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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2014, 2015 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.
*/
/*! \file analyticpdfhestonengine.cpp
\brief Analytic engine for arbitrary European payoffs under the Heston model
*/
#include <ql/pricingengines/vanilla/analyticpdfhestonengine.hpp>
#include <ql/math/integrals/gausslobattointegral.hpp>
#include <ql/methods/finitedifferences/utilities/hestonrndcalculator.hpp>
#include <utility>
namespace QuantLib {
AnalyticPDFHestonEngine::AnalyticPDFHestonEngine(ext::shared_ptr<HestonModel> model,
Real integrationEps_,
Size maxIntegrationIterations)
: maxIntegrationIterations_(maxIntegrationIterations), integrationEps_(integrationEps_),
model_(std::move(model)) {}
void AnalyticPDFHestonEngine::calculate() const {
// this is an European option pricer
QL_REQUIRE(arguments_.exercise->type() == Exercise::European,
"not an European option");
const ext::shared_ptr<HestonProcess>& process = model_->process();
const Time t = process->time(arguments_.exercise->lastDate());
const Real xMax = 8.0 * std::sqrt(process->theta()*t
+ (process->v0() - process->theta())
*(1-std::exp(-process->kappa()*t))/process->kappa());
const Real x0 = std::log(process->s0()->value());
const Real rD = process->riskFreeRate()->discount(t);
const Real qD = process->dividendYield()->discount(t);
const Real drift = x0 + std::log(rD/qD);
results_.value = GaussLobattoIntegral(maxIntegrationIterations_, integrationEps_)(
[&](Real _x){ return weightedPayoff(_x, t); },
-xMax+drift, xMax+drift);
}
Real AnalyticPDFHestonEngine::Pv(Real x_t, Time t) const {
return HestonRNDCalculator(
model_->process(), integrationEps_, maxIntegrationIterations_)
.pdf(x_t, t);
}
Real AnalyticPDFHestonEngine::cdf(Real s, Time t) const {
const Real x_t = std::log(s);
return HestonRNDCalculator(
model_->process(), integrationEps_, maxIntegrationIterations_)
.cdf(x_t, t);
}
Real AnalyticPDFHestonEngine::weightedPayoff(Real x_t, Time t) const {
const DiscountFactor rD
= model_->process()->riskFreeRate()->discount(t);
const Real s_t = std::exp(x_t);
const Real payoff = (*arguments_.payoff)(s_t);
return (payoff != 0.0) ? payoff*Pv(x_t, t)*rD : Real(0.0);
}
}
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