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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) 2003 Ferdinando Ametrano
Copyright (C) 2004, 2005, 2006, 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
<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/processes/ornsteinuhlenbeckprocess.hpp>
namespace QuantLib {
OrnsteinUhlenbeckProcess::OrnsteinUhlenbeckProcess(Real speed,
Volatility vol,
Real x0,
Real level)
: x0_(x0), speed_(speed), level_(level), volatility_(vol) {
QL_REQUIRE(speed_ >= 0.0, "negative speed given");
QL_REQUIRE(volatility_ >= 0.0, "negative volatility given");
}
Real OrnsteinUhlenbeckProcess::x0() const {
return x0_;
}
Real OrnsteinUhlenbeckProcess::speed() const {
return speed_;
}
Real OrnsteinUhlenbeckProcess::volatility() const {
return volatility_;
}
Real OrnsteinUhlenbeckProcess::level() const {
return level_;
}
Real OrnsteinUhlenbeckProcess::drift(Time, Real x) const {
return speed_ * (level_ - x);
}
Real OrnsteinUhlenbeckProcess::diffusion(Time, Real) const {
return volatility_;
}
Real OrnsteinUhlenbeckProcess::expectation(Time, Real x0,
Time dt) const {
return level_ + (x0 - level_) * std::exp(-speed_*dt);
}
Real OrnsteinUhlenbeckProcess::stdDeviation(Time t, Real x0,
Time dt) const {
return std::sqrt(variance(t,x0,dt));
}
Real OrnsteinUhlenbeckProcess::variance(Time, Real, Time dt) const {
if (speed_ < std::sqrt(QL_EPSILON)) {
// algebraic limit for small speed
return volatility_*volatility_*dt;
} else {
return 0.5*volatility_*volatility_/speed_*
(1.0 - std::exp(-2.0*speed_*dt));
}
}
}
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