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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2005, 2007, 2009, 2014 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 hestonprocess.hpp
\brief Heston stochastic process
*/
#ifndef quantlib_heston_process_hpp
#define quantlib_heston_process_hpp
#include <ql/stochasticprocess.hpp>
#include <ql/termstructures/yieldtermstructure.hpp>
#include <ql/quote.hpp>
namespace QuantLib {
//! Square-root stochastic-volatility Heston process
/*! This class describes the square root stochastic volatility
process governed by
\f[
\begin{array}{rcl}
dS(t, S) &=& \mu S dt + \sqrt{v} S dW_1 \\
dv(t, S) &=& \kappa (\theta - v) dt + \sigma \sqrt{v} dW_2 \\
dW_1 dW_2 &=& \rho dt
\end{array}
\f]
\ingroup processes
*/
class HestonProcess : public StochasticProcess {
public:
enum Discretization { PartialTruncation,
FullTruncation,
Reflection,
NonCentralChiSquareVariance,
QuadraticExponential,
QuadraticExponentialMartingale,
BroadieKayaExactSchemeLobatto,
BroadieKayaExactSchemeLaguerre,
BroadieKayaExactSchemeTrapezoidal };
HestonProcess(Handle<YieldTermStructure> riskFreeRate,
Handle<YieldTermStructure> dividendYield,
Handle<Quote> s0,
Real v0,
Real kappa,
Real theta,
Real sigma,
Real rho,
Discretization d = QuadraticExponentialMartingale);
Size size() const override;
Size factors() const override;
Array initialValues() const override;
Array drift(Time t, const Array& x) const override;
Matrix diffusion(Time t, const Array& x) const override;
Array apply(const Array& x0, const Array& dx) const override;
Array evolve(Time t0, const Array& x0, Time dt, const Array& dw) const override;
Real v0() const { return v0_; }
Real rho() const { return rho_; }
Real kappa() const { return kappa_; }
Real theta() const { return theta_; }
Real sigma() const { return sigma_; }
const Handle<Quote>& s0() const;
const Handle<YieldTermStructure>& dividendYield() const;
const Handle<YieldTermStructure>& riskFreeRate() const;
Time time(const Date&) const override;
// probability densitiy function,
// semi-analytical solution of the Fokker-Planck equation in x=ln(s)
Real pdf(Real x, Real v, Time t, Real eps=1e-3) const;
private:
Real varianceDistribution(Real v, Real dw, Time dt) const;
Handle<YieldTermStructure> riskFreeRate_, dividendYield_;
Handle<Quote> s0_;
Real v0_, kappa_, theta_, sigma_, rho_;
Discretization discretization_;
};
}
#endif
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