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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2010 Master IMAFA - Polytech'Nice Sophia - Université de Nice Sophia Antipolis
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/pricingengines/exotic/analyticeuropeanmargrabeengine.hpp>
#include <ql/instruments/payoffs.hpp>
#include <ql/math/distributions/normaldistribution.hpp>
#include <utility>
namespace QuantLib {
AnalyticEuropeanMargrabeEngine::AnalyticEuropeanMargrabeEngine(
ext::shared_ptr<GeneralizedBlackScholesProcess> process1,
ext::shared_ptr<GeneralizedBlackScholesProcess> process2,
Real correlation)
: process1_(std::move(process1)), process2_(std::move(process2)), rho_(correlation) {
registerWith(process1_);
registerWith(process2_);
}
void AnalyticEuropeanMargrabeEngine::calculate() const {
QL_REQUIRE(arguments_.exercise->type() == Exercise::European,
"not an European Option");
ext::shared_ptr<EuropeanExercise> exercise =
ext::dynamic_pointer_cast<EuropeanExercise>(arguments_.exercise);
QL_REQUIRE(exercise, "not an European Option");
ext::shared_ptr<NullPayoff> payoff =
ext::dynamic_pointer_cast<NullPayoff>(arguments_.payoff);
QL_REQUIRE(payoff, "non a Null Payoff type");
Integer quantity1 = arguments_.Q1;
Integer quantity2 = arguments_.Q2;
Real s1 = process1_->stateVariable()->value();
Real s2 = process2_->stateVariable()->value();
Real variance1 = process1_->blackVolatility()->blackVariance(
exercise->lastDate(), s1);
Real variance2 = process2_->blackVolatility()->blackVariance(
exercise->lastDate(), s2);
DiscountFactor riskFreeDiscount =
process1_->riskFreeRate()->discount(exercise->lastDate());
DiscountFactor dividendDiscount1 =
process1_->dividendYield()->discount(exercise->lastDate());
DiscountFactor dividendDiscount2 =
process2_->dividendYield()->discount(exercise->lastDate());
Real forward1 = process1_->stateVariable()->value() *
dividendDiscount1 / riskFreeDiscount;
Real forward2 = process2_->stateVariable()->value() *
dividendDiscount2 / riskFreeDiscount;
Real stdDev1 = std::sqrt(variance1);
Real stdDev2 = std::sqrt(variance2);
Real variance = variance1 + variance2 - 2*rho_*stdDev1*stdDev2;
Real stdDev = std::sqrt(variance);
Real d1 = (std::log((quantity1*forward1)/(quantity2*forward2))
+ 0.5*variance) / stdDev;
Real d2 = d1 - stdDev;
Real Nd1, Nd2, nd1, nd2;
CumulativeNormalDistribution cum;
NormalDistribution norm;
Nd1 = cum(d1);
Nd2 = cum(d2);
nd1 = norm(d1);
nd2 = norm(d2);
DayCounter rfdc = process1_->riskFreeRate()->dayCounter();
Time t = rfdc.yearFraction(process1_->riskFreeRate()->referenceDate(),
arguments_.exercise->lastDate());
Real sqt = std::sqrt(t);
Real q1 = -std::log(dividendDiscount1)/(sqt*sqt);
Real q2 = -std::log(dividendDiscount2)/(sqt*sqt);
results_.value =
riskFreeDiscount * (quantity1*forward1*Nd1 - quantity2*forward2*Nd2);
// Greeks
results_.delta1 = riskFreeDiscount*(quantity1*forward1*Nd1)/s1;
results_.delta2 = -riskFreeDiscount*(quantity2*forward2*Nd2)/s2;
results_.gamma1 = (riskFreeDiscount*(quantity1*forward1*nd1)/s1)/(quantity1*s1*stdDev);
results_.gamma2 = (-riskFreeDiscount*(quantity2*forward2*nd2)/s2)/(-quantity2*s2*stdDev);
Real vega = riskFreeDiscount*(quantity1*forward1*nd1)*sqt;
results_.theta = -((stdDev*vega/sqt)/(2*t)-(q1*quantity1*s1*results_.delta1)-(q2*quantity2*s2*results_.delta2));
results_.rho = 0.0;
}
}
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