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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2006 Warren Chou
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/pricingengines/lookback/analyticcontinuouspartialfloatinglookback.hpp>
#include <utility>
namespace QuantLib {
AnalyticContinuousPartialFloatingLookbackEngine::
AnalyticContinuousPartialFloatingLookbackEngine(
ext::shared_ptr<GeneralizedBlackScholesProcess> process)
: process_(std::move(process)) {
registerWith(process_);
}
void AnalyticContinuousPartialFloatingLookbackEngine::calculate() const {
ext::shared_ptr<FloatingTypePayoff> payoff =
ext::dynamic_pointer_cast<FloatingTypePayoff>(arguments_.payoff);
QL_REQUIRE(payoff, "Non-floating payoff given");
QL_REQUIRE(process_->x0() > 0.0, "negative or null underlying");
switch (payoff->optionType()) {
case Option::Call:
results_.value = A(1);
break;
case Option::Put:
results_.value = A(-1);
break;
default:
QL_FAIL("Unknown type");
}
}
Real AnalyticContinuousPartialFloatingLookbackEngine::underlying() const {
return process_->x0();
}
Time AnalyticContinuousPartialFloatingLookbackEngine::residualTime() const {
return process_->time(arguments_.exercise->lastDate());
}
Volatility AnalyticContinuousPartialFloatingLookbackEngine::volatility() const {
return process_->blackVolatility()->blackVol(residualTime(), minmax());
}
Real AnalyticContinuousPartialFloatingLookbackEngine::stdDeviation() const {
return volatility() * std::sqrt(residualTime());
}
Rate AnalyticContinuousPartialFloatingLookbackEngine::riskFreeRate() const {
return process_->riskFreeRate()->zeroRate(residualTime(), Continuous,
NoFrequency);
}
DiscountFactor AnalyticContinuousPartialFloatingLookbackEngine::riskFreeDiscount()
const {
return process_->riskFreeRate()->discount(residualTime());
}
Rate AnalyticContinuousPartialFloatingLookbackEngine::dividendYield() const {
return process_->dividendYield()->zeroRate(residualTime(),
Continuous, NoFrequency);
}
DiscountFactor AnalyticContinuousPartialFloatingLookbackEngine::dividendDiscount()
const {
return process_->dividendYield()->discount(residualTime());
}
Real AnalyticContinuousPartialFloatingLookbackEngine::minmax() const {
return arguments_.minmax;
}
Real AnalyticContinuousPartialFloatingLookbackEngine::lambda() const {
return arguments_.lambda;
}
Time AnalyticContinuousPartialFloatingLookbackEngine::lookbackPeriodEndTime() const {
return process_->time(arguments_.lookbackPeriodEnd);
}
Real AnalyticContinuousPartialFloatingLookbackEngine::A(Real eta) const {
bool fullLookbackPeriod = lookbackPeriodEndTime() == residualTime();
Real carry = riskFreeRate() - dividendYield();
Volatility vol = volatility();
Real x = 2.0*carry/(vol*vol);
Real s = underlying()/minmax();
Real ls = std::log(s);
Real d1 = ls/stdDeviation() + 0.5*(x+1.0)*stdDeviation();
Real d2 = d1 - stdDeviation();
Real e1 = 0, e2 = 0;
if (!fullLookbackPeriod)
{
e1 = (carry + vol * vol / 2) * (residualTime() - lookbackPeriodEndTime()) / (vol * std::sqrt(residualTime() - lookbackPeriodEndTime()));
e2 = e1 - vol * std::sqrt(residualTime() - lookbackPeriodEndTime());
}
Real f1 = (ls + (carry + vol * vol / 2) * lookbackPeriodEndTime()) / (vol * std::sqrt(lookbackPeriodEndTime()));
Real f2 = f1 - vol * std::sqrt(lookbackPeriodEndTime());
Real l1 = std::log(lambda()) / vol;
Real g1 = l1 / std::sqrt(residualTime());
Real n1 = f_(eta*(d1 - g1));
Real n2 = f_(eta*(d2 - g1));
BivariateCumulativeNormalDistributionWe04DP cnbn1(1), cnbn2(0), cnbn3(-1);
if (!fullLookbackPeriod) {
cnbn1 = BivariateCumulativeNormalDistributionWe04DP (std::sqrt(lookbackPeriodEndTime() / residualTime()));
cnbn2 = BivariateCumulativeNormalDistributionWe04DP (-std::sqrt(1 - lookbackPeriodEndTime() / residualTime()));
cnbn3 = BivariateCumulativeNormalDistributionWe04DP (-std::sqrt(lookbackPeriodEndTime() / residualTime()));
}
Real n3 = cnbn1(eta*(-f1+2.0* carry * std::sqrt(lookbackPeriodEndTime()) / vol), eta*(-d1+x*stdDeviation()-g1));
Real n4 = 0, n5 = 0, n6 = 0, n7 = 0;
if (!fullLookbackPeriod)
{
Real g2 = l1 / std::sqrt(residualTime() - lookbackPeriodEndTime());
n4 = cnbn2(-eta*(d1+g1), eta*(e1 + g2));
n5 = cnbn2(-eta*(d1-g1), eta*(e1 - g2));
n6 = cnbn3(eta*-f2, eta*(d2 - g1));
n7 = f_(eta*(e2 - g2));
}
else
{
n4 = f_(-eta*(d1+g1));
}
Real n8 = f_(-eta*f1);
Real pow_s = std::pow(s, -x);
Real pow_l = std::pow(lambda(), x);
if (!fullLookbackPeriod)
{
return eta*(underlying() * dividendDiscount() * n1 -
lambda() * minmax() * riskFreeDiscount() * n2 +
underlying() * riskFreeDiscount() * lambda() / x *
(pow_s * n3 - dividendDiscount() / riskFreeDiscount() * pow_l * n4)
+ underlying() * dividendDiscount() * n5 +
riskFreeDiscount() * lambda() * minmax() * n6 -
std::exp(-carry * (residualTime() - lookbackPeriodEndTime())) *
dividendDiscount() * (1 + 0.5 * vol * vol / carry) * lambda() *
underlying() * n7 * n8);
}
else
{
//Simpler calculation
return eta*(underlying() * dividendDiscount() * n1 -
lambda() * minmax() * riskFreeDiscount() * n2 +
underlying() * riskFreeDiscount() * lambda() / x *
(pow_s * n3 - dividendDiscount() / riskFreeDiscount() * pow_l * n4));
}
}
}
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