mesher
const ext::shared_ptr<HestonProcess> hestonProcess=model_->process();
const Time maturity=hestonProcess->time(arguments_.exercise->lastDate());
// 2.1 The variance mesher
const Size tGridMin = 5;
const ext::shared_ptr<FdmHestonVarianceMesher> varianceMesher(
new FdmHestonVarianceMesher(vGrid_, hestonProcess,
maturity,std::max(tGridMin,tGrid_/50)));
// 2.2 The equity mesher
const ext::shared_ptr<StrikedTypePayoff> payoff =
ext::dynamic_pointer_cast<StrikedTypePayoff>(arguments_.payoff);
QL_REQUIRE(payoff, "wrong payoff type given");
ext::shared_ptr<Fdm1dMesher> equityMesher;
if (strikes_.empty()) {
equityMesher = ext::shared_ptr<Fdm1dMesher>(
new FdmBlackScholesMesher(
xGrid_,
FdmBlackScholesMesher::processHelper(
hestonProcess->s0(), hestonProcess->dividendYield(),
hestonProcess->riskFreeRate(),
varianceMesher->volaEstimate()),
maturity, payoff->strike(),
Null<Real>(), Null<Real>(), 0.0001, 1.5,
std::pair<Real, Real>(payoff->strike(), 0.1),
dividends_));
}
else {
QL_REQUIRE(dividends_.empty(),
"multiple strikes engine does not work with discrete dividends");
equityMesher = ext::shared_ptr<Fdm1dMesher>(
new FdmBlackScholesMultiStrikeMesher(
xGrid_,
FdmBlackScholesMesher::processHelper(
hestonProcess->s0(), hestonProcess->dividendYield(),
hestonProcess->riskFreeRate(),
varianceMesher->volaEstimate()),
maturity, strikes_, 0.0001, 1.5,
std::pair<Real, Real>(payoff->strike(), 0.075)));
}
//2.3 The short rate mesher
const ext::shared_ptr<OrnsteinUhlenbeckProcess> ouProcess(
new OrnsteinUhlenbeckProcess(hwProcess_->a(),hwProcess_->sigma()));
const ext::shared_ptr<Fdm1dMesher> shortRateMesher(
new FdmSimpleProcess1dMesher(rGrid_, ouProcess, maturity));
const ext::shared_ptr<FdmMesher> mesher(
new FdmMesherComposite(equityMesher, varianceMesher,
shortRateMesher));
// 3. Calculator
const ext::shared_ptr<FdmInnerValueCalculator> calculator(
new FdmLogInnerValue(arguments_.payoff, mesher, 0));
// 4. Step conditions
const ext::shared_ptr<FdmStepConditionComposite> conditions =
FdmStepConditionComposite::vanillaComposite(
dividends_, arguments_.exercise,
mesher, calculator,
hestonProcess->riskFreeRate()->referenceDate(),
hestonProcess->riskFreeRate()->dayCounter());
// 5. Boundary conditions
const FdmBoundaryConditionSet boundaries;
// 6. Solver
const FdmSolverDesc solverDesc = { mesher, boundaries, conditions,
calculator, maturity,
tGrid_, dampingSteps_ };
const ext::shared_ptr<FdmHestonHullWhiteSolver> solver(
new FdmHestonHullWhiteSolver(Handle<HestonProcess>(hestonProcess),
Handle<HullWhiteProcess>(hwProcess_),
corrEquityShortRate_,
solverDesc, schemeDesc_));
const Real spot = hestonProcess->s0()->value();
const Real v0 = hestonProcess->v0();
results_.value = solver->valueAt(spot, v0, 0);
results_.delta = solver->deltaAt(spot, v0, 0, spot*0.01);
results_.gamma = solver->gammaAt(spot, v0, 0, spot*0.01);
results_.theta = solver->thetaAt(spot, v0, 0);
cachedArgs2results_.resize(strikes_.size());
for (Size i=0; i < strikes_.size(); ++i) {
cachedArgs2results_[i].first.exercise = arguments_.exercise;
cachedArgs2results_[i].first.payoff =
ext::make_shared<PlainVanillaPayoff>(
payoff->optionType(), strikes_[i]);
const Real d = payoff->strike()/strikes_[i];
VanillaOption::results& results = cachedArgs2results_[i].second;
results.value = solver->valueAt(spot*d, v0, 0)/d;
results.delta = solver->deltaAt(spot*d, v0, 0, spot*d*0.01);
results.gamma = solver->gammaAt(spot*d, v0, 0, spot*d*0.01)*d;
results.theta = solver->thetaAt(spot*d, v0, 0)/d;
}
if (controlVariate_) {
ext::shared_ptr<PricingEngine> analyticEngine(
new AnalyticHestonEngine(*model_, 164));
ext::shared_ptr<Exercise> exercise(
new EuropeanExercise(arguments_.exercise->lastDate()));
VanillaOption option(payoff, exercise);
option.setPricingEngine(analyticEngine);
Real analyticNPV = option.NPV();
ext::shared_ptr<FdHestonVanillaEngine> fdEngine(
new FdHestonVanillaEngine(*model_, tGrid_, xGrid_,
vGrid_, dampingSteps_,
schemeDesc_));
fdEngine->enableMultipleStrikesCaching(strikes_);
option.setPricingEngine(fdEngine);
Real fdNPV = option.NPV();
results_.value += analyticNPV - fdNPV;
for (Size i=0; i < strikes_.size(); ++i) {
VanillaOption controlVariateOption(
ext::shared_ptr<StrikedTypePayoff>(
new PlainVanillaPayoff(payoff->optionType(),
strikes_[i])), exercise);
controlVariateOption.setPricingEngine(analyticEngine);
analyticNPV = controlVariateOption.NPV();
controlVariateOption.setPricingEngine(fdEngine);
fdNPV = controlVariateOption.NPV();
cachedArgs2results_[i].second.value += analyticNPV - fdNPV;
}
}
}
void FdHestonHullWhiteVanillaEngine::update() {
cachedArgs2results_.clear();
GenericModelEngine<HestonModel,
VanillaOption::arguments,
VanillaOption::results>::update();
}
void FdHestonHullWhiteVanillaEngine::enableMultipleStrikesCaching(
const std::vector<Real>& strikes) {
strikes_ = strikes;
update();
}
}
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