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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/exotic/analyticcomplexchooserengine.hpp>
#include <ql/math/distributions/bivariatenormaldistribution.hpp>
#include <utility>
using std::pow;
using std::log;
using std::exp;
using std::sqrt;
namespace QuantLib {
AnalyticComplexChooserEngine::AnalyticComplexChooserEngine(
ext::shared_ptr<GeneralizedBlackScholesProcess> process)
: process_(std::move(process)) {
registerWith(process_);
}
void AnalyticComplexChooserEngine::calculate() const {
Real S = process_->x0();
Real b;
Real v;
Real Xc = arguments_.strikeCall;
Real Xp = arguments_.strikePut;
Time T = choosingTime();
Time Tc = callMaturity() - T;
Time Tp = putMaturity() - T;
Real i = criticalValue();
b = riskFreeRate(T) - dividendYield(T);
v = volatility(T);
Real d1 = (log(S / i) + (b + pow(v, 2) / 2)*T) / (v*sqrt(T));
Real d2 = d1 - v*sqrt(T);
b = riskFreeRate(T + Tc) - dividendYield(T + Tc);
v = volatility(Tc);
Real y1 = (log(S / Xc) + (b + pow(v, 2) / 2)*Tc) / (v*sqrt(Tc));
b = riskFreeRate(T + Tp) - dividendYield(T + Tp);
v = volatility(Tp);
Real y2 = (log(S / Xp) + (b + pow(v, 2) / 2)*Tp) / (v*sqrt(Tp));
Real rho1 = sqrt(T / Tc);
Real rho2 = sqrt(T / Tp);
b = riskFreeRate(T + Tc) - dividendYield(T + Tc);
Real r = riskFreeRate(T + Tc);
Real ComplexChooser = S * exp((b - r)*Tc) * BivariateCumulativeNormalDistributionDr78(rho1)(d1, y1)
- Xc * exp(-r*Tc)*BivariateCumulativeNormalDistributionDr78(rho1)(d2, y1 - v * sqrt(Tc)) ;
b = riskFreeRate(T + Tp) - dividendYield(T + Tp);
r = riskFreeRate(T + Tp);
ComplexChooser -= S * exp((b - r)*Tp) * BivariateCumulativeNormalDistributionDr78(rho2)(-d1, -y2);
ComplexChooser += Xp * exp(-r*Tp) * BivariateCumulativeNormalDistributionDr78(rho2)(-d2, -y2 + v * sqrt(Tp));
results_.value = ComplexChooser;
}
BlackScholesCalculator AnalyticComplexChooserEngine::bsCalculator(
Real spot, Option::Type optionType) const {
Real vol;
DiscountFactor growth;
DiscountFactor discount;
Time T = choosingTime();
// payoff
ext::shared_ptr<PlainVanillaPayoff > vanillaPayoff;
if (optionType == Option::Call){
//TC-T
Time t=callMaturity()-2*T;
vanillaPayoff = ext::make_shared<PlainVanillaPayoff>(
Option::Call, strike(Option::Call));
//QuantLib requires sigma * sqrt(t) rather than just sigma/volatility
vol = volatility(t) * std::sqrt(t);
growth = dividendDiscount(t);
discount = riskFreeDiscount(t);
} else{
Time t=putMaturity()-2*T;
vanillaPayoff = ext::make_shared<PlainVanillaPayoff>(
Option::Put, strike(Option::Put));
vol = volatility(t) * std::sqrt(t);
growth = dividendDiscount(t);
discount = riskFreeDiscount(t);
}
BlackScholesCalculator bs(vanillaPayoff, spot, growth, vol, discount);
return bs;
}
Real AnalyticComplexChooserEngine::criticalValue() const{
Real Sv = process_->x0();
BlackScholesCalculator bs=bsCalculator(Sv,Option::Call);
Real ci = bs.value();
Real dc = bs.delta();
bs=bsCalculator(Sv,Option::Put);
Real Pi = bs.value();
Real dp = bs.delta();
Real yi = ci - Pi;
Real di = dc - dp;
Real epsilon = 0.001;
//Newton-Raphson process
while (std::fabs(yi) > epsilon){
Sv = Sv - yi / di;
bs=bsCalculator(Sv,Option::Call);
ci = bs.value();
dc = bs.delta();
bs=bsCalculator(Sv,Option::Put);
Pi = bs.value();
dp = bs.delta();
yi = ci - Pi;
di = dc - dp;
}
return Sv;
}
Real AnalyticComplexChooserEngine::strike(Option::Type optionType) const {
if (optionType == Option::Call)
return arguments_.strikeCall;
else
return arguments_.strikePut;
}
Time AnalyticComplexChooserEngine::choosingTime() const {
return process_->time(arguments_.choosingDate);
}
Time AnalyticComplexChooserEngine::putMaturity() const {
return process_->time(arguments_.exercisePut->lastDate());
}
Time AnalyticComplexChooserEngine::callMaturity() const {
return process_->time(arguments_.exerciseCall->lastDate());
}
Volatility AnalyticComplexChooserEngine::volatility(Time t) const {
return process_->blackVolatility()->blackVol(t, arguments_.strikeCall);
}
Rate AnalyticComplexChooserEngine::dividendYield(Time t) const {
return process_->dividendYield()->zeroRate(t, Continuous, NoFrequency);
}
DiscountFactor AnalyticComplexChooserEngine::dividendDiscount(Time t) const {
return process_->dividendYield()->discount(t);
}
Rate AnalyticComplexChooserEngine::riskFreeRate(Time t) const {
return process_->riskFreeRate()->zeroRate(t, Continuous, NoFrequency);
}
DiscountFactor AnalyticComplexChooserEngine::riskFreeDiscount(Time t) const {
return process_->riskFreeRate()->discount(t);
}
}
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