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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
<http://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/lookback/analyticcontinuousfixedlookback.hpp>
#include <ql/exercise.hpp>
namespace QuantLib {
AnalyticContinuousFixedLookbackEngine::
AnalyticContinuousFixedLookbackEngine(
const boost::shared_ptr<GeneralizedBlackScholesProcess>& process)
: process_(process) {
registerWith(process_);
}
void AnalyticContinuousFixedLookbackEngine::calculate() const {
boost::shared_ptr<PlainVanillaPayoff> payoff =
boost::dynamic_pointer_cast<PlainVanillaPayoff>(arguments_.payoff);
QL_REQUIRE(payoff, "Non-plain payoff given");
QL_REQUIRE(process_->x0() > 0.0, "negative or null underlying");
Real strike = payoff->strike();
switch (payoff->optionType()) {
case Option::Call:
QL_REQUIRE(payoff->strike()>=0.0,
"Strike must be positive or null");
if (strike <= minmax())
results_.value = A(1) + C(1);
else
results_.value = B(1);
break;
case Option::Put:
QL_REQUIRE(payoff->strike()>0.0,
"Strike must be positive");
if (strike >= minmax())
results_.value = A(-1) + C(-1);
else
results_.value = B(-1);
break;
default:
QL_FAIL("Unknown type");
}
}
Real AnalyticContinuousFixedLookbackEngine::underlying() const {
return process_->x0();
}
Real AnalyticContinuousFixedLookbackEngine::strike() const {
boost::shared_ptr<PlainVanillaPayoff> payoff =
boost::dynamic_pointer_cast<PlainVanillaPayoff>(arguments_.payoff);
QL_REQUIRE(payoff, "Non-plain payoff given");
return payoff->strike();
}
Time AnalyticContinuousFixedLookbackEngine::residualTime() const {
return process_->time(arguments_.exercise->lastDate());
}
Volatility AnalyticContinuousFixedLookbackEngine::volatility() const {
return process_->blackVolatility()->blackVol(residualTime(), strike());
}
Real AnalyticContinuousFixedLookbackEngine::stdDeviation() const {
return volatility() * std::sqrt(residualTime());
}
Rate AnalyticContinuousFixedLookbackEngine::riskFreeRate() const {
return process_->riskFreeRate()->zeroRate(residualTime(), Continuous,
NoFrequency);
}
DiscountFactor AnalyticContinuousFixedLookbackEngine::riskFreeDiscount()
const {
return process_->riskFreeRate()->discount(residualTime());
}
Rate AnalyticContinuousFixedLookbackEngine::dividendYield() const {
return process_->dividendYield()->zeroRate(residualTime(),
Continuous, NoFrequency);
}
DiscountFactor AnalyticContinuousFixedLookbackEngine::dividendDiscount()
const {
return process_->dividendYield()->discount(residualTime());
}
Real AnalyticContinuousFixedLookbackEngine::minmax() const {
return arguments_.minmax;
}
Real AnalyticContinuousFixedLookbackEngine::A(Real eta) const {
Volatility vol = volatility();
Real lambda = 2.0*(riskFreeRate() - dividendYield())/(vol*vol);
Real ss = underlying()/minmax();
Real d1 =
std::log(ss)/stdDeviation() + 0.5*(lambda+1.0)*stdDeviation();
Real N1 = f_(eta*d1);
Real N2 = f_(eta*(d1-stdDeviation()));
Real N3 = f_(eta*(d1-lambda*stdDeviation()));
Real N4 = f_(eta*d1);
Real powss = std::pow(ss, -lambda);
return eta*(underlying() * dividendDiscount() * N1 -
minmax() * riskFreeDiscount() * N2 -
underlying() * riskFreeDiscount() *
(powss * N3 - dividendDiscount()* N4/riskFreeDiscount())/
lambda);
}
Real AnalyticContinuousFixedLookbackEngine::B(Real eta) const {
Volatility vol = volatility();
Real lambda = 2.0*(riskFreeRate() - dividendYield())/(vol*vol);
Real ss = underlying()/strike();
Real d1 =
std::log(ss)/stdDeviation() + 0.5*(lambda+1.0)*stdDeviation();
Real N1 = f_(eta*d1);
Real N2 = f_(eta*(d1-stdDeviation()));
Real N3 = f_(eta*(d1-lambda*stdDeviation()));
Real N4 = f_(eta*d1);
Real powss = std::pow(ss, -lambda);
return eta*(underlying() * dividendDiscount() * N1 -
strike() * riskFreeDiscount() * N2 -
underlying() * riskFreeDiscount() *
(powss * N3 - dividendDiscount()* N4/riskFreeDiscount())/
lambda);
}
Real AnalyticContinuousFixedLookbackEngine::C(Real eta) const {
return eta*(riskFreeDiscount()*(minmax() - strike()));
}
}
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