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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2015 Thema Consulting SA
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/barrier/analyticdoublebarrierengine.hpp>
#include <ql/pricingengines/blackcalculator.hpp>
#include <utility>
namespace QuantLib {
AnalyticDoubleBarrierEngine::AnalyticDoubleBarrierEngine(
ext::shared_ptr<GeneralizedBlackScholesProcess> process, int series)
: process_(std::move(process)), series_(series) {
registerWith(process_);
}
void AnalyticDoubleBarrierEngine::calculate() const {
QL_REQUIRE(arguments_.exercise->type() == Exercise::European,
"this engine handles only european options");
ext::shared_ptr<PlainVanillaPayoff> payoff =
ext::dynamic_pointer_cast<PlainVanillaPayoff>(arguments_.payoff);
QL_REQUIRE(payoff, "non-plain payoff given");
Real strike = payoff->strike();
QL_REQUIRE(strike>0.0,
"strike must be positive");
Real spot = underlying();
QL_REQUIRE(spot > 0.0, "negative or null underlying given");
QL_REQUIRE(!triggered(spot), "barrier(s) already touched");
DoubleBarrier::Type barrierType = arguments_.barrierType;
if (triggered(spot)) {
if (barrierType == DoubleBarrier::KnockIn)
results_.value = vanillaEquivalent(); // knocked in
else
results_.value = 0.0; // knocked out
} else {
switch (payoff->optionType()) {
case Option::Call:
switch (barrierType) {
case DoubleBarrier::KnockIn:
results_.value = callKI();
break;
case DoubleBarrier::KnockOut:
results_.value = callKO();
break;
case DoubleBarrier::KIKO:
case DoubleBarrier::KOKI:
QL_FAIL("unsupported double-barrier type: "
<< barrierType);
default:
QL_FAIL("unknown double-barrier type: "
<< barrierType);
}
break;
case Option::Put:
switch (barrierType) {
case DoubleBarrier::KnockIn:
results_.value = putKI();
break;
case DoubleBarrier::KnockOut:
results_.value = putKO();
break;
case DoubleBarrier::KIKO:
case DoubleBarrier::KOKI:
QL_FAIL("unsupported double-barrier type: "
<< barrierType);
default:
QL_FAIL("unknown double-barrier type: "
<< barrierType);
}
break;
default:
QL_FAIL("unknown type");
}
}
}
Real AnalyticDoubleBarrierEngine::underlying() const {
return process_->x0();
}
Real AnalyticDoubleBarrierEngine::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 AnalyticDoubleBarrierEngine::residualTime() const {
return process_->time(arguments_.exercise->lastDate());
}
Volatility AnalyticDoubleBarrierEngine::volatility() const {
return process_->blackVolatility()->blackVol(residualTime(), strike());
}
Real AnalyticDoubleBarrierEngine::volatilitySquared() const {
return volatility() * volatility();
}
Real AnalyticDoubleBarrierEngine::stdDeviation() const {
return volatility() * std::sqrt(residualTime());
}
Real AnalyticDoubleBarrierEngine::barrierLo() const {
return arguments_.barrier_lo;
}
Real AnalyticDoubleBarrierEngine::barrierHi() const {
return arguments_.barrier_hi;
}
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());
}
Rate AnalyticDoubleBarrierEngine::costOfCarry() const {
return riskFreeRate() - dividendYield();
}
Real AnalyticDoubleBarrierEngine::vanillaEquivalent() const {
// Call KI equates to vanilla - callKO
ext::shared_ptr<StrikedTypePayoff> payoff =
ext::dynamic_pointer_cast<StrikedTypePayoff>(arguments_.payoff);
Real forwardPrice = underlying() * dividendDiscount() / riskFreeDiscount();
BlackCalculator black(payoff, forwardPrice, stdDeviation(), riskFreeDiscount());
