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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2011 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.
*/
/*! \file exponentialjump1dmesher.hpp
\brief mesher for a exponential jump mesher with high
mean reversion rate and low jump intensity
*/
#ifndef quantlib_exponential_jump_1d_mesher_hpp
#define quantlib_exponential_jump_1d_mesher_hpp
#include <ql/methods/finitedifferences/meshers/fdm1dmesher.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearopiterator.hpp>
namespace QuantLib {
/*! Mesher for a exponential jump process with high
mean reversion rate and low jump intensity
\f[
\begin{array}{rcl}
dY_t &=& -\beta Y_{t-}dt + J_tdN_t \\
\omega(J)&=&\frac{1}{\eta_u}e^{-\frac{1}{\eta_u}J}
\end{array}
\f]
*/
/*! References:
B. Hambly, S. Howison, T. Kluge, Modelling spikes and pricing
swing options in electricity markets,
http://people.maths.ox.ac.uk/hambly/PDF/Papers/elec.pdf
*/
class ExponentialJump1dMesher : public Fdm1dMesher {
public:
ExponentialJump1dMesher(Size steps, Real beta, Real jumpIntensity,
Real eta, Real eps = 1e-3);
// approximation. see Hambly et.al.
Real jumpSizeDensity(Real x) const; // t->\inf
Real jumpSizeDensity(Real x, Time t) const;
Real jumpSizeDistribution(Real x) const; // t->\inf
Real jumpSizeDistribution(Real x, Time t) const;
private:
const Real beta_, jumpIntensity_, eta_;
};
}
#endif
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