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integralengine.cpp

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

/*
 Copyright (C) 2003, 2004 Ferdinando Ametrano

 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.
*/

#include <ql/PricingEngines/Vanilla/integralengine.hpp>
#include <ql/Processes/blackscholesprocess.hpp>
#include <ql/Math/segmentintegral.hpp>

namespace QuantLib {

    namespace {

        class Integrand : std::unary_function<Real,Real> {
          public:
            Integrand(const boost::shared_ptr<Payoff>& payoff,
                      Real s0,
                      Rate drift,
                      Real variance)
           : payoff_(payoff), s0_(s0), drift_(drift), variance_(variance) {}
            Real operator()(Real x) const {
                Real temp = s0_ * std::exp(x);
                Real result = (*payoff_)(temp);
                return result *
                    std::exp(-(x - drift_)*(x -drift_)/(2.0*variance_)) ;
            }
          private:
            boost::shared_ptr<Payoff> payoff_;
            Real s0_;
            Rate drift_;
            Real variance_;
        };
    }

    void IntegralEngine::calculate() const {

        QL_REQUIRE(arguments_.exercise->type() == Exercise::European,
                   "not an European Option");

        boost::shared_ptr<StrikedTypePayoff> payoff =
            boost::dynamic_pointer_cast<StrikedTypePayoff>(arguments_.payoff);
        QL_REQUIRE(payoff, "non-striked payoff given");

        boost::shared_ptr<BlackScholesProcess> process =
            boost::dynamic_pointer_cast<BlackScholesProcess>(
                                                arguments_.stochasticProcess);
        QL_REQUIRE(process, "Black-Scholes process required");

        Real variance =
            process->blackVolatility()->blackVariance(
                           arguments_.exercise->lastDate(), payoff->strike());

        DiscountFactor dividendDiscount =
            process->dividendYield()->discount(
                                             arguments_.exercise->lastDate());
        DiscountFactor riskFreeDiscount =
            process->riskFreeRate()->discount(
                                             arguments_.exercise->lastDate());
        Rate drift = std::log(dividendDiscount/riskFreeDiscount)-0.5*variance;

        Integrand f(arguments_.payoff,
                    process->stateVariable()->value(),
                    drift, variance);
        SegmentIntegral integrator(5000);

        Real infinity = 10.0*std::sqrt(variance);
        results_.value =
            process->riskFreeRate()->discount(
                                            arguments_.exercise->lastDate()) /
            std::sqrt(2.0*M_PI*variance) *
            integrator(f, drift-infinity, drift+infinity);
    }

}


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