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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2006, 2007 Ferdinando Ametrano
Copyright (C) 2006 Cristina Duminuco
Copyright (C) 2005, 2006 Klaus Spanderen
Copyright (C) 2007 Giorgio Facchinetti
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/termstructures/volatility/abcd.hpp>
#include <ql/math/comparison.hpp>
#include <algorithm>
namespace QuantLib {
AbcdFunction::AbcdFunction(Real a, Real b, Real c, Real d)
: AbcdMathFunction(a, b, c, d) {}
Real AbcdFunction::volatility(Time tMin, Time tMax, Time T) const {
if (tMax==tMin)
return instantaneousVolatility(tMax, T);
QL_REQUIRE(tMax>tMin, "tMax must be > tMin");
return std::sqrt(variance(tMin, tMax, T)/(tMax-tMin));
}
Real AbcdFunction::variance(Time tMin, Time tMax, Time T) const {
return covariance(tMin, tMax, T, T);
}
Real AbcdFunction::covariance(Time t, Time T, Time S) const {
return (*this)(T-t) * (*this)(S-t);
}
Real AbcdFunction::covariance(Time t1, Time t2, Time T, Time S) const {
QL_REQUIRE(t1<=t2,
"integrations bounds (" << t1 <<
"," << t2 << ") are in reverse order");
Time cutOff = std::min(S,T);
if (t1>=cutOff) {
return 0.0;
} else {
cutOff = std::min(t2, cutOff);
return primitive(cutOff, T, S) - primitive(t1, T, S);
}
}
// INSTANTANEOUS
Real AbcdFunction::instantaneousVolatility(Time u, Time T) const {
return std::sqrt(instantaneousVariance(u, T));
}
Real AbcdFunction::instantaneousVariance(Time u, Time T) const {
return instantaneousCovariance(u, T, T);
}
Real AbcdFunction::instantaneousCovariance(Time u, Time T, Time S) const {
return (*this)(T-u)*(*this)(S-u);
}
// PRIMITIVE
Real AbcdFunction::primitive(Time t, Time T, Time S) const {
if (T<t || S<t) return 0.0;
if (close(c_,0.0)) {
Real v = a_+d_;
return t*(v*v+v*b_*S+v*b_*T-v*b_*t+b_*b_*S*T-0.5*b_*b_*t*(S+T)+b_*b_*t*t/3.0);
}
Real k1=std::exp(c_*t), k2=std::exp(c_*S), k3=std::exp(c_*T);
return (b_*b_*(-1 - 2*c_*c_*S*T - c_*(S + T)
+ k1*k1*(1 + c_*(S + T - 2*t) + 2*c_*c_*(S - t)*(T - t)))
+ 2*c_*c_*(2*d_*a_*(k2 + k3)*(k1 - 1)
+a_*a_*(k1*k1 - 1)+2*c_*d_*d_*k2*k3*t)
+ 2*b_*c_*(a_*(-1 - c_*(S + T) + k1*k1*(1 + c_*(S + T - 2*t)))
-2*d_*(k3*(1 + c_*S) + k2*(1 + c_*T)
- k1*k3*(1 + c_*(S - t))
- k1*k2*(1 + c_*(T - t)))
)
) / (4*c_*c_*c_*k2*k3);
}
//===========================================================================//
// AbcdSquared //
//===========================================================================//
AbcdSquared::AbcdSquared(Real a, Real b, Real c, Real d, Time T, Time S)
: abcd_(new AbcdFunction(a,b,c,d)),
T_(T), S_(S) {}
Real AbcdSquared::operator()(Time t) const {
return abcd_->covariance(t, T_, S_);
}
}
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