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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2014 Peter Caspers
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/volatility/noarbsabrsmilesection.hpp>
#include <ql/pricingengines/blackformula.hpp>
#include <ql/termstructures/volatility/sabr.hpp>
namespace QuantLib {
NoArbSabrSmileSection::NoArbSabrSmileSection(
Time timeToExpiry, Rate forward, const std::vector<Real> &sabrParams,
Real shift)
: SmileSection(timeToExpiry, DayCounter()), forward_(forward),
params_(sabrParams), shift_(shift) {
init();
}
NoArbSabrSmileSection::NoArbSabrSmileSection(
const Date &d, Rate forward, const std::vector<Real> &sabrParams,
const DayCounter &dc, Real shift)
: SmileSection(d, dc, Date()), forward_(forward), params_(sabrParams), shift_(shift) {
init();
}
void NoArbSabrSmileSection::init() {
QL_REQUIRE(params_.size() >= 4,
"sabr expects 4 parameters (alpha,beta,nu,rho) but ("
<< params_.size() << ") given");
QL_REQUIRE(forward_ > 0.0, "forward (" << forward_ << ") must be positive");
QL_REQUIRE(
shift_ == 0.0,
"shift (" << shift_
<< ") must be zero, other shifts are not implemented yet");
model_ =
ext::make_shared<NoArbSabrModel>(exerciseTime(), forward_, params_[0],
params_[1], params_[2], params_[3]);
}
Real NoArbSabrSmileSection::optionPrice(Rate strike, Option::Type type,
Real discount) const {
Real call = model_->optionPrice(strike);
return discount *
(type == Option::Call ? call : call - (forward_ - strike));
}
Real NoArbSabrSmileSection::digitalOptionPrice(Rate strike, Option::Type type,
Real discount, Real) const {
Real call = model_->digitalOptionPrice(strike);
return discount * (type == Option::Call ? call : 1.0 - call);
}
Real NoArbSabrSmileSection::density(Rate strike, Real discount, Real) const {
return discount * model_->density(strike);
}
Real NoArbSabrSmileSection::volatilityImpl(Rate strike) const {
Real impliedVol = 0.0;
try {
Option::Type type;
if (strike >= forward_)
type = Option::Call;
else
type = Option::Put;
impliedVol =
blackFormulaImpliedStdDev(type, strike, forward_,
optionPrice(strike, type, 1.0), 1.0) /
std::sqrt(exerciseTime());
} catch (...) {
}
if (impliedVol == 0.0)
// fall back on Hagan 2002 expansion
impliedVol =
unsafeSabrVolatility(strike, forward_, exerciseTime(), params_[0],
params_[1], params_[2], params_[3]);
return impliedVol;
}
} // namespace QuantLib
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