mc_discr_geom_av_price_heston.hpp

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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
 
/*
 Copyright (C) 2020 Jack Gillett
 
 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 mc_discr_geom_av_price_heston.hpp
    \brief Heston MC engine for discrete geometric average price Asian
*/
 
#ifndef quantlib_mc_discrete_geometric_average_price_asian_heston_engine_hpp
#define quantlib_mc_discrete_geometric_average_price_asian_heston_engine_hpp
 
#include <ql/exercise.hpp>
#include <ql/pricingengines/asian/mcdiscreteasianenginebase.hpp>
#include <ql/processes/hestonprocess.hpp>
#include <utility>
 
namespace QuantLib {
 
    //!  Heston MC pricing engine for discrete geometric average price Asian
    /*!
         By default, the MC discretization will use 1 time step per fixing date, but
         this can be controlled via timeSteps or timeStepsPerYear parameter, which
         will provide additional timesteps. The grid tries to space as evenly as it
         can and does not guarantee to match an exact number of steps, the precise
         grid used can be found in results_.additionalResults["TimeGrid"]
 
         \ingroup asianengines
         \test the correctness of the returned value is tested by
               reproducing results available in literature.
    */
    template <class RNG = PseudoRandom,
              class S = Statistics, class P = HestonProcess>
    class MCDiscreteGeometricAPHestonEngine
        : public MCDiscreteAveragingAsianEngineBase<MultiVariate,RNG,S> {
      public:
        typedef typename MCDiscreteAveragingAsianEngineBase<MultiVariate,RNG,S>::path_generator_type path_generator_type;
        typedef typename MCDiscreteAveragingAsianEngineBase<MultiVariate,RNG,S>::path_pricer_type path_pricer_type;
        typedef typename MCDiscreteAveragingAsianEngineBase<MultiVariate,RNG,S>::stats_type stats_type;
        // constructor
        MCDiscreteGeometricAPHestonEngine(const ext::shared_ptr<P>& process,
                                          bool antitheticVariate,
                                          Size requiredSamples,
                                          Real requiredTolerance,
                                          Size maxSamples,
                                          BigNatural seed,
                                          Size timeSteps = Null<Size>(),
                                          Size timeStepsPerYear = Null<Size>());
      protected:
        ext::shared_ptr<path_pricer_type> pathPricer() const override;
    };
 
 
    template <class RNG = PseudoRandom,
              class S = Statistics, class P = HestonProcess>
    class MakeMCDiscreteGeometricAPHestonEngine {
      public:
        explicit MakeMCDiscreteGeometricAPHestonEngine(ext::shared_ptr<P> process);
        // named parameters
        MakeMCDiscreteGeometricAPHestonEngine& withSamples(Size samples);
        MakeMCDiscreteGeometricAPHestonEngine& withAbsoluteTolerance(Real tolerance);
        MakeMCDiscreteGeometricAPHestonEngine& withMaxSamples(Size samples);
        MakeMCDiscreteGeometricAPHestonEngine& withSeed(BigNatural seed);
        MakeMCDiscreteGeometricAPHestonEngine& withAntitheticVariate(bool b = true);
        MakeMCDiscreteGeometricAPHestonEngine& withSteps(Size steps);
        MakeMCDiscreteGeometricAPHestonEngine& withStepsPerYear(Size steps);
        // conversion to pricing engine
        operator ext::shared_ptr<PricingEngine>() const;
      private:
        ext::shared_ptr<P> process_;
        bool antithetic_ = false;
        Size samples_, maxSamples_, steps_, stepsPerYear_;
        Real tolerance_;
        BigNatural seed_ = 0;
    };
 
    class GeometricAPOHestonPathPricer : public PathPricer<MultiPath> {
      public:
        GeometricAPOHestonPathPricer(Option::Type type,
                                     Real strike,
                                     DiscountFactor discount,
                                     std::vector<Size> fixingIndices,
                                     Real runningProduct = 1.0,
                                     Size pastFixings = 0);
        Real operator()(const MultiPath& multiPath) const override;
 
      private:
        PlainVanillaPayoff payoff_;
        DiscountFactor discount_;
        std::vector<Size> fixingIndices_;
        Real runningProduct_;
        Size pastFixings_;
    };
 
 
    // inline definitions
 
    template <class RNG, class S, class P>
    inline
    MCDiscreteGeometricAPHestonEngine<RNG,S,P>::MCDiscreteGeometricAPHestonEngine(
             const ext::shared_ptr<P>& process,
             bool antitheticVariate,
             Size requiredSamples,
             Real requiredTolerance,
             Size maxSamples,
             BigNatural seed,
             Size timeSteps,
             Size timeStepsPerYear)
    : MCDiscreteAveragingAsianEngineBase<MultiVariate,RNG,S>(process,
                                                             false,
                                                             antitheticVariate,
                                                             false,
                                                             requiredSamples,
                                                             requiredTolerance,
                                                             maxSamples,
                                                             seed,
                                                             timeSteps,
                                                             timeStepsPerYear) {
        QL_REQUIRE(timeSteps == Null<Size>() || timeStepsPerYear == Null<Size>(),
                   "both time steps and time steps per year were provided");
    }
 
    template <class RNG, class S, class P>
    inline ext::shared_ptr<
            typename MCDiscreteGeometricAPHestonEngine<RNG,S,P>::path_pricer_type>
        MCDiscreteGeometricAPHestonEngine<RNG,S,P>::pathPricer() const {
 
