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

/*
 Copyright (C) 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 analyticpdfhestonengine.hpp
    \brief Analytic engine for arbitrary European payoffs under the Heston model
*/

#ifndef quantlib_analytic_pdf_heston_engine_hpp
#define quantlib_analytic_pdf_heston_engine_hpp

#include <ql/instruments/vanillaoption.hpp>
#include <ql/models/equity/hestonmodel.hpp>
#include <ql/pricingengines/genericmodelengine.hpp>

namespace QuantLib {

    //! Analytic engine for arbitrary European payoffs under the Heston model

    /*! References:

        The formulas are taken from A. Dragulescu, V. Yakovenko, 2002.
        Probability distribution of returns in the Heston model
        with stochastic volatility.
        http://arxiv.org/pdf/cond-mat/0203046.pdf

        \test the correctness of the returned value is tested by
              reproducing digital prices using call spreads and the
              AnalyticHestonEngine.

    */
    class AnalyticPDFHestonEngine
       : public GenericModelEngine<HestonModel,
                                   VanillaOption::arguments,
                                   VanillaOption::results> {
      public:
        explicit AnalyticPDFHestonEngine(ext::shared_ptr<HestonModel> model,
                                         Real gaussLobattoEps = 1e-6,
                                         Size gaussLobattoIntegrationOrder = 10000UL);
        void calculate() const override;


        // probability in x_t = ln(s_t)
        Real Pv(Real x_t, Time t) const;

        // cumulative distribution function Pr(x < X)
        Real cdf(Real X, Time t) const;

      private:
        Real weightedPayoff(Real x_t, Time t) const;

        const Size maxIntegrationIterations_;
        const Real integrationEps_;

        const ext::shared_ptr<HestonModel> model_;
    };
}


#endif
