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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2014 Master IMAFA - Polytech'Nice Sophia - Université de Nice Sophia Antipolis
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/analyticpartialtimebarrieroptionengine.hpp>
#include <ql/math/distributions/bivariatenormaldistribution.hpp>
#include <ql/pricingengines/vanilla/analyticeuropeanengine.hpp>
#include <utility>
namespace QuantLib {
AnalyticPartialTimeBarrierOptionEngine::AnalyticPartialTimeBarrierOptionEngine(
ext::shared_ptr<GeneralizedBlackScholesProcess> process)
: process_(std::move(process)) {
registerWith(process_);
}
Real AnalyticPartialTimeBarrierOptionEngine::calculate(PartialTimeBarrierOption::arguments& arguments,
const ext::shared_ptr<PlainVanillaPayoff>& payoff,
const ext::shared_ptr<GeneralizedBlackScholesProcess>& process) const {
Barrier::Type barrierType = arguments.barrierType;
PartialBarrier::Range barrierRange = arguments.barrierRange;
Rate r = process->riskFreeRate()->zeroRate(residualTime(), Continuous,
NoFrequency);
Rate q = process->dividendYield()->zeroRate(residualTime(), Continuous,
NoFrequency);
Real barrier = arguments.barrier;
Real strike = payoff->strike();
switch (barrierType) {
case Barrier::DownOut:
switch (barrierRange) {
case PartialBarrier::Start:
return CA(1, barrier, strike, r, q);
case PartialBarrier::EndB1:
return CoB1(barrier, strike, r, q);
case PartialBarrier::EndB2:
return CoB2(Barrier::DownOut, barrier, strike, r, q);
default:
QL_FAIL("invalid barrier range");
}
break;
case Barrier::DownIn:
switch (barrierRange) {
case PartialBarrier::Start:
return CIA(1, barrier, strike, r, q);
case PartialBarrier::EndB1:
case PartialBarrier::EndB2:
QL_FAIL("Down-and-in partial-time end barrier is not implemented");
default:
QL_FAIL("invalid barrier range");
}
break;
case Barrier::UpOut:
switch (barrierRange) {
case PartialBarrier::Start:
return CA(-1, barrier, strike, r, q);
case PartialBarrier::EndB1:
return CoB1(barrier, strike, r, q);
case PartialBarrier::EndB2:
return CoB2(Barrier::UpOut, barrier, strike, r, q);
default:
QL_FAIL("invalid barrier range");
}
break;
case Barrier::UpIn:
switch (barrierRange) {
case PartialBarrier::Start:
return CIA(-1, barrier, strike, r, q);
case PartialBarrier::EndB1:
case PartialBarrier::EndB2:
QL_FAIL("Up-and-in partial-time end barrier is not implemented");
default:
QL_FAIL("invalid barrier range");
}
break;
default:
QL_FAIL("unknown barrier type");
}
}
void AnalyticPartialTimeBarrierOptionEngine::calculate() const {
ext::shared_ptr<PlainVanillaPayoff> payoff =
ext::dynamic_pointer_cast<PlainVanillaPayoff>(arguments_.payoff);
QL_REQUIRE(payoff, "non-plain payoff given");
QL_REQUIRE(payoff->strike()>0.0,
"strike must be positive");
Real spot = process_->x0();
QL_REQUIRE(spot > 0.0, "negative or null underlying given");
auto getSymmetricBarrierType = [](Barrier::Type barrierType) -> Barrier::Type {
if (barrierType == Barrier::UpIn) return Barrier::DownIn;