        // Keep track of the fixing indices, the path pricer will need to sum only these
        TimeGrid timeGrid = this->timeGrid();
        std::vector<Time> fixingTimes = timeGrid.mandatoryTimes();
        std::vector<Size> fixingIndexes;
        fixingIndexes.reserve(fixingTimes.size());
        for (Real fixingTime : fixingTimes) {
            fixingIndexes.push_back(timeGrid.closestIndex(fixingTime));
        }
 
        ext::shared_ptr<PlainVanillaPayoff> payoff =
            ext::dynamic_pointer_cast<PlainVanillaPayoff>(
                this->arguments_.payoff);
        QL_REQUIRE(payoff, "non-plain payoff given");
 
        ext::shared_ptr<EuropeanExercise> exercise =
            ext::dynamic_pointer_cast<EuropeanExercise>(
                this->arguments_.exercise);
        QL_REQUIRE(exercise, "wrong exercise given");
 
        ext::shared_ptr<P> process =
            ext::dynamic_pointer_cast<P>(this->process_);
        QL_REQUIRE(process, "Heston like process required");
 
        return ext::shared_ptr<typename
            MCDiscreteGeometricAPHestonEngine<RNG,S,P>::path_pricer_type>(
                new GeometricAPOHestonPathPricer(
                    payoff->optionType(),
                    payoff->strike(),
                    process->riskFreeRate()->discount(exercise->lastDate()),
                    fixingIndexes,
                    this->arguments_.runningAccumulator,
                    this->arguments_.pastFixings));
    }
 
    template <class RNG, class S, class P>
    inline MakeMCDiscreteGeometricAPHestonEngine<RNG, S, P>::MakeMCDiscreteGeometricAPHestonEngine(
        ext::shared_ptr<P> process)
    : process_(std::move(process)), samples_(Null<Size>()), maxSamples_(Null<Size>()),
      steps_(Null<Size>()), stepsPerYear_(Null<Size>()), tolerance_(Null<Real>()) {}
 
    template<class RNG, class S, class P>
    inline MakeMCDiscreteGeometricAPHestonEngine<RNG,S,P>&
    MakeMCDiscreteGeometricAPHestonEngine<RNG,S,P>::withSamples(Size samples) {
        QL_REQUIRE(tolerance_ == Null<Real>(),
                   "tolerance already set");
        samples_ = samples;
        return *this;
    }
 
    template <class RNG, class S, class P>
    inline MakeMCDiscreteGeometricAPHestonEngine<RNG,S,P>&
    MakeMCDiscreteGeometricAPHestonEngine<RNG,S,P>::withAbsoluteTolerance(
                                                             Real tolerance) {
        QL_REQUIRE(samples_ == Null<Size>(),
                   "number of samples already set");
        QL_REQUIRE(RNG::allowsErrorEstimate,
                   "chosen random generator policy "
                   "does not allow an error estimate");
        tolerance_ = tolerance;
        return *this;
    }
 
    template <class RNG, class S, class P>
    inline MakeMCDiscreteGeometricAPHestonEngine<RNG,S,P>&
    MakeMCDiscreteGeometricAPHestonEngine<RNG,S,P>::withMaxSamples(Size samples) {
        maxSamples_ = samples;
        return *this;
    }
 
    template <class RNG, class S, class P>
    inline MakeMCDiscreteGeometricAPHestonEngine<RNG,S,P>&
    MakeMCDiscreteGeometricAPHestonEngine<RNG,S,P>::withSeed(BigNatural seed) {
        seed_ = seed;
        return *this;
    }
 
    template <class RNG, class S, class P>
    inline MakeMCDiscreteGeometricAPHestonEngine<RNG,S,P>&
    MakeMCDiscreteGeometricAPHestonEngine<RNG,S,P>::withAntitheticVariate(bool b) {
        antithetic_ = b;
        return *this;
    }
 
    template<class RNG, class S, class P>
    inline MakeMCDiscreteGeometricAPHestonEngine<RNG,S,P>&
    MakeMCDiscreteGeometricAPHestonEngine<RNG,S,P>::withSteps(Size steps) {
        QL_REQUIRE(stepsPerYear_ == Null<Size>(),
                   "number of steps per year already set");
        steps_ = steps;
        return *this;
    }
 
    template<class RNG, class S, class P>
    inline MakeMCDiscreteGeometricAPHestonEngine<RNG,S,P>&
    MakeMCDiscreteGeometricAPHestonEngine<RNG,S,P>::withStepsPerYear(Size steps) {
        QL_REQUIRE(steps_ == Null<Size>(),
                   "number of steps already set");
        stepsPerYear_ = steps;
        return *this;
    }
 
    template <class RNG, class S, class P>
    inline MakeMCDiscreteGeometricAPHestonEngine<RNG,S,P>::operator ext::shared_ptr<PricingEngine>() const {
        return ext::shared_ptr<PricingEngine>(new
            MCDiscreteGeometricAPHestonEngine<RNG,S,P>(process_,
                                                       antithetic_,
                                                       samples_,
                                                       tolerance_,
                                                       maxSamples_,
                                                       seed_,
                                                       steps_,
                                                       stepsPerYear_));
    }
}
 
#endif