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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2018 Klaus Spanderen
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.
*/
/*! \file analyticcevengine.cpp */
#include <ql/exercise.hpp>
#include <ql/math/functional.hpp>
#include <ql/pricingengines/vanilla/analyticcevengine.hpp>
#include <boost/math/distributions/non_central_chi_squared.hpp>
#include <boost/math/special_functions/gamma.hpp>
#include <utility>
namespace QuantLib {
CEVCalculator::CEVCalculator(Real f0, Real alpha, Real beta)
: f0_(f0),
alpha_(alpha),
beta_(beta),
delta_((1.0-2.0*beta)/(1.0-beta)),
x0_(X(f0)) { }
Real CEVCalculator::X(Real f) const {
return std::pow(f, 2.0*(1.0-beta_))/squared(alpha_*(1.0-beta_));
}
Real CEVCalculator::value(
Option::Type optionType, Real strike, Time t) const {
typedef boost::math::non_central_chi_squared_distribution<Real>
nc_chi2;
const Real kTilde = X(strike);
if (optionType == Option::Call) {
if (delta_ < 2.0) {
return f0_ * (1.0 - boost::math::cdf(
nc_chi2(4.0-delta_, x0_/t), kTilde/t))
- strike * boost::math::cdf(
nc_chi2(2.0-delta_, kTilde/t), x0_/t);
}
else {
const Real g =
boost::math::gamma_p(0.5*delta_-1.0,x0_/(2.0*t));
return f0_ * (g - boost::math::cdf(
nc_chi2(delta_-2.0, kTilde/t), x0_/t))
- strike * boost::math::cdf(
nc_chi2(delta_, x0_/t), kTilde/t);
}
}
else if (optionType == Option::Put) {
if (delta_ < 2.0) {
return - f0_ * boost::math::cdf(
nc_chi2(4.0-delta_, x0_/t), kTilde/t)
+ strike * (1.0 - boost::math::cdf(
nc_chi2(2.0-delta_, kTilde/t), x0_/t));
}
else {
return - f0_ * boost::math::cdf(
nc_chi2(delta_-2.0, kTilde/t), x0_/t)
+ strike * (1.0 - boost::math::cdf(
nc_chi2(delta_, x0_/t), kTilde/t));
}
}
else
QL_FAIL("unknown option type");
}
AnalyticCEVEngine::AnalyticCEVEngine(Real f0,
Real alpha,
Real beta,
Handle<YieldTermStructure> discountCurve)
: calculator_(ext::make_shared<CEVCalculator>(f0, alpha, beta)),
discountCurve_(std::move(discountCurve)) {
registerWith(discountCurve_);
}
void AnalyticCEVEngine::calculate() const {
QL_REQUIRE(arguments_.exercise->type() == Exercise::European,
"not an European option");
ext::shared_ptr<StrikedTypePayoff> payoff =
ext::dynamic_pointer_cast<StrikedTypePayoff>(arguments_.payoff);
QL_REQUIRE(payoff, "non-striked payoff given");
const Date exerciseDate = arguments_.exercise->lastDate();
results_.value = calculator_->value(
payoff->optionType(),
payoff->strike(),
discountCurve_->timeFromReference(exerciseDate))
* discountCurve_->discount(exerciseDate);
}
}
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