/* -*- 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