mcamericanbasketengine.hpp

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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
 
/*
 Copyright (C) 2004 Neil Firth
 Copyright (C) 2006 Klaus Spanderen
 Copyright (C) 2007, 2008 StatPro Italia srl
 
 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 mcamericanbasketengine.hpp
    \brief Least-square Monte Carlo engines
*/
 
#ifndef quantlib_american_basket_montecarlo_engine_hpp
#define quantlib_american_basket_montecarlo_engine_hpp
 
#include <ql/exercise.hpp>
#include <ql/functional.hpp>
#include <ql/instruments/basketoption.hpp>
#include <ql/methods/montecarlo/lsmbasissystem.hpp>
#include <ql/pricingengines/mclongstaffschwartzengine.hpp>
#include <ql/processes/blackscholesprocess.hpp>
#include <ql/processes/stochasticprocessarray.hpp>
#include <ql/qldefines.hpp>
#include <utility>
 
namespace QuantLib {
 
    //! least-square Monte Carlo engine
    /*! \warning This method is intrinsically weak for out-of-the-money
                 options.
 
        \ingroup basketengines
    */
    template <class RNG = PseudoRandom>
    class MCAmericanBasketEngine
        : public MCLongstaffSchwartzEngine<BasketOption::engine,
                                           MultiVariate,RNG> {
      public:
        MCAmericanBasketEngine(const ext::shared_ptr<StochasticProcessArray>&,
                               Size timeSteps,
                               Size timeStepsPerYear,
                               bool brownianBridge,
                               bool antitheticVariate,
                               Size requiredSamples,
                               Real requiredTolerance,
                               Size maxSamples,
                               BigNatural seed,
                               Size nCalibrationSamples = Null<Size>(),
                               Size polynomialOrder = 2,
                               LsmBasisSystem::PolynomialType polynomialType = LsmBasisSystem::Monomial);
      protected:
        ext::shared_ptr<LongstaffSchwartzPathPricer<MultiPath> > lsmPathPricer() const override;
 
      private:
        const Size polynomialOrder_;
        const LsmBasisSystem::PolynomialType polynomialType_;
    };
 
 
    //! Monte Carlo American basket-option engine factory
    template <class RNG = PseudoRandom>
    class MakeMCAmericanBasketEngine {
      public:
        MakeMCAmericanBasketEngine(ext::shared_ptr<StochasticProcessArray>);
        // named parameters
        MakeMCAmericanBasketEngine& withSteps(Size steps);
        MakeMCAmericanBasketEngine& withStepsPerYear(Size steps);
        MakeMCAmericanBasketEngine& withBrownianBridge(bool b = true);
        MakeMCAmericanBasketEngine& withAntitheticVariate(bool b = true);
        MakeMCAmericanBasketEngine& withSamples(Size samples);
        MakeMCAmericanBasketEngine& withAbsoluteTolerance(Real tolerance);
        MakeMCAmericanBasketEngine& withMaxSamples(Size samples);
        MakeMCAmericanBasketEngine& withSeed(BigNatural seed);
        MakeMCAmericanBasketEngine& withCalibrationSamples(Size samples);
        MakeMCAmericanBasketEngine& withPolynomialOrder(Size polynmOrder);
        MakeMCAmericanBasketEngine& withBasisSystem(LsmBasisSystem::PolynomialType polynomialType);
 
        // conversion to pricing engine
        operator ext::shared_ptr<PricingEngine>() const;
      private:
        ext::shared_ptr<StochasticProcessArray> process_;
        bool brownianBridge_ = false, antithetic_ = false;
        Size steps_, stepsPerYear_, samples_, maxSamples_, calibrationSamples_,
            polynomialOrder_ = 2;
        LsmBasisSystem::PolynomialType polynomialType_ = LsmBasisSystem::Monomial;
        Real tolerance_;
        BigNatural seed_ = 0;
    };
 
 
    class AmericanBasketPathPricer
        : public EarlyExercisePathPricer<MultiPath>  {
      public:
        AmericanBasketPathPricer(
            Size assetNumber,
            ext::shared_ptr<Payoff> payoff,
            Size polynomialOrder = 2,
            LsmBasisSystem::PolynomialType polynomialType = LsmBasisSystem::Monomial);
 
        Array state(const MultiPath& path, Size t) const override;
        Real operator()(const MultiPath& path, Size t) const override;
 
        std::vector<ext::function<Real(Array)> > basisSystem() const override;
 
      protected:
        Real payoff(const Array& state) const;
 
        const Size assetNumber_;
        const ext::shared_ptr<Payoff> payoff_;
 
        Real scalingValue_ = 1.0;
        std::vector<ext::function<Real(Array)> > v_;
    };
 
    template <class RNG> inline
    MCAmericanBasketEngine<RNG>::MCAmericanBasketEngine(
                   const ext::shared_ptr<StochasticProcessArray>& processes,
                   Size timeSteps,
                   Size timeStepsPerYear,
                   bool brownianBridge,
                   bool antitheticVariate,
                   Size requiredSamples,
                   Real requiredTolerance,
                   Size maxSamples,
                   BigNatural seed,
                   Size nCalibrationSamples,
                   Size polynomialOrder,
                   LsmBasisSystem::PolynomialType polynomialType)
        : MCLongstaffSchwartzEngine<BasketOption::engine,
                                    MultiVariate,RNG>(processes,
                                                      timeSteps,
                                                      timeStepsPerYear,
                                                      brownianBridge,
                                                      antitheticVariate,
                                                      false,
                                                      requiredSamples,
                                                      requiredTolerance,
                                                      maxSamples,
                                                      seed,
                                                      nCalibrationSamples),
          polynomialOrder_(polynomialOrder), polynomialType_(polynomialType) {}
 
