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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2003, 2004 Ferdinando Ametrano
Copyright (C) 2007 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
<https://www.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.
*/
#include <ql/exercise.hpp>
#include <ql/math/integrals/segmentintegral.hpp>
#include <ql/pricingengines/vanilla/integralengine.hpp>
#include <utility>
namespace QuantLib {
namespace {
class Integrand {
public:
Integrand(ext::shared_ptr<Payoff> payoff, Real s0, Rate drift, Real variance)
: payoff_(std::move(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:
ext::shared_ptr<Payoff> payoff_;
Real s0_;
Rate drift_;
Real variance_;
};
}
IntegralEngine::IntegralEngine(ext::shared_ptr<GeneralizedBlackScholesProcess> process)
: process_(std::move(process)) {
registerWith(process_);
}
void IntegralEngine::calculate() const {
QL_REQUIRE(arguments_.exercise->type() == Exercise::European,
"not an European Option");
ext::shared_ptr<StrikedTypePayoff> payoff =
ext::dynamic_pointer_cast<StrikedTypePayoff>(arguments_.payoff);
QL_REQUIRE(payoff, "non-striked payoff given");
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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