if (barrierType == Barrier::DownIn) return Barrier::UpIn;
if (barrierType == Barrier::UpOut) return Barrier::DownOut;
return Barrier::UpOut;
};
auto tmp_arguments_ = arguments_;
if (payoff->optionType() == Option::Put)
{
Real spotSq = spot * spot;
Real callStrike = spotSq / payoff->strike();
ext::shared_ptr<PlainVanillaPayoff> callPayoff =
ext::make_shared<PlainVanillaPayoff>(Option::Call, callStrike);
tmp_arguments_.barrierType = getSymmetricBarrierType(arguments_.barrierType);
tmp_arguments_.barrier = spotSq / arguments_.barrier;
tmp_arguments_.payoff = callPayoff;
auto callProcess = ext::make_shared<GeneralizedBlackScholesProcess>(
process_->stateVariable(),
process_->riskFreeRate(),
process_->dividendYield(),
process_->blackVolatility()
);
results_.value = payoff->strike() / spot * calculate(tmp_arguments_, callPayoff, callProcess);
} else
results_.value = calculate(tmp_arguments_, payoff, process_);
}
Real AnalyticPartialTimeBarrierOptionEngine::CoB2(
Barrier::Type barrierType,
Real barrier, Real strike, Rate r, Rate q) const {
Real result = 0.0;
Real b = r - q;
Real T = residualTime();
Real S = underlying();
Real mu_ = mu(strike, b);
Real g1_ = g1(barrier, strike, b);
Real g2_ = g2(barrier, strike, b);
Real g3_ = g3(barrier, strike, b);
Real g4_ = g4(barrier, strike, b);
Real e1_ = e1(barrier, strike, b);
Real e2_ = e2(barrier, strike, b);
Real e3_ = e3(barrier, strike, b);
Real e4_ = e4(barrier, strike, b);
Real rho_ = rho();
Real HSMu = HS(S, barrier, 2 * mu_);
Real HSMu1 = HS(S, barrier, 2 * (mu_ + 1));
Real X1 = strike * std::exp(-r * T);
if (strike < barrier){
switch (barrierType) {
case Barrier::DownOut:
result = S * std::exp((b - r) * T);
result *= (M(g1_, e1_, rho_) - HSMu1 * M(g3_, -e3_, -rho_));
result -= X1 * (M(g2_, e2_, rho_)-HSMu*M(g4_, -e4_, -rho_));
return result;
case Barrier::UpOut:
result = S * std::exp((b - r) * T);
result *= (M(-g1_, -e1_, rho_) - HSMu1 * M(-g3_, e3_, -rho_));
result -= X1 * (M(-g2_, -e2_, rho_) - HSMu * M(-g4_, e4_, -rho_));
result -= S * std::exp((b - r) * T) *
(M(-d1(strike, b), -e1_, rho_) - HSMu1 *
M(e3_, -f1(barrier, strike, b),-rho_));
result += X1 * (M(-d2(strike, b), -e2_, rho_) - HSMu *
M(e4_, -f2(barrier, strike, b), -rho_));
return result;
default:
QL_FAIL("invalid barrier type");
}
} else {
QL_FAIL("case of strike>barrier is not implemented for OutEnd B2 type");
}
}
Real AnalyticPartialTimeBarrierOptionEngine::CoB1(Real barrier, Real strike, Rate r, Rate q) const {
Real result = 0.0;
Rate b = r - q;
Real T = residualTime();
Real S = underlying();
Real mu_ = mu(strike, b);
Real g1_ = g1(barrier, strike, b);
Real g2_ = g2(barrier, strike, b);
Real g3_ = g3(barrier, strike, b);
Real g4_ = g4(barrier, strike, b);
Real e1_ = e1(barrier, strike, b);
Real e2_ = e2(barrier, strike, b);
Real e3_ = e3(barrier, strike, b);
Real e4_ = e4(barrier, strike, b);
Real rho_ = rho();
Real HSMu = HS(S, barrier, 2 * mu_);
Real HSMu1 = HS(S, barrier, 2 * (mu_ + 1));
Real X1 = strike * std::exp(-r * T);
