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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2011 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/experimental/exoticoptions/kirkspreadoptionengine.hpp>
#include <ql/math/distributions/normaldistribution.hpp>
#include <utility>
using namespace std;
namespace QuantLib {
QL_DEPRECATED_DISABLE_WARNING
KirkSpreadOptionEngine::KirkSpreadOptionEngine(ext::shared_ptr<BlackProcess> process1,
ext::shared_ptr<BlackProcess> process2,
Handle<Quote> correlation)
: process1_(std::move(process1)), process2_(std::move(process2)), rho_(std::move(correlation)) {
registerWith(process1_);
registerWith(process2_);
registerWith(rho_);
}
void KirkSpreadOptionEngine::calculate() const {
// First: tests on types
QL_REQUIRE(arguments_.exercise->type() == Exercise::European,
"not an European Option");
ext::shared_ptr<PlainVanillaPayoff> payoff =
ext::dynamic_pointer_cast<PlainVanillaPayoff>(arguments_.payoff);
QL_REQUIRE(payoff, "not a plain-vanilla payoff");
// forward values - futures, so b=0
Real forward1 = process1_->stateVariable()->value();
Real forward2 = process2_->stateVariable()->value();
Date exerciseDate = arguments_.exercise->lastDate();
// Volatilities
Real sigma1 =
process1_->blackVolatility()->blackVol(exerciseDate,forward1);
Real sigma2 =
process2_->blackVolatility()->blackVol(exerciseDate,forward2);
DiscountFactor riskFreeDiscount =
process1_->riskFreeRate()->discount(exerciseDate);
Real strike = payoff->strike();
// Unique F (forward) value for pricing
Real F = forward1/(forward2+strike);
// Its volatility
Real sigma =
sqrt(pow(sigma1,2)
+ pow((sigma2*(forward2/(forward2+strike))),2)
- 2*rho_->value()*sigma1*sigma2*(forward2/(forward2+strike)));
// Day counter and Dates handling variables
DayCounter rfdc = process1_->riskFreeRate()->dayCounter();
Time t = rfdc.yearFraction(process1_->riskFreeRate()->referenceDate(),
arguments_.exercise->lastDate());
// Black-Scholes solution values
Real d1 = (log(F)+ 0.5*pow(sigma,2)*t) / (sigma*sqrt(t));
Real d2 = d1 - sigma*sqrt(t);
NormalDistribution pdf;
CumulativeNormalDistribution cum;
Real Nd1 = cum(d1);
Real Nd2 = cum(d2);
Real NMd1 = cum(-d1);
Real NMd2 = cum(-d2);
Option::Type optionType = payoff->optionType();
if (optionType==Option::Call) {
results_.value = riskFreeDiscount*(F*Nd1-Nd2)*(forward2+strike);
} else {
results_.value = riskFreeDiscount*(NMd2 -F*NMd1)*(forward2+strike);
}
Real callValue = optionType == Option::Call ? results_.value : riskFreeDiscount*(F*Nd1-Nd2)*(forward2+strike);
results_.theta = -((log(riskFreeDiscount)/t)*callValue
+ riskFreeDiscount*(forward1*sigma)/(2*sqrt(t))*pdf(d1));
}
QL_DEPRECATED_ENABLE_WARNING
}
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