/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */

/*

 Copyright (C) 2020 Lew Wei Hao

 Copyright (C) 2021 Magnus Mencke

 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 coxingersollrossprocess.hpp

    \brief CoxIngersollRoss process

*/

#ifndef quantlib_coxingersollross_process_hpp

#define quantlib_coxingersollross_process_hpp

#include <ql/stochasticprocess.hpp>

#include <ql/math/distributions/normaldistribution.hpp>

namespace QuantLib {

    //! CoxIngersollRoss process class

    /*! This class describes the CoxIngersollRoss process governed by

        \f[

            dx(t) = k (\theta - x(t)) dt + \sigma \sqrt{x(t)} dW(t).

        \f]

        The process is discretized using the Quadratic Exponential scheme.

        For details see Leif Andersen,

        Efficient Simulation of the Heston Stochastic Volatility Model.

        \ingroup processes

    */

    class CoxIngersollRossProcess : public StochasticProcess1D {

      public:

        CoxIngersollRossProcess(Real speed,

                                 Volatility vol,

                                 Real x0 = 0.0,

                                 Real level = 0.0);

        //@{

        Real drift(Time t, Real x) const override;

        Real diffusion(Time t, Real x) const override;

        Real expectation(Time t0, Real x0, Time dt) const override;

        Real stdDeviation(Time t0, Real x0, Time dt) const override;

        //@}

        Real x0() const override;

        Real speed() const;

        Real volatility() const;

        Real level() const;

        Real variance(Time t0, Real x0, Time dt) const override;

        Real evolve (Time t0,

                     Real x0,

                     Time dt,

                     Real dw) const override;

      private:

        Real x0_, speed_, level_;

        Volatility volatility_;

    };

    // inline

    inline Real CoxIngersollRossProcess::x0() const {

        return x0_;

    }

    inline Real CoxIngersollRossProcess::speed() const {

        return speed_;

    }

    inline Real CoxIngersollRossProcess::volatility() const {

        return volatility_;

    }

    inline Real CoxIngersollRossProcess::level() const {

        return level_;

    }

    inline Real CoxIngersollRossProcess::drift(Time, Real x) const {

        return speed_ * (level_ - x);

    }

    inline Real CoxIngersollRossProcess::diffusion(Time, Real) const {

        return volatility_;

    }

    inline Real CoxIngersollRossProcess::expectation(Time, Real x0,

                                               Time dt) const {

        return level_ + (x0 - level_) * std::exp(-speed_*dt);

    }

    inline Real CoxIngersollRossProcess::stdDeviation(Time t, Real x0,

                                                Time dt) const {

        return std::sqrt(variance(t,x0,dt));

    }

    inline Real CoxIngersollRossProcess::evolve (Time t0,

      Real x0,

                                    Time dt,

                                    Real dw) const {

        Real result;

        const Real ex = std::exp(-speed_*dt);

        const Real m  =  level_+(x0-level_)*ex;

        const Real s2 =  x0*volatility_*volatility_*ex/speed_*(1-ex)

                       + level_*volatility_*volatility_/(2*speed_)*(1-ex)*(1-ex);

        const Real psi = s2/(m*m);

        if (psi <= 1.5) {

            const Real b2 = 2/psi-1+std::sqrt(2/psi*(2/psi-1));

            const Real b  = std::sqrt(b2);

            const Real a  = m/(1+b2);

            result = a*(b+dw)*(b+dw);

        }

        else {

            const Real p = (psi-1)/(psi+1);

            const Real beta = (1-p)/m;

            const Real u = CumulativeNormalDistribution()(dw);

            result = ((u <= p) ? 0.0 : Real(std::log((1-p)/(1-u))/beta));

        }

        return result;

    }

}

#endif