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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2013 Peter Caspers
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/mfstateprocess.hpp>
namespace QuantLib {
MfStateProcess::MfStateProcess(Real reversion, const Array ×,
const Array &vols)
: reversion_(reversion), reversionZero_(false), times_(times),
vols_(vols) {
if (reversion_ < QL_EPSILON && -reversion_ < QL_EPSILON)
reversionZero_ = true;
QL_REQUIRE(times.size() == vols.size() - 1,
"number of volatilities ("
<< vols.size() << ") compared to number of times ("
<< times_.size() << " must be bigger by one");
for (int i = 0; i < ((int)times.size()) - 1; i++)
QL_REQUIRE(times[i] < times[i + 1], "times must be increasing ("
<< times[i] << "@" << i
<< " , " << times[i + 1]
<< "@" << i + 1 << ")");
for (Size i = 0; i < vols.size(); i++)
QL_REQUIRE(vols[i] >= 0.0, "volatilities must be non negative ("
<< vols[i] << "@" << i << ")");
}
Real MfStateProcess::x0() const { return 0.0; }
Real MfStateProcess::drift(Time, Real) const { return 0.0; }
Real MfStateProcess::diffusion(Time t, Real) const {
Size i =
std::upper_bound(times_.begin(), times_.end(), t) - times_.begin();
return vols_[i];
}
Real MfStateProcess::expectation(Time, Real x0, Time dt) const {
return x0;
}
Real MfStateProcess::stdDeviation(Time t, Real x0, Time dt) const {
return std::sqrt(variance(t, x0, dt));
}
Real MfStateProcess::variance(Time t, Real, Time dt) const {
if (dt < QL_EPSILON)
return 0.0;
if (times_.empty())
return reversionZero_ ? dt
: 1.0 / (2.0 * reversion_) *
(std::exp(2.0 * reversion_ * (t + dt)) -
std::exp(2.0 * reversion_ * t));
Size i =
std::upper_bound(times_.begin(), times_.end(), t) - times_.begin();
Size j = std::upper_bound(times_.begin(), times_.end(), t + dt) -
times_.begin();
Real v = 0.0;
for (Size k = i; k < j; k++) {
if (reversionZero_)
v += vols_[k] * vols_[k] *
(times_[k] - std::max(k > 0 ? times_[k - 1] : 0.0, t));
else
v += 1.0 / (2.0 * reversion_) * vols_[k] * vols_[k] *
(std::exp(2.0 * reversion_ * times_[k]) -
std::exp(2.0 * reversion_ *
std::max(k > 0 ? times_[k - 1] : 0.0, t)));
}
if (reversionZero_)
v += vols_[j] * vols_[j] *
(t + dt - std::max(j > 0 ? times_[j - 1] : 0.0, t));
else
v += 1.0 / (2.0 * reversion_) * vols_[j] * vols_[j] *
(std::exp(2.0 * reversion_ * (t + dt)) -
std::exp(2.0 * reversion_ *
(std::max(j > 0 ? times_[j - 1] : 0.0, t))));
return v;
}
}
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