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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2017 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 coshestonengine.hpp
\brief Heston engine based on Fourier-Cosine series expansions
*/
#ifndef quantlib_cos_heston_engine_hpp
#define quantlib_cos_heston_engine_hpp
#include <ql/models/equity/hestonmodel.hpp>
#include <ql/instruments/vanillaoption.hpp>
#include <ql/pricingengines/genericmodelengine.hpp>
#include <complex>
namespace QuantLib {
//! COS-method Heston engine based on efficient Fourier series expansions
/*! References:
F. Fang, C.W. Oosterlee: A Novel Pricing Method for European Ooptions
based on Fourier-Cosine Series Expansions,
http://ta.twi.tudelft.nl/mf/users/oosterle/oosterlee/COS.pdf
Fabien Le Floc'h: Fourier Integration and Stochastic Volatility
Calibration,
https://papers.ssrn.com/sol3/papers2.cfm?abstract_id=2362968
\ingroup vanillaengines
\test the correctness of the returned value is tested by
reproducing results available in web/literature
and comparison with Black pricing.
*/
class COSHestonEngine
: public GenericModelEngine<HestonModel,
VanillaOption::arguments,
VanillaOption::results> {
public:
explicit COSHestonEngine(const ext::shared_ptr<HestonModel>& model,
Real L = 16, Size N=200);
void update() override;
void calculate() const override;
// normalized characteristic function
std::complex<Real> chF(Real u, Real t) const;
Real c1(Time t) const;
Real c2(Time t) const;
Real c3(Time t) const;
Real c4(Time t) const;
Real mu(Time t) const;
Real var(Time t) const;
Real skew(Time t) const;
Real kurtosis(Time t) const;
private:
Real muT(Time t) const;
const Real L_;
const Size N_;
Real kappa_, theta_, sigma_, rho_, v0_;
};
}
#endif
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