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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2010 SunTrust Bank
Copyright (C) 2010 Cavit Hafizoglu
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/shortrate/generalizedornsteinuhlenbeckprocess.hpp>
namespace QuantLib {
GeneralizedOrnsteinUhlenbeckProcess::GeneralizedOrnsteinUhlenbeckProcess(
const boost::function<Real (Time)>& speed,
const boost::function<Real (Time)>& vol,
Real x0,
Real level)
: x0_(x0), level_(level), speed_(speed), volatility_(vol) {
QL_REQUIRE(x0 >= 0.0, "negative initial data given");
QL_REQUIRE(level >= 0.0, "negative level given");
}
Real GeneralizedOrnsteinUhlenbeckProcess::x0() const {
return x0_;
}
Real GeneralizedOrnsteinUhlenbeckProcess::drift(Time t, Real x) const {
return speed_(t) * (level_ - x);;
}
Real GeneralizedOrnsteinUhlenbeckProcess::diffusion(Time t, Real) const {
return volatility_(t);
}
Real GeneralizedOrnsteinUhlenbeckProcess::expectation(
Time t, Real x0, Time dt) const {
return level_ + (x0 - level_) * std::exp(-speed_(t)*dt);
}
Real GeneralizedOrnsteinUhlenbeckProcess::stdDeviation(
Time t, Real x0, Time dt) const {
return std::sqrt(variance(t,x0,dt));
}
Real GeneralizedOrnsteinUhlenbeckProcess::variance(
Time t, Real, Time dt) const {
Real speed = speed_(t);
Volatility vol = volatility_(t);
if (speed < std::sqrt(QL_EPSILON)) {
// algebraic limit for small speed
return vol*vol*dt;
} else {
return 0.5*vol*vol/speed*(1.0 - std::exp(-2.0*speed*dt));
}
}
Real GeneralizedOrnsteinUhlenbeckProcess::speed(Time t) const {
return speed_(t);
}
Real GeneralizedOrnsteinUhlenbeckProcess::volatility(Time t) const {
return volatility_(t);
}
Real GeneralizedOrnsteinUhlenbeckProcess::level() const {
return level_;
}
}
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