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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2011 Master IMAFA - Polytech'Nice Sophia - Universit 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
<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/exoticoptions/analyticwriterextensibleoptionengine.hpp>
#include <ql/math/distributions/bivariatenormaldistribution.hpp>
#include <ql/pricingengines/blackformula.hpp>
using namespace std;
namespace QuantLib {
AnalyticWriterExtensibleOptionEngine::AnalyticWriterExtensibleOptionEngine(
const boost::shared_ptr<GeneralizedBlackScholesProcess>& process)
: process_(process) {
registerWith(process_);
}
void AnalyticWriterExtensibleOptionEngine::calculate() const {
// We take all the arguments:
boost::shared_ptr<PlainVanillaPayoff> payoff1 =
boost::dynamic_pointer_cast<PlainVanillaPayoff>(arguments_.payoff);
QL_REQUIRE(payoff1, "not a plain vanilla payoff");
boost::shared_ptr<PlainVanillaPayoff> payoff2 =
boost::dynamic_pointer_cast<PlainVanillaPayoff>(arguments_.payoff2);
QL_REQUIRE(payoff2, "not a plain vanilla payoff");
boost::shared_ptr<Exercise> exercise1 = arguments_.exercise;
boost::shared_ptr<Exercise> exercise2 = arguments_.exercise2;
// We create and apply the calculate process:
Option::Type type = payoff1->optionType();
// STEP 1:
// S = spot
Real spot = process_->stateVariable()->value();
// For the B&S formulae:
DayCounter dividendDC = process_->dividendYield()->dayCounter();
Rate dividend = process_->dividendYield()->zeroRate(
exercise1->lastDate(), dividendDC, Continuous, NoFrequency);
DayCounter riskFreeDC = process_->riskFreeRate()->dayCounter();
Rate riskFree = process_->riskFreeRate()->zeroRate(
exercise1->lastDate(), riskFreeDC, Continuous, NoFrequency);
// The time to maturity:
Time t1 = riskFreeDC.yearFraction(
process_->riskFreeRate()->referenceDate(),
arguments_.exercise->lastDate());
Time t2 = riskFreeDC.yearFraction(
process_->riskFreeRate()->referenceDate(),
arguments_.exercise2->lastDate());
// b = r-q:
Real b = riskFree - dividend;
Real forwardPrice = spot * std::exp(b*t1);
Volatility volatility = process_->blackVolatility()->blackVol(
exercise1->lastDate(), payoff1->strike());
Real stdDev = volatility*std::sqrt(t1);
Real discount = std::exp(-riskFree*t1);
// Call the B&S method:
Real black = blackFormula(type, payoff1->strike(),
forwardPrice, stdDev, discount);
// STEP 2:
// Standard bivariate normal distribution:
Real ro = std::sqrt(t1/t2);
Real z1 = (std::log(spot/payoff2->strike()) +
(b+std::pow(volatility, 2)/2)*t2)/(volatility*std::sqrt(t2));
Real z2 = (std::log(spot/payoff1->strike()) +
(b+std::pow(volatility, 2)/2)*t1)/(volatility*std::sqrt(t1));
// Call the bivariate method:
BivariateCumulativeNormalDistributionWe04DP biv(-ro);
// STEP 3:
Real bivariate1, bivariate2, result;
// Final computing:
if (type == Option::Call) {
// Call case:
bivariate1 = biv(z1, -z2);
bivariate2 = biv(z1-volatility*std::sqrt(t2),
-z2+volatility*std::sqrt(t1));
result = black + spot*std::exp((b-riskFree)*t2)*bivariate1
- payoff2->strike()*std::exp((-riskFree)*t2)*bivariate2;
} else {
// Put case:
bivariate1 = biv(-z1, z2);
bivariate2 = biv(-z1+volatility*std::sqrt(t2),
z2-volatility*std::sqrt(t1));
result = black - spot*std::exp((b-riskFree)*t2)*bivariate1
+ payoff2->strike()*std::exp((-riskFree)*t2)*bivariate2;
}
// Save the result:
results_.value = result;
}
}
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