qdfpamericanengine.hpp

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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
 
/*
 Copyright (C) 2022 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 qdfpamericanengine.hpp
*/
 
#ifndef quantlib_qd_fp_american_engine_hpp
#define quantlib_qd_fp_american_engine_hpp
 
#include <ql/pricingengines/vanilla/qdplusamericanengine.hpp>
 
namespace QuantLib {
 
    class Integrator;
 
    //! Iteration scheme for fixed-point QD American engine
    class QdFpIterationScheme {
      public:
        virtual Size getNumberOfChebyshevInterpolationNodes() const = 0;
        virtual Size getNumberOfNaiveFixedPointSteps() const = 0;
        virtual Size getNumberOfJacobiNewtonFixedPointSteps() const = 0;
 
        virtual ext::shared_ptr<Integrator> getFixedPointIntegrator() const = 0;
        virtual ext::shared_ptr<Integrator> getExerciseBoundaryToPriceIntegrator() const = 0;
 
        virtual ~QdFpIterationScheme() = default;
    };
 
    //! Gauss-Legendre (l,m,n)-p Scheme
    /*! \param l  order of Gauss-Legendre integration within every fixed point iteration step
        \param m  fixed point iteration steps, first step is a partial Jacobi-Newton,
                  the rest are naive Richardson fixed point iterations
        \param n  number of Chebyshev nodes to interpolate the exercise boundary
        \param p  order of Gauss-Legendre integration in final conversion of the
                  exercise boundary into option prices
    */
    class QdFpLegendreScheme: public QdFpIterationScheme {
      public:
        QdFpLegendreScheme(Size l, Size m, Size n, Size p);
 
        Size getNumberOfChebyshevInterpolationNodes() const override;
        Size getNumberOfNaiveFixedPointSteps() const override;
        Size getNumberOfJacobiNewtonFixedPointSteps() const override;
 
        ext::shared_ptr<Integrator> getFixedPointIntegrator() const override;
        ext::shared_ptr<Integrator> getExerciseBoundaryToPriceIntegrator() const override;
 
      private:
        const Size m_, n_;
        const ext::shared_ptr<Integrator> fpIntegrator_;
        const ext::shared_ptr<Integrator> exerciseBoundaryIntegrator_;
    };
 
    //! Legendre-Tanh-Sinh (l,m,n)-eps Scheme
    /*! \param l    order of Gauss-Legendre integration within every fixed point iteration step
        \param m    fixed point iteration steps, first step is a partial Jacobi-Newton,
                    the rest are naive Richardson fixed point iterations
        \param n    number of Chebyshev nodes to interpolate the exercise boundary
        \param eps  final conversion of the exercise boundary into option prices
                    is carried out by a tanh-sinh integration with accuracy eps
    */
    class QdFpLegendreTanhSinhScheme: public QdFpLegendreScheme {
      public:
        QdFpLegendreTanhSinhScheme(Size l, Size m, Size n, Real eps);
 
        ext::shared_ptr<Integrator> getExerciseBoundaryToPriceIntegrator() const override;
 
      private:
        const Real eps_;
    };
 
    //! tanh-sinh (m,n)-eps Scheme
    /*! \param m    fixed point iteration steps, first step is a partial Jacobi-Newton,
                    the rest are naive Richardson fixed point iterations
        \param n    number of Chebyshev nodes to interpolate the exercise boundary
        \param eps  tanh-sinh integration precision
    */
    class QdFpTanhSinhIterationScheme: public QdFpIterationScheme {
      public:
        QdFpTanhSinhIterationScheme(Size m, Size n, Real eps);
 
        Size getNumberOfChebyshevInterpolationNodes() const override;
        Size getNumberOfNaiveFixedPointSteps() const override;
        Size getNumberOfJacobiNewtonFixedPointSteps() const override;
 
        ext::shared_ptr<Integrator> getFixedPointIntegrator() const override;
        ext::shared_ptr<Integrator> getExerciseBoundaryToPriceIntegrator() const override;
      private:
        const Size m_, n_;
        const ext::shared_ptr<Integrator> integrator_;
    };
 
 
    //! High performance/precision American engine based on fixed point iteration for the exercise boundary
    /*! References:
        Leif Andersen, Mark Lake and Dimitri Offengenden (2015)
        "High Performance American Option Pricing",
        https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2547027
 
        Leif Andersen, Mark Lake (2021)
        "Fast American Option Pricing: The Double-Boundary Case"
 
        https://onlinelibrary.wiley.com/doi/abs/10.1002/wilm.10969
    */
    class QdFpAmericanEngine : public detail::QdPutCallParityEngine {
      public:
        enum FixedPointEquation { FP_A, FP_B, Auto };
 
        explicit QdFpAmericanEngine(
          ext::shared_ptr<GeneralizedBlackScholesProcess> bsProcess,
          ext::shared_ptr<QdFpIterationScheme> iterationScheme = accurateScheme(),
          FixedPointEquation fpEquation = Auto);
 
        static ext::shared_ptr<QdFpIterationScheme> fastScheme();
        static ext::shared_ptr<QdFpIterationScheme> accurateScheme();
        static ext::shared_ptr<QdFpIterationScheme> highPrecisionScheme();
 
      protected:
        Real calculatePut(
            Real S, Real K, Rate r, Rate q, Volatility vol, Time T) const override;
 
      private:
        const ext::shared_ptr<QdFpIterationScheme> iterationScheme_;
        const FixedPointEquation fpEquation_;
    };
 
}
 
#endif