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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2010 Adrian O' Neill
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
<http://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/experimental/variancegamma/fftvariancegammaengine.hpp>
#include <ql/exercise.hpp>
#include <complex>
namespace QuantLib {
FFTVarianceGammaEngine::FFTVarianceGammaEngine(
const boost::shared_ptr<VarianceGammaProcess>& process, Real logStrikeSpacing)
: FFTEngine(process, logStrikeSpacing)
{
}
std::auto_ptr<FFTEngine> FFTVarianceGammaEngine::clone() const
{
boost::shared_ptr<VarianceGammaProcess> process =
boost::dynamic_pointer_cast<VarianceGammaProcess>(process_);
return std::auto_ptr<FFTEngine>(new FFTVarianceGammaEngine(process, lambda_));
}
void FFTVarianceGammaEngine::precalculateExpiry(Date d)
{
boost::shared_ptr<VarianceGammaProcess> process =
boost::dynamic_pointer_cast<VarianceGammaProcess>(process_);
dividendDiscount_ =
process->dividendYield()->discount(d);
riskFreeDiscount_ =
process->riskFreeRate()->discount(d);
DayCounter rfdc = process->riskFreeRate()->dayCounter();
t_ = rfdc.yearFraction(process->riskFreeRate()->referenceDate(), d);
sigma_ = process->sigma();
nu_ = process->nu();
theta_ = process->theta();
}
std::complex<Real> FFTVarianceGammaEngine::complexFourierTransform(std::complex<Real> u) const
{
Real s = process_->x0();
std::complex<Real> i1(0, 1);
Real omega = std::log(1.0 - theta_ * nu_ - sigma_*sigma_ * nu_ / 2.0) / nu_;
std::complex<Real> phi = std::exp(i1 * u * (std::log(s) + omega * t_))
* std::pow(dividendDiscount_/ riskFreeDiscount_, i1 * u);
phi = phi * (std::pow((1.0 - i1 * theta_ * nu_ * u + sigma_*sigma_ * nu_ * u*u / 2.0), (-t_ / nu_)));
return phi;
}
Real FFTVarianceGammaEngine::discountFactor(Date d) const
{
boost::shared_ptr<VarianceGammaProcess> process =
boost::dynamic_pointer_cast<VarianceGammaProcess>(process_);
return process->riskFreeRate()->discount(d);
}
Real FFTVarianceGammaEngine::dividendYield(Date d) const
{
boost::shared_ptr<VarianceGammaProcess> process =
boost::dynamic_pointer_cast<VarianceGammaProcess>(process_);
return process->dividendYield()->discount(d);
}
}
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