if (strike > barrier) {
result = S * std::exp((b - r) * T);
result *= (M(d1(strike, b), e1_, rho_) - HSMu1 * M(f1(barrier, strike, b), -e3_, -rho_));
result -= X1 * (M(d2(strike, b), e2_, rho_) - HSMu * M(f2(barrier, strike, b), -e4_, -rho_));
return result;
} else {
Real S1 = S * std::exp((b - r) * T);
result = S1;
result *= (M(-g1_, -e1_, rho_) - HSMu1 * M(-g3_,e3_,-rho_));
result -= X1 * (M(-g2_, -e2_, rho_) - HSMu * M(-g4_, e4_, -rho_));
result -= S1 * (M(-d1(strike, b), -e1_, rho_) - HSMu1 * M(-f1(barrier, strike, b), e3_, -rho_));
result += X1 * (M(-d2(strike, b), -e2_, rho_) - HSMu * M(-f2(barrier, strike, b), e4_, -rho_));
result += S1 * (M(g1_, e1_, rho_) - HSMu1 * M(g3_, -e3_, -rho_));
result -= X1 * (M(g2_, e2_, rho_) - HSMu * M(g4_, -e4_, -rho_));
return result;
}
}
// eta = -1: Up-and-In Call
// eta = 1: Down-and-In Call
Real AnalyticPartialTimeBarrierOptionEngine::CIA(Integer eta, Real barrier, Real strike, Rate r, Rate q) const {
ext::shared_ptr<EuropeanExercise> exercise =
ext::dynamic_pointer_cast<EuropeanExercise>(arguments_.exercise);
ext::shared_ptr<PlainVanillaPayoff> payoff =
ext::dynamic_pointer_cast<PlainVanillaPayoff>(arguments_.payoff);
VanillaOption europeanOption(payoff, exercise);
europeanOption.setPricingEngine(
ext::make_shared<AnalyticEuropeanEngine>(process_));
return europeanOption.NPV() - CA(eta, barrier, strike, r, q);
}
Real AnalyticPartialTimeBarrierOptionEngine::CA(Integer eta, Real barrier, Real strike, Rate r, Rate q) const {
//Partial-Time-Start- OUT Call Option calculation
Real b = r - q;
Real rho_ = rho();
Real T = residualTime();
Real S = underlying();
Real mu_ = mu(strike, b);
Real e1_ = e1(barrier, strike, b);
Real e2_ = e2(barrier, strike, b);
Real e3_ = e3(barrier, strike, b);
Real e4_ = e4(barrier, strike, b);
Real HSMu = HS(S, barrier,2 * mu_);
Real HSMu1 = HS(S, barrier, 2 * (mu_ + 1));
Real result;
result = S * std::exp((b - r) * T);
result *= (M(d1(strike, b), eta * e1_, eta * rho_)-HSMu1 *
M(f1(barrier, strike, b), eta * e3_, eta * rho_));
result -= (strike * std::exp(-r * T) *
(M(d2(strike, b),eta * e2_, eta * rho_) - HSMu *
M(f2(barrier, strike, b), eta * e4_, eta * rho_)));
return result;
}
Real AnalyticPartialTimeBarrierOptionEngine::underlying() const {
return process_->x0();
}
Time AnalyticPartialTimeBarrierOptionEngine::residualTime() const {
return process_->time(arguments_.exercise->lastDate());
}
Time AnalyticPartialTimeBarrierOptionEngine::coverEventTime() const {
return process_->time(arguments_.coverEventDate);
}
Volatility AnalyticPartialTimeBarrierOptionEngine::volatility(Time t, Real strike) const {
return process_->blackVolatility()->blackVol(t, strike);
}
Real AnalyticPartialTimeBarrierOptionEngine::f1(Real barrier, Real strike, Rate b) const {
Real S = underlying();
Real T = residualTime();
Real sigma = volatility(T, strike);
return (std::log(S / strike) + 2 * std::log(barrier / S) +
(b + (std::pow(sigma, 2) / 2))*T) / (sigma*std::sqrt(T));
}