Real vanilla = black.value();
if (vanilla < 0.0)
vanilla = 0.0;
return vanilla;
}
Real AnalyticDoubleBarrierEngine::callKO() const {
// N.B. for flat barriers mu3=mu1 and mu2=0
Real mu1 = 2 * costOfCarry() / volatilitySquared() + 1;
Real bsigma = (costOfCarry() + volatilitySquared() / 2.0) * residualTime() / stdDeviation();
Real acc1 = 0;
Real acc2 = 0;
for (int n = -series_ ; n <= series_ ; ++n) {
Real L2n = std::pow(barrierLo(), 2 * n);
Real U2n = std::pow(barrierHi(), 2 * n);
Real d1 = std::log( underlying()* U2n / (strike() * L2n) ) / stdDeviation() + bsigma;
Real d2 = std::log( underlying()* U2n / (barrierHi() * L2n) ) / stdDeviation() + bsigma;
Real d3 = std::log( std::pow(barrierLo(), 2 * n + 2) / (strike() * underlying() * U2n) ) / stdDeviation() + bsigma;
Real d4 = std::log( std::pow(barrierLo(), 2 * n + 2) / (barrierHi() * underlying() * U2n) ) / stdDeviation() + bsigma;
acc1 += std::pow( std::pow(barrierHi(), n) / std::pow(barrierLo(), n), mu1 ) *
(f_(d1) - f_(d2)) -
std::pow( std::pow(barrierLo(), n+1) / (std::pow(barrierHi(), n) * underlying()), mu1 ) *
(f_(d3) - f_(d4));
acc2 += std::pow( std::pow(barrierHi(), n) / std::pow(barrierLo(), n), mu1-2) *
(f_(d1 - stdDeviation()) - f_(d2 - stdDeviation())) -
std::pow( std::pow(barrierLo(), n+1) / (std::pow(barrierHi(), n) * underlying()), mu1-2 ) *
(f_(d3-stdDeviation()) - f_(d4-stdDeviation()));
}
Real rend = std::exp(-dividendYield() * residualTime());
Real kov = underlying() * rend * acc1 - strike() * riskFreeDiscount() * acc2;
return std::max(0.0, kov);
}
Real AnalyticDoubleBarrierEngine::callKI() const {
// Call KI equates to vanilla - callKO
return std::max(0.0, vanillaEquivalent() - callKO());
}
Real AnalyticDoubleBarrierEngine::putKO() const {
Real mu1 = 2 * costOfCarry() / volatilitySquared() + 1;
Real bsigma = (costOfCarry() + volatilitySquared() / 2.0) * residualTime() / stdDeviation();
Real acc1 = 0;
Real acc2 = 0;
for (int n = -series_ ; n <= series_ ; ++n) {
Real L2n = std::pow(barrierLo(), 2 * n);
Real U2n = std::pow(barrierHi(), 2 * n);
Real y1 = std::log( underlying()* U2n / (std::pow(barrierLo(), 2 * n + 1)) ) / stdDeviation() + bsigma;
Real y2 = std::log( underlying()* U2n / (strike() * L2n) ) / stdDeviation() + bsigma;
Real y3 = std::log( std::pow(barrierLo(), 2 * n + 2) / (barrierLo() * underlying() * U2n) ) / stdDeviation() + bsigma;
Real y4 = std::log( std::pow(barrierLo(), 2 * n + 2) / (strike() * underlying() * U2n) ) / stdDeviation() + bsigma;
acc1 += std::pow( std::pow(barrierHi(), n) / std::pow(barrierLo(), n), mu1-2) *
(f_(y1 - stdDeviation()) - f_(y2 - stdDeviation())) -
std::pow( std::pow(barrierLo(), n+1) / (std::pow(barrierHi(), n) * underlying()), mu1-2 ) *
(f_(y3-stdDeviation()) - f_(y4-stdDeviation()));
acc2 += std::pow( std::pow(barrierHi(), n) / std::pow(barrierLo(), n), mu1 ) *
(f_(y1) - f_(y2)) -
std::pow( std::pow(barrierLo(), n+1) / (std::pow(barrierHi(), n) * underlying()), mu1 ) *
(f_(y3) - f_(y4));
}
Real rend = std::exp(-dividendYield() * residualTime());
Real kov = strike() * riskFreeDiscount() * acc1 - underlying() * rend * acc2;
return std::max(0.0, kov);
}
Real AnalyticDoubleBarrierEngine::putKI() const {
// Put KI equates to vanilla - putKO
return std::max(0.0, vanillaEquivalent() - putKO());
}
}
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