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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2001, 2002, 2003 Sadruddin Rejeb
Copyright (C) 2007 StatPro Italia srl
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.
*/
#include <ql/models/shortrate/onefactormodels/vasicek.hpp>
#include <ql/pricingengines/blackformula.hpp>
namespace QuantLib {
Vasicek::Vasicek(Rate r0, Real a, Real b, Real sigma, Real lambda)
: OneFactorAffineModel(4), r0_(r0),
a_(arguments_[0]), b_(arguments_[1]), sigma_(arguments_[2]),
lambda_(arguments_[3]) {
a_ = ConstantParameter(a, PositiveConstraint());
b_ = ConstantParameter(b, NoConstraint());
sigma_ = ConstantParameter(sigma, PositiveConstraint());
lambda_ = ConstantParameter(lambda, NoConstraint());
}
Real Vasicek::A(Time t, Time T) const {
Real _a = a();
if (_a < std::sqrt(QL_EPSILON)) {
return 0.0;
} else {
Real sigma2 = sigma()*sigma();
Real bt = B(t, T);
return std::exp((b() + lambda()*sigma()/_a
- 0.5*sigma2/(_a*_a))*(bt - (T - t))
- 0.25*sigma2*bt*bt/_a);
}
}
Real Vasicek::B(Time t, Time T) const {
Real _a = a();
if (_a < std::sqrt(QL_EPSILON))
return (T - t);
else
return (1.0 - std::exp(-_a*(T - t)))/_a;
}
Real Vasicek::discountBondOption(Option::Type type,
Real strike, Time maturity,
Time bondMaturity) const {
Real v;
Real _a = a();
if (std::fabs(maturity) < QL_EPSILON) {
v = 0.0;
} else if (_a < std::sqrt(QL_EPSILON)) {
v = sigma()*B(maturity, bondMaturity)* std::sqrt(maturity);
} else {
v = sigma()*B(maturity, bondMaturity)*
std::sqrt(0.5*(1.0 - std::exp(-2.0*_a*maturity))/_a);
}
Real f = discountBond(0.0, bondMaturity, r0_);
Real k = discountBond(0.0, maturity, r0_)*strike;
return blackFormula(type, k, f, v);
}
}
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