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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/analyticcontinuouspartialfixedlookback.hpp>
#include <utility>
namespace QuantLib {
AnalyticContinuousPartialFixedLookbackEngine::AnalyticContinuousPartialFixedLookbackEngine(
ext::shared_ptr<GeneralizedBlackScholesProcess> process)
: process_(std::move(process)) {
registerWith(process_);
}
void AnalyticContinuousPartialFixedLookbackEngine::calculate() const {
ext::shared_ptr<PlainVanillaPayoff> payoff =
ext::dynamic_pointer_cast<PlainVanillaPayoff>(arguments_.payoff);
QL_REQUIRE(payoff, "Non-plain payoff given");
QL_REQUIRE(process_->x0() > 0.0, "negative or null underlying");
switch (payoff->optionType()) {
case Option::Call:
QL_REQUIRE(payoff->strike()>=0.0,
"Strike must be positive or null");
results_.value = A(1);
break;
case Option::Put:
QL_REQUIRE(payoff->strike()>0.0,
"Strike must be positive");
results_.value = A(-1);
break;
default:
QL_FAIL("Unknown type");
}
}
Real AnalyticContinuousPartialFixedLookbackEngine::underlying() const {
return process_->x0();
}
Real AnalyticContinuousPartialFixedLookbackEngine::strike() const {
ext::shared_ptr<PlainVanillaPayoff> payoff =
ext::dynamic_pointer_cast<PlainVanillaPayoff>(arguments_.payoff);
QL_REQUIRE(payoff, "Non-plain payoff given");
return payoff->strike();
}
Time AnalyticContinuousPartialFixedLookbackEngine::residualTime() const {
return process_->time(arguments_.exercise->lastDate());
}
Volatility AnalyticContinuousPartialFixedLookbackEngine::volatility() const {
return process_->blackVolatility()->blackVol(residualTime(), strike());
}
Real AnalyticContinuousPartialFixedLookbackEngine::stdDeviation() const {
return volatility() * std::sqrt(residualTime());
}
Rate AnalyticContinuousPartialFixedLookbackEngine::riskFreeRate() const {
return process_->riskFreeRate()->zeroRate(residualTime(), Continuous,
NoFrequency);
}
DiscountFactor AnalyticContinuousPartialFixedLookbackEngine::riskFreeDiscount()
const {
return process_->riskFreeRate()->discount(residualTime());
}
Rate AnalyticContinuousPartialFixedLookbackEngine::dividendYield() const {
return process_->dividendYield()->zeroRate(residualTime(),
Continuous, NoFrequency);
}
DiscountFactor AnalyticContinuousPartialFixedLookbackEngine::dividendDiscount()
const {
return process_->dividendYield()->discount(residualTime());
}
Time AnalyticContinuousPartialFixedLookbackEngine::lookbackPeriodStartTime() const {
return process_->time(arguments_.lookbackPeriodStart);
}
Real AnalyticContinuousPartialFixedLookbackEngine::A(Real eta) const {
bool differentStartOfLookback = lookbackPeriodStartTime() != residualTime();
Real carry = riskFreeRate() - dividendYield();
Volatility vol = volatility();
Real x = 2.0*carry/(vol*vol);
Real s = underlying()/strike();
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 (differentStartOfLookback)
{
e1 = (carry + vol * vol / 2) * (residualTime() - lookbackPeriodStartTime()) / (vol * std::sqrt(residualTime() - lookbackPeriodStartTime()));
e2 = e1 - vol * std::sqrt(residualTime() - lookbackPeriodStartTime());
}
Real f1 = (ls + (carry + vol * vol / 2) * lookbackPeriodStartTime()) / (vol * std::sqrt(lookbackPeriodStartTime()));
Real f2 = f1 - vol * std::sqrt(lookbackPeriodStartTime());
Real n1 = f_(eta*d1);
Real n2 = f_(eta*d2);
BivariateCumulativeNormalDistributionWe04DP cnbn1(-1), cnbn2(0), cnbn3(0);
if (differentStartOfLookback) {
cnbn1 = BivariateCumulativeNormalDistributionWe04DP (-std::sqrt(lookbackPeriodStartTime() / residualTime()));
cnbn2 = BivariateCumulativeNormalDistributionWe04DP (std::sqrt(1 - lookbackPeriodStartTime() / residualTime()));
cnbn3 = BivariateCumulativeNormalDistributionWe04DP (-std::sqrt(1 - lookbackPeriodStartTime() / residualTime()));
}
Real n3 = cnbn1(eta*(d1-x*stdDeviation()), eta*(-f1+2.0* carry * std::sqrt(lookbackPeriodStartTime()) / vol));
Real n4 = cnbn2(eta*e1, eta*d1);
Real n5 = cnbn3(-eta*e1, eta*d1);
Real n6 = cnbn1(eta*f2, -eta*d2);
Real n7 = f_(eta*f1);
Real n8 = f_(-eta*e2);
Real pow_s = std::pow(s, -x);
Real carryDiscount = std::exp(-carry * (residualTime() - lookbackPeriodStartTime()));
return eta*(underlying() * dividendDiscount() * n1
- strike() * riskFreeDiscount() * n2
+ underlying() * riskFreeDiscount() / x
* (-pow_s * n3 + dividendDiscount() / riskFreeDiscount() * n4)
- underlying() * dividendDiscount() * n5
- strike() * riskFreeDiscount() * n6
+ carryDiscount * dividendDiscount()
* (1 - 0.5 * vol * vol / carry) *
underlying() * n7 * n8);
}
}
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