hestonprocess.hpp

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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
 <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.
*/
 
/*! \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