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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/continuousarithmeticasianlevyengine.hpp>
#include <ql/pricingengines/blackcalculator.hpp>
#include <ql/math/distributions/normaldistribution.hpp>
#include <ql/exercise.hpp>
using namespace std;
namespace QuantLib {
ContinuousArithmeticAsianLevyEngine::ContinuousArithmeticAsianLevyEngine(
const boost::shared_ptr<GeneralizedBlackScholesProcess>& process,
const Handle<Quote>& currentAverage,
Date startDate)
: process_(process), currentAverage_(currentAverage),
startDate_(startDate) {
registerWith(process_);
registerWith(currentAverage_);
}
void ContinuousArithmeticAsianLevyEngine::calculate() const {
QL_REQUIRE(arguments_.averageType == Average::Arithmetic,
"not an Arithmetic average option");
QL_REQUIRE(arguments_.exercise->type() == Exercise::European,
"not an European Option");
DayCounter rfdc = process_->riskFreeRate()->dayCounter();
DayCounter divdc = process_->dividendYield()->dayCounter();
DayCounter voldc = process_->blackVolatility()->dayCounter();
Real spot = process_->stateVariable()->value();
// payoff
boost::shared_ptr<StrikedTypePayoff> payoff =
boost::dynamic_pointer_cast<StrikedTypePayoff>(arguments_.payoff);
QL_REQUIRE(payoff, "non-plain payoff given");
// original time to maturity
Date maturity = arguments_.exercise->lastDate();
Time T = rfdc.yearFraction(startDate_,
arguments_.exercise->lastDate());
// remaining time to maturity
Time T2 = rfdc.yearFraction(process_->riskFreeRate()->referenceDate(),
arguments_.exercise->lastDate());
Real strike = payoff->strike();
Volatility volatility =
process_->blackVolatility()->blackVol(maturity, strike);
CumulativeNormalDistribution N;
Rate riskFreeRate = process_->riskFreeRate()->
zeroRate(maturity, rfdc, Continuous, NoFrequency);
Rate dividendYield = process_->dividendYield()->
zeroRate(maturity, divdc, Continuous, NoFrequency);
Real b = riskFreeRate - dividendYield;
QL_REQUIRE(b != 0.0, "null cost of carry not allowed by Levy engine");
Real Se = (spot/(T*b))*(exp((b-riskFreeRate)*T2)-exp(-riskFreeRate*T2));
Real X;
if (T2 < T) {
QL_REQUIRE(!currentAverage_.empty() && currentAverage_->isValid(),
"current average required");
X = strike - ((T-T2)/T)*currentAverage_->value();
} else {
X = strike;
}
Real M = (2*spot*spot/(b+volatility*volatility)) *
(((exp((2*b+volatility*volatility)*T2)-1)
/ (2*b+volatility*volatility))-((exp(b*T2)-1)/b));
Real D = M/(T*T);
Real V = log(D)-2*(riskFreeRate*T2+log(Se));
Real d1 = (1/sqrt(V))*((log(D)/2)-log(X));
Real d2 = d1-sqrt(V);
if(payoff->optionType()==Option::Call)
results_.value = Se*N(d1) - X*exp(-riskFreeRate*T2)*N(d2);
else
results_.value = Se*N(d1) - X*exp(-riskFreeRate*T2)*N(d2)
- Se + X*exp(-riskFreeRate*T2);
}
}
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