fdminnervaluecalculator.cpp

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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
 
/*
 Copyright (C) 2008 Andreas Gaida
 Copyright (C) 2008, 2009 Ralph Schreyer
 Copyright (C) 2008, 2009 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 fdminnervaluecalculator.cpp
    \brief layer of abstraction to calculate the inner value
*/
 
#include <ql/instruments/basketoption.hpp>
#include <ql/math/integrals/simpsonintegral.hpp>
#include <ql/methods/finitedifferences/meshers/fdmmesher.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/methods/finitedifferences/utilities/fdminnervaluecalculator.hpp>
#include <ql/payoff.hpp>
#include <deque>
#include <utility>
 
namespace QuantLib {
 
    namespace {
        struct mapped_payoff {
            explicit mapped_payoff(
                const Payoff& payoff,
                const ext::function<Real(Real)>& gridMapping)
            : payoff(payoff), gridMapping_(gridMapping) {}
 
            Real operator()(Real x) const { return payoff(gridMapping_(x)); }
 
            const Payoff& payoff;
            const ext::function<Real(Real)>& gridMapping_;
        };
    }
 
    FdmCellAveragingInnerValue::FdmCellAveragingInnerValue(ext::shared_ptr<Payoff> payoff,
                                                           ext::shared_ptr<FdmMesher> mesher,
                                                           Size direction,
                                                           ext::function<Real(Real)> gridMapping)
    : payoff_(std::move(payoff)), mesher_(std::move(mesher)), direction_(direction),
      gridMapping_(std::move(gridMapping)) {}
 
    Real FdmCellAveragingInnerValue::innerValue(const FdmLinearOpIterator& iter, Time) {
        const Real loc = mesher_->location(iter, direction_);
        return (*payoff_)(gridMapping_(loc));
    }
 
    Real FdmCellAveragingInnerValue::avgInnerValue(const FdmLinearOpIterator& iter, Time t) {
        if (avgInnerValues_.empty()) {
            // calculate caching values
            avgInnerValues_.resize(mesher_->layout()->dim()[direction_]);
            std::deque<bool> initialized(avgInnerValues_.size(), false);
 
            for (const auto& i : *mesher_->layout()) {
                const Size xn = i.coordinates()[direction_];
                if (!initialized[xn]) {
                    initialized[xn]     = true;
                    avgInnerValues_[xn] = avgInnerValueCalc(i, t);
                }
            }
        }
 
        return avgInnerValues_[iter.coordinates()[direction_]];
    }
 
    Real FdmCellAveragingInnerValue::avgInnerValueCalc(const FdmLinearOpIterator& iter, Time t) {
        const Size dim = mesher_->layout()->dim()[direction_];
        const Size coord = iter.coordinates()[direction_];
 
        if (coord == 0 || coord == dim-1)
            return innerValue(iter, t);
 
        const Real loc = mesher_->location(iter,direction_);
        const Real a = loc - mesher_->dminus(iter, direction_)/2.0;
        const Real b = loc + mesher_->dplus(iter, direction_)/2.0;
 
        mapped_payoff f(*payoff_, gridMapping_);
 
        Real retVal;
        try {
            const Real acc
                = ((f(a) != 0.0 || f(b) != 0.0) ? Real((f(a)+f(b))*5e-5) : 1e-4);
            retVal = SimpsonIntegral(acc, 8)(f, a, b)/(b-a);
        }
        catch (Error&) {
            // use default value
            retVal = innerValue(iter, t);
        }
 
        return retVal;
    }
 
    FdmLogInnerValue::FdmLogInnerValue(
        const ext::shared_ptr<Payoff>& payoff,
        const ext::shared_ptr<FdmMesher>& mesher,
        Size direction)
    : FdmCellAveragingInnerValue(
        payoff, mesher, direction,
        [](Real x) -> Real { return std::exp(x); }) {}
 
 
    FdmLogBasketInnerValue::FdmLogBasketInnerValue(ext::shared_ptr<BasketPayoff> payoff,
                                                   ext::shared_ptr<FdmMesher> mesher)
    : payoff_(std::move(payoff)), mesher_(std::move(mesher)) {}
 
    Real FdmLogBasketInnerValue::innerValue(
                                    const FdmLinearOpIterator& iter, Time) {
        Array x(mesher_->layout()->dim().size());
        for (Size i=0; i < x.size(); ++i) {
            x[i] = std::exp(mesher_->location(iter, i));
        }
        
        return (*payoff_)(x);
    }
    
    Real 
    FdmLogBasketInnerValue::avgInnerValue(
                                    const FdmLinearOpIterator& iter, Time t) {
        return innerValue(iter, t);
    }
}