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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2005, 2006 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
<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/legacy/libormarketmodels/lmlinexpvolmodel.hpp>
namespace QuantLib {
LmLinearExponentialVolatilityModel::LmLinearExponentialVolatilityModel(
const std::vector<Time>& fixingTimes,
Real a, Real b, Real c, Real d)
: LmVolatilityModel(fixingTimes.size(), 4),
fixingTimes_(fixingTimes) {
arguments_[0] = ConstantParameter(a, PositiveConstraint());
arguments_[1] = ConstantParameter(b, PositiveConstraint());
arguments_[2] = ConstantParameter(c, PositiveConstraint());
arguments_[3] = ConstantParameter(d, PositiveConstraint());
}
Disposable<Array> LmLinearExponentialVolatilityModel::volatility(
Time t, const Array&) const {
const Real a = arguments_[0](0.0);
const Real b = arguments_[1](0.0);
const Real c = arguments_[2](0.0);
const Real d = arguments_[3](0.0);
Array tmp(size_, 0.0);
for (Size i=0; i<size_; ++i) {
const Time T = fixingTimes_[i];
if (T>t) {
tmp[i] = (a*(T-t)+d)*std::exp(-b*(T-t)) + c;
}
}
return tmp;
}
Volatility LmLinearExponentialVolatilityModel::volatility(
Size i, Time t, const Array&) const {
const Real a = arguments_[0](0.0);
const Real b = arguments_[1](0.0);
const Real c = arguments_[2](0.0);
const Real d = arguments_[3](0.0);
const Time T = fixingTimes_[i];
return (T>t) ? (a*(T-t)+d)*std::exp(-b*(T-t)) + c : 0.0;
}
Real LmLinearExponentialVolatilityModel::integratedVariance(
Size i, Size j, Time u, const Array&) const {
const Real a = arguments_[0](0.0);
const Real b = arguments_[1](0.0);
const Real c = arguments_[2](0.0);
const Real d = arguments_[3](0.0);
const Time T = fixingTimes_[i];
const Time S = fixingTimes_[j];
const Real k1=std::exp(b*u);
const Real k2=std::exp(b*S);
const Real k3=std::exp(b*T);
return (a*a*(-1 - 2*b*b*S*T - b*(S + T)
+ k1*k1*(1 + b*(S + T - 2*u) + 2*b*b*(S - u)*(T - u)))
+ 2*b*b*(2*c*d*(k2 + k3)*(k1 - 1)
+d*d*(k1*k1 - 1)+2*b*c*c*k2*k3*u)
+ 2*a*b*(d*(-1 - b*(S + T) + k1*k1*(1 + b*(S + T - 2*u)))
-2*c*(k3*(1 + b*S) + k2*(1 + b*T)
- k1*k3*(1 + b*(S - u))
- k1*k2*(1 + b*(T - u)))
)
) / (4*b*b*b*k2*k3);
}
void LmLinearExponentialVolatilityModel::generateArguments() {}
}
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