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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2010 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/math/integrals/gausslobattointegral.hpp>
#include <ql/processes/ornsteinuhlenbeckprocess.hpp>
#include <ql/experimental/processes/extendedornsteinuhlenbeckprocess.hpp>
namespace QuantLib {
namespace {
class integrand {
ext::function<Real (Real)> b;
Real speed;
public:
integrand(const ext::function<Real (Real)>& b, Real speed)
: b(b), speed(speed) {}
Real operator()(Real x) const {
return b(x) * std::exp(speed*x);
}
};
}
ExtendedOrnsteinUhlenbeckProcess::ExtendedOrnsteinUhlenbeckProcess(
Real speed, Volatility vol, Real x0,
const ext::function<Real (Real)>& b,
Discretization discretization,
Real intEps)
: speed_ (speed),
vol_ (vol),
b_ (b),
intEps_ (intEps),
ouProcess_(new OrnsteinUhlenbeckProcess(speed, vol, x0)),
discretization_(discretization) {
QL_REQUIRE(speed_ >= 0.0, "negative a given");
QL_REQUIRE(vol_ >= 0.0, "negative volatility given");
}
Real ExtendedOrnsteinUhlenbeckProcess::x0() const {
return ouProcess_->x0();
}
Real ExtendedOrnsteinUhlenbeckProcess::drift(Time t, Real x) const {
return ouProcess_->drift(t, x) + speed_*b_(t);
}
Real ExtendedOrnsteinUhlenbeckProcess::diffusion(Time t, Real x) const{
return ouProcess_->diffusion(t, x);
}
Real ExtendedOrnsteinUhlenbeckProcess::stdDeviation(
Time t0, Real x0, Time dt) const{
return ouProcess_->stdDeviation(t0, x0, dt);
}
Real ExtendedOrnsteinUhlenbeckProcess::variance(
Time t0, Real x0, Time dt) const{
return ouProcess_->variance(t0, x0, dt);
}
Real ExtendedOrnsteinUhlenbeckProcess::speed() const {
return speed_;
}
Real ExtendedOrnsteinUhlenbeckProcess::volatility() const {
return vol_;
}
Real ExtendedOrnsteinUhlenbeckProcess::expectation(
Time t0, Real x0, Time dt) const {
switch (discretization_) {
case MidPoint:
return ouProcess_->expectation(t0, x0, dt)
+ b_(t0+0.5*dt)*(1.0 - std::exp(-speed_*dt));
break;
case Trapezodial:
{
const Time t = t0+dt;
const Time u = t0;
const Real bt = b_(t);
const Real bu = b_(u);
const Real ex = std::exp(-speed_*dt);
return ouProcess_->expectation(t0, x0, dt)
+ bt-ex*bu - (bt-bu)/(speed_*dt)*(1-ex);
}
break;
case GaussLobatto:
return ouProcess_->expectation(t0, x0, dt)
+ speed_*std::exp(-speed_*(t0+dt))
* GaussLobattoIntegral(100000, intEps_)(integrand(b_, speed_),
t0, t0+dt);
break;
default:
QL_FAIL("unknown discretization scheme");
}
}
}
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