    template <class RNG>
    inline ext::shared_ptr<LongstaffSchwartzPathPricer<MultiPath> >
    MCAmericanBasketEngine<RNG>::lsmPathPricer() const {
 
        ext::shared_ptr<StochasticProcessArray> processArray =
            ext::dynamic_pointer_cast<StochasticProcessArray>(
                                                              this->process_);
        QL_REQUIRE(processArray && processArray->size()>0,
                   "Stochastic process array required");
 
        ext::shared_ptr<GeneralizedBlackScholesProcess> process =
            ext::dynamic_pointer_cast<GeneralizedBlackScholesProcess>(
               processArray->process(0));
        QL_REQUIRE(process, "generalized Black-Scholes process required");
 
        ext::shared_ptr<EarlyExercise> exercise =
            ext::dynamic_pointer_cast<EarlyExercise>(
                this->arguments_.exercise);
        QL_REQUIRE(exercise, "wrong exercise given");
        QL_REQUIRE(!exercise->payoffAtExpiry(),
                   "payoff at expiry not handled");
 
        ext::shared_ptr<AmericanBasketPathPricer> earlyExercisePathPricer(
            new AmericanBasketPathPricer(processArray->size(),
                                         this->arguments_.payoff,
                                         polynomialOrder_,
                                         polynomialType_));
 
        return ext::make_shared<LongstaffSchwartzPathPricer<MultiPath> > (
             
                     this->timeGrid(),
                     earlyExercisePathPricer,
                     *(process->riskFreeRate()));
    }
 
 
    template <class RNG>
    inline MakeMCAmericanBasketEngine<RNG>::MakeMCAmericanBasketEngine(
        ext::shared_ptr<StochasticProcessArray> process)
    : process_(std::move(process)), steps_(Null<Size>()), stepsPerYear_(Null<Size>()),
      samples_(Null<Size>()), maxSamples_(Null<Size>()), calibrationSamples_(Null<Size>()),
      tolerance_(Null<Real>()) {}
 
    template <class RNG>
    inline MakeMCAmericanBasketEngine<RNG>&
    MakeMCAmericanBasketEngine<RNG>::withSteps(Size steps) {
        steps_ = steps;
        return *this;
    }
 
    template <class RNG>
    inline MakeMCAmericanBasketEngine<RNG>&
    MakeMCAmericanBasketEngine<RNG>::withStepsPerYear(Size steps) {
        stepsPerYear_ = steps;
        return *this;
    }
 
    template <class RNG>
    inline MakeMCAmericanBasketEngine<RNG>&
    MakeMCAmericanBasketEngine<RNG>::withBrownianBridge(bool brownianBridge) {
        brownianBridge_ = brownianBridge;
        return *this;
    }
 
    template <class RNG>
    inline MakeMCAmericanBasketEngine<RNG>&
    MakeMCAmericanBasketEngine<RNG>::withAntitheticVariate(bool b) {
        antithetic_ = b;
        return *this;
    }
 
    template <class RNG>
    inline MakeMCAmericanBasketEngine<RNG>&
    MakeMCAmericanBasketEngine<RNG>::withSamples(Size samples) {
        QL_REQUIRE(tolerance_ == Null<Real>(),
                   "tolerance already set");
        samples_ = samples;
        return *this;
    }
 
    template <class RNG>
    inline MakeMCAmericanBasketEngine<RNG>&
    MakeMCAmericanBasketEngine<RNG>::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>
    inline MakeMCAmericanBasketEngine<RNG>&
    MakeMCAmericanBasketEngine<RNG>::withMaxSamples(Size samples) {
        maxSamples_ = samples;
        return *this;
    }
 
    template <class RNG>
    inline MakeMCAmericanBasketEngine<RNG>&
    MakeMCAmericanBasketEngine<RNG>::withSeed(BigNatural seed) {
        seed_ = seed;
        return *this;
    }
 
    template <class RNG>
    inline MakeMCAmericanBasketEngine<RNG>&
    MakeMCAmericanBasketEngine<RNG>::withCalibrationSamples(Size samples) {
        calibrationSamples_ = samples;
        return *this;
    }
 
    template <class RNG>
    inline MakeMCAmericanBasketEngine<RNG>&
    MakeMCAmericanBasketEngine<RNG>::withPolynomialOrder(Size polynomialOrder) {
        polynomialOrder_ = polynomialOrder;
        return *this;
    }
 
    template <class RNG>
    inline MakeMCAmericanBasketEngine<RNG>&
    MakeMCAmericanBasketEngine<RNG>::withBasisSystem(LsmBasisSystem::PolynomialType polynomialType) {
        polynomialType_ = polynomialType;
        return *this;
    }
 
    template <class RNG>
    inline
    MakeMCAmericanBasketEngine<RNG>::operator
    ext::shared_ptr<PricingEngine>() const {
        QL_REQUIRE(steps_ != Null<Size>() || stepsPerYear_ != Null<Size>(),
                   "number of steps not given");
        QL_REQUIRE(steps_ == Null<Size>() || stepsPerYear_ == Null<Size>(),
                   "number of steps overspecified");
        return ext::shared_ptr<PricingEngine>(new
            MCAmericanBasketEngine<RNG>(process_,
                                        steps_,
                                        stepsPerYear_,
                                        brownianBridge_,
                                        antithetic_,
                                        samples_,
                                        tolerance_,
                                        maxSamples_,
                                        seed_,
                                        calibrationSamples_,
                                        polynomialOrder_,
                                        polynomialType_));
    }
 
}
 
#endif