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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2024 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
<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/pricingengines/basket/bjerksundstenslandspreadengine.hpp>
#include <ql/math/distributions/normaldistribution.hpp>
#include <utility>
namespace QuantLib {
BjerksundStenslandSpreadEngine::BjerksundStenslandSpreadEngine(
ext::shared_ptr<GeneralizedBlackScholesProcess> process1,
ext::shared_ptr<GeneralizedBlackScholesProcess> process2,
Real correlation)
: SpreadBlackScholesVanillaEngine(std::move(process1), std::move(process2), correlation) {
}
Real BjerksundStenslandSpreadEngine::calculate(
Real f1, Real f2, Real k, Option::Type optionType,
Real variance1, Real variance2, DiscountFactor df) const {
const Real cp = (optionType == Option::Call) ? 1 : -1;
const Real a = f2 + k;
const Real b = f2/a;
const Real sigma1 = std::sqrt(variance1);
const Real sigma2 = std::sqrt(variance2);
const Real stdev = std::sqrt(
variance1 + b*b*variance2 - 2*rho_*b*sigma1*sigma2);
const Real lfa = std::log(f1/a);
const Real d1 =
(lfa + (0.5*variance1 + 0.5*b*b*variance2 - b*rho_*sigma1*sigma2))/stdev;
const Real d2 =
(lfa + (-0.5*variance1 + variance2*b*(0.5*b - 1) + rho_*sigma1*sigma2))/stdev;
const Real d3 = (lfa + (-0.5*variance1 + 0.5*b*b*variance2))/stdev;
const CumulativeNormalDistribution phi;
return df*cp*(f1*phi(cp*d1) - f2*phi(cp*d2) - k*phi(cp*d3));
}
}
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