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longstaffschwartzpathpricer.hpp

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

/*
 Copyright (C) 2006 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/reference/license.html>.

 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 longstaffschwartzpathpricer.hpp
    \brief Longstaff-Schwarz path pricer for early exercise options
*/

#ifndef quantlib_longstaff_schwartz_path_pricer_hpp
#define quantlib_longstaff_schwartz_path_pricer_hpp

#include <ql/yieldtermstructure.hpp>
#include <ql/Math/functional.hpp>
#include <ql/Math/linearleastsquaresregression.hpp>
#include <ql/MonteCarlo/pathpricer.hpp>
#include <ql/MonteCarlo/earlyexercisepathpricer.hpp>
#include <boost/bind.hpp>
#include <boost/function.hpp>

namespace QuantLib {

    //! Longstaff-Schwarz path pricer for early exercise options
    /*! References:

        Francis Longstaff, Eduardo Schwartz, 2001. Valuing American Options
        by Simulation: A Simple Least-Squares Approach, The Review of
        Financial Studies, Volume 14, No. 1, 113-147

        \ingroup mcarlo

        \test the correctness of the returned value is tested by
              reproducing results available in web/literature
    */
    template <class PathType>
00050     class LongstaffSchwartzPathPricer : public PathPricer<PathType> {
      public:
        typedef typename EarlyExerciseTraits<PathType>::StateType StateType;

        LongstaffSchwartzPathPricer(
            const TimeGrid& times,
            const boost::shared_ptr<EarlyExercisePathPricer<PathType> >& ,
            const boost::shared_ptr<YieldTermStructure>& termStructure);

        Real operator()(const PathType& path) const;
        virtual void calibrate();

      protected:
        bool  calibrationPhase_;
        const boost::shared_ptr<EarlyExercisePathPricer<PathType> >
            pathPricer_;

        boost::scoped_array<Array> coeff_;
        boost::scoped_array<DiscountFactor> dF_;

        mutable std::vector<PathType> paths_;
        const   std::vector<boost::function1<Real, StateType> > v_;
    };

    template <class PathType> inline
    LongstaffSchwartzPathPricer<PathType>::LongstaffSchwartzPathPricer(
        const TimeGrid& times,
        const boost::shared_ptr<EarlyExercisePathPricer<PathType> >&
            pathPricer,
        const boost::shared_ptr<YieldTermStructure>& termStructure)
    : calibrationPhase_(true),
      pathPricer_(pathPricer),
      coeff_     (new Array[times.size()-1]),
      dF_        (new DiscountFactor[times.size()-1]),
      v_         (pathPricer_->basisSystem()) {

        for (Size i=0; i<times.size()-1; ++i) {
            dF_[i] =   termStructure->discount(times[i+1])
                     / termStructure->discount(times[i]);
        }
    }

    template <class PathType> inline
    Real LongstaffSchwartzPathPricer<PathType>::operator()
        (const PathType& path) const {
        if (calibrationPhase_) {
            // store paths for the calibration
            paths_.push_back(path);
            // result doesn't matter
            return 0.0;
        }

        const Size len = EarlyExerciseTraits<PathType>::pathLength(path);
        Real price = (*pathPricer_)(path, len-1);
        for (Size i=len-2; i>0; --i) {
            price*=dF_[i];

            const Real exercise = (*pathPricer_)(path, i);
            if (exercise > 0.0) {
                const StateType regValue = pathPricer_->state(path, i);

                Real continuationValue = 0.0;
                for (Size l=0; l<v_.size(); ++l) {
                    continuationValue += coeff_[i][l] * v_[l](regValue);
                }

                if (continuationValue < exercise) {
                    price = exercise;
                }
            }
        }

        return price*dF_[0];
    }

    template <class PathType> inline
    void LongstaffSchwartzPathPricer<PathType>::calibrate() {
        const Size n = paths_.size();
        Array prices(n), exercise(n);
        const Size len = EarlyExerciseTraits<PathType>::pathLength(paths_[0]);

        std::transform(paths_.begin(), paths_.end(), prices.begin(),
                       boost::bind(&EarlyExercisePathPricer<PathType>
                                     ::operator(),
                                   pathPricer_.get(), _1, len-1));

        for (Size i=len-2; i>0; --i) {
            std::vector<Real>      y;
            std::vector<StateType> x;

            //roll back step
            for (Size j=0; j<n; ++j) {
                exercise[j]=(*pathPricer_)(paths_[j], i);

                if (exercise[j]>0.0) {
                    x.push_back(pathPricer_->state(paths_[j], i));
                    y.push_back(dF_[i]*prices[j]);
                }
            }

            if (v_.size() <=  x.size()) {
                coeff_[i]
                    = LinearLeastSquaresRegression<StateType>(x, y, v_).a();
            }
            else {
            // if number of itm paths is smaller then the number of
            // calibration functions -> no early exercise
                coeff_[i] = Array(v_.size(), 0.0);
            }

            for (Size j=0, k=0; j<n; ++j) {
                prices[j]*=dF_[i];
                if (exercise[j]>0.0) {
                    Real continuationValue = 0.0;
                    for (Size l=0; l<v_.size(); ++l) {
                        continuationValue += coeff_[i][l] * v_[l](x[k]);
                    }
                    if (continuationValue < exercise[j]) {
                        prices[j] = exercise[j];
                    }
                    ++k;
                }
            }
        }

        // remove calibration paths
        paths_.clear();
        // entering the calculation phase
        calibrationPhase_ = false;
    }
}


#endif

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