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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2013 Yue Tian
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/experimental/barrieroption/analyticdoublebarrierengine.hpp>
#include <ql/instruments/europeanoption.hpp>
#include <ql/pricingengines/vanilla/analyticeuropeanengine.hpp>
#include <ql/exercise.hpp>
#include <boost/make_shared.hpp>
namespace QuantLib {
AnalyticDoubleBarrierEngine::AnalyticDoubleBarrierEngine(
const boost::shared_ptr<GeneralizedBlackScholesProcess>& process,
int series)
: process_(process), series_(series) {
registerWith(process_);
}
void AnalyticDoubleBarrierEngine::calculate() const {
boost::shared_ptr<PlainVanillaPayoff> payoff =
boost::dynamic_pointer_cast<PlainVanillaPayoff>(arguments_.payoff);
QL_REQUIRE(payoff, "non-plain payoff given");
QL_REQUIRE(payoff->strike()>0.0,
"strike must be positive");
Real K = payoff->strike();
Real S = process_->x0();
QL_REQUIRE(S >= 0.0, "negative or null underlying given");
QL_REQUIRE(!triggered(S), "barrier touched");
std::vector<Barrier::Type> barrierType = arguments_.barrierType;
Real L = arguments_.barrier[0];
Real H = arguments_.barrier[1];
Real K_up = std::min(H, K);
Real K_down = std::max(L, K);
Time T = residualTime();
Real rd = riskFreeRate();
Real dd = riskFreeDiscount();
Real rf = dividendYield();
Real df = dividendDiscount();
Real vol = volatility();
Real mu = rd - rf - vol*vol/2.0;
Real sgn = mu > 0 ? 1.0 :(mu < 0 ? -1.0: 0.0);
//rebate
Real R_L = arguments_.rebate[0];
Real R_H = arguments_.rebate[1];
//european option
EuropeanOption europeanOption(payoff, arguments_.exercise);
boost::shared_ptr<PricingEngine> analyticEuropeanEngine =
boost::make_shared<AnalyticEuropeanEngine>(process_);
europeanOption.setPricingEngine(analyticEuropeanEngine);
Real european = europeanOption.NPV();
Real barrierOut = 0;
Real rebateIn = 0;
for(int n = -series_; n < series_; n++){
Real d1 = D(S/H*std::pow(L/H, 2.0*n), vol*vol+mu, vol, T);
Real d2 = d1 - vol*std::sqrt(T);
Real g1 = D(H/S*std::pow(L/H, 2.0*n - 1.0), vol*vol+mu, vol, T);
Real g2 = g1 - vol*std::sqrt(T);
Real h1 = D(S/H*std::pow(L/H, 2.0*n - 1.0), vol*vol+mu, vol, T);
Real h2 = h1 - vol*std::sqrt(T);
Real k1 = D(L/S*std::pow(L/H, 2.0*n - 1.0), vol*vol+mu, vol, T);
Real k2 = k1 - vol*std::sqrt(T);
Real d1_down = D(S/K_down*std::pow(L/H, 2.0*n), vol*vol+mu, vol, T);
Real d2_down = d1_down - vol*std::sqrt(T);
Real d1_up = D(S/K_up*std::pow(L/H, 2.0*n), vol*vol+mu, vol, T);
Real d2_up = d1_up - vol*std::sqrt(T);
Real k1_down = D((H*H)/(K_down*S)*std::pow(L/H, 2.0*n), vol*vol+mu, vol, T);
Real k2_down = k1_down - vol*std::sqrt(T);
Real k1_up = D((H*H)/(K_up*S)*std::pow(L/H, 2.0*n), vol*vol+mu, vol, T);
Real k2_up = k1_up - vol*std::sqrt(T);
if( payoff->optionType() == Option::Call) {
barrierOut += std::pow(L/H, 2.0 * n * mu/(vol*vol))*
(df*S*std::pow(L/H, 2.0*n)*(f_(d1_down)-f_(d1))
-dd*K*(f_(d2_down)-f_(d2))
-df*std::pow(L/H, 2.0*n)*H*H/S*std::pow(H/S, 2.0*mu/(vol*vol))*(f_(k1_down)-f_(k1))
+dd*K*std::pow(H/S,2.0*mu/(vol*vol))*(f_(k2_down)-f_(k2)));
}
else if(payoff->optionType() == Option::Put){
barrierOut += std::pow(L/H, 2.0 * n * mu/(vol*vol))*
(dd*K*(f_(h2)-f_(d2_up))
-df*S*std::pow(L/H, 2.0*n)*(f_(h1)-f_(d1_up))
-dd*K*std::pow(H/S,2.0*mu/(vol*vol))*(f_(g2)-f_(k2_up))
+df*std::pow(L/H, 2.0*n)*H*H/S*std::pow(H/S, 2.0*mu/(vol*vol))*(f_(g1)-f_(k1_up)));
}
else {
QL_FAIL("option type not recognized");
}
Real v1 = D(H/S*std::pow(H/L, 2.0*n), -mu, vol, T);
Real v2 = D(H/S*std::pow(H/L, 2.0*n), mu, vol, T);
Real v3 = D(S/L*std::pow(H/L, 2.0*n), -mu, vol, T);
Real v4 = D(S/L*std::pow(H/L, 2.0*n), mu, vol, T);
rebateIn += dd * R_H * sgn * (std::pow(L/H, 2.0*n*mu/(vol*vol)) * f_(sgn * v1) - std::pow(H/S, 2.0*mu/(vol*vol)) * f_(-sgn * v2))
+ dd * R_L * sgn * (std::pow(L/S, 2.0*mu/(vol*vol)) * f_(-sgn * v3) - std::pow(H/L, 2.0*n*mu/(vol*vol)) * f_(sgn * v4));
}
//rebate paid at maturity
if(barrierType[0] == Barrier::DownOut){
results_.value = barrierOut ;
results_.additionalResults["vanilla"] = european;
results_.additionalResults["barrierOut"] = barrierOut;
results_.additionalResults["barrierIn"] = european - barrierOut;
}
else{
results_.value = barrierOut;
results_.additionalResults["vanilla"] = european;
results_.additionalResults["barrierOut"] = barrierOut;
results_.additionalResults["barrierIn"] = european - barrierOut;
}
}
Real AnalyticDoubleBarrierEngine::underlying() const {
return process_->x0();
}
Real AnalyticDoubleBarrierEngine::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 AnalyticDoubleBarrierEngine::residualTime() const {
return process_->time(arguments_.exercise->lastDate());
}
Volatility AnalyticDoubleBarrierEngine::volatility() const {
return process_->blackVolatility()->blackVol(residualTime(), strike());
}
Real AnalyticDoubleBarrierEngine::stdDeviation() const {
return volatility() * std::sqrt(residualTime());
}
Rate AnalyticDoubleBarrierEngine::riskFreeRate() const {
return process_->riskFreeRate()->zeroRate(residualTime(), Continuous,
NoFrequency);
}
DiscountFactor AnalyticDoubleBarrierEngine::riskFreeDiscount() const {
return process_->riskFreeRate()->discount(residualTime());
}
Rate AnalyticDoubleBarrierEngine::dividendYield() const {
return process_->dividendYield()->zeroRate(residualTime(),
Continuous, NoFrequency);
}
DiscountFactor AnalyticDoubleBarrierEngine::dividendDiscount() const {
return process_->dividendYield()->discount(residualTime());
}
Real AnalyticDoubleBarrierEngine::D(Real X, Real lambda, Real sigma, Real T) const {
return (std::log(X) + lambda * T)/(sigma * std::sqrt(T));
}
}
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