Real AnalyticPartialTimeBarrierOptionEngine::f2(Real barrier, Real strike, Rate b) const {
Time T = residualTime();
return f1(barrier, strike, b) - volatility(T, strike) * std::sqrt(T);
}
Real AnalyticPartialTimeBarrierOptionEngine::M(Real a, Real b, Real rho) const {
BivariateCumulativeNormalDistributionDr78 CmlNormDist(rho);
return CmlNormDist(a,b);
}
Real AnalyticPartialTimeBarrierOptionEngine::rho() const {
return std::sqrt(coverEventTime() / residualTime());
}
Rate AnalyticPartialTimeBarrierOptionEngine::mu(Real strike, Rate b) const {
Volatility vol = volatility(coverEventTime(), strike);
return (b - (vol * vol) / 2) / (vol * vol);
}
Real AnalyticPartialTimeBarrierOptionEngine::d1(Real strike, Rate b) const {
Time T2 = residualTime();
Volatility vol = volatility(T2, strike);
return (std::log(underlying() / strike) + (b + vol * vol / 2) * T2) / (std::sqrt(T2) * vol);
}
Real AnalyticPartialTimeBarrierOptionEngine::d2(Real strike, Rate b) const {
Time T2 = residualTime();
Volatility vol = volatility(T2, strike);
return d1(strike, b) - vol * std::sqrt(T2);
}
Real AnalyticPartialTimeBarrierOptionEngine::e1(Real barrier, Real strike, Rate b) const {
Time T1 = coverEventTime();
Volatility vol = volatility(T1, strike);
return (std::log(underlying() / barrier) + (b + vol * vol / 2) * T1) / (std::sqrt(T1) * vol);
}
Real AnalyticPartialTimeBarrierOptionEngine::e2(Real barrier, Real strike, Rate b) const {
Time T1 = coverEventTime();
Volatility vol = volatility(T1, strike);
return e1(barrier, strike, b) - vol * std::sqrt(T1);
}
Real AnalyticPartialTimeBarrierOptionEngine::e3(Real barrier, Real strike, Rate b) const {
Time T1 = coverEventTime();
Real vol = volatility(T1, strike);
return e1(barrier, strike, b) + (2 * std::log(barrier / underlying()) / (vol * std::sqrt(T1)));
}
Real AnalyticPartialTimeBarrierOptionEngine::e4(Real barrier, Real strike, Rate b) const {
Time t = coverEventTime();
return e3(barrier, strike, b) - volatility(t, strike) * std::sqrt(t);
}
Real AnalyticPartialTimeBarrierOptionEngine::g1(Real barrier, Real strike, Rate b) const {
Time T2 = residualTime();
Volatility vol = volatility(T2, strike);
return (std::log(underlying() / barrier) + (b + vol * vol / 2) * T2) / (std::sqrt(T2) * vol);
}
Real AnalyticPartialTimeBarrierOptionEngine::g2(Real barrier, Real strike, Rate b) const {
Time T2 = residualTime();
Volatility vol = volatility(T2, strike);
return g1(barrier, strike, b) - vol * std::sqrt(T2);
}
Real AnalyticPartialTimeBarrierOptionEngine::g3(Real barrier, Real strike, Rate b) const {
Time T2 = residualTime();
Real vol = volatility(T2, strike);
return g1(barrier, strike, b) + (2 * std::log(barrier / underlying()) /(vol * std::sqrt(T2)));
}
Real AnalyticPartialTimeBarrierOptionEngine::g4(Real barrier, Real strike, Rate b) const {
Time T2 = residualTime();
Real vol = volatility(T2, strike);
return g3(barrier, strike, b) - vol * std::sqrt(T2);
}
Real AnalyticPartialTimeBarrierOptionEngine::HS(Real S, Real H, Real power) const {
return std::pow((H / S), power);
}
}
|
