analyticptdhestonengine.hpp

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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
 
/*
 Copyright (C) 2010, 2017 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 analyticptdhestonengine.hpp
    \brief analytic piecewise time dependent Heston-model engine
*/
 
#ifndef quantlib_analytic_piecewise_time_dependent_heston_engine_hpp
#define quantlib_analytic_piecewise_time_dependent_heston_engine_hpp
 
#include <ql/instruments/vanillaoption.hpp>
#include <ql/pricingengines/vanilla/analytichestonengine.hpp>
#include <ql/models/equity/piecewisetimedependenthestonmodel.hpp>
 
 
namespace QuantLib {
 
    //! analytic piecewise constant time dependent Heston-model engine
 
    /*! References:
 
        Heston, Steven L., 1993. A Closed-Form Solution for Options
        with Stochastic Volatility with Applications to Bond and
        Currency Options.  The review of Financial Studies, Volume 6,
        Issue 2, 327-343.
 
        J. Gatheral, The Volatility Surface: A Practitioner's Guide,
        Wiley Finance
 
        A. Elices, Models with time-dependent parameters using 
        transform methods: application to Heston’s model,
        http://arxiv.org/pdf/0708.2020
 
        \ingroup vanillaengines
    */
    class AnalyticPTDHestonEngine
        : public GenericModelEngine<PiecewiseTimeDependentHestonModel,
                                    VanillaOption::arguments,
                                    VanillaOption::results> {
      public:
        enum ComplexLogFormula { Gatheral, AndersenPiterbarg };
        typedef AnalyticHestonEngine::Integration Integration;
 
        // Simple to use constructor: Using adaptive
        // Gauss-Lobatto integration and Gatheral's version of complex log.
        // Be aware: using a too large number for maxEvaluations might result
        // in a stack overflow as the Lobatto integration is a recursive
        // algorithm.
        AnalyticPTDHestonEngine(
            const ext::shared_ptr<PiecewiseTimeDependentHestonModel>& model,
            Real relTolerance, Size maxEvaluations);
 
        // Constructor using Laguerre integration
        // and Gatheral's version of complex log.
        explicit AnalyticPTDHestonEngine(
            const ext::shared_ptr<PiecewiseTimeDependentHestonModel>& model,
            Size integrationOrder = 144);
 
        // Constructor giving full control over Fourier integration algorithm
        AnalyticPTDHestonEngine(
            const ext::shared_ptr<PiecewiseTimeDependentHestonModel>& model,
            ComplexLogFormula cpxLog,
            const Integration& itg,
            Real andersenPiterbargEpsilon = 1e-8);
 
 
        void calculate() const override;
        Size numberOfEvaluations() const;
 
        // normalized characteristic function
        std::complex<Real> chF(const std::complex<Real>& z, Time t) const;
        std::complex<Real> lnChF(const std::complex<Real>& z, Time t) const;
 
      private:
        class Fj_Helper;
        class AP_Helper;
        
        mutable Size evaluations_;
        const ComplexLogFormula cpxLog_;
        const ext::shared_ptr<Integration> integration_;
        const Real andersenPiterbargEpsilon_;
    };
}
 
#endif