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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2008 Yee Man Chan
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 gjrgarchprocess.hpp
\brief GJR-GARCH(1,1) stochastic process
*/
#ifndef quantlib_gjrgarch_process_hpp
#define quantlib_gjrgarch_process_hpp
#include <ql/stochasticprocess.hpp>
#include <ql/termstructures/yieldtermstructure.hpp>
#include <ql/quote.hpp>
namespace QuantLib {
//! Stochastic-volatility GJR-GARCH(1,1) process
// parameters supplied should be daily constants
// they are annualized by setting the parameter daysPerYear
/*! This class describes the stochastic volatility
process governed by
\f[
\begin{array}{rcl}
dS(t, S) &=& \mu S dt + \sqrt{v} S dW_1 \\
dv(t, S) &=& (\omega + (\beta + \alpha * q_{2}
+ \gamma * q_{3} - 1) v) dt + (\alpha \sigma_{12}
+ \gamma \sigma_{13}) v dW_1
+ \sqrt{\alpha^{2} (\sigma^{2}_{2} - \sigma^{2}_{12})
+ \gamma^{2} (\sigma^{2}_{3} - \sigma^{2}_{13})
+ 2 \alpha \gamma (\sigma_{23} - \sigma_{12} \sigma_{13})} v dW_2 \ \
N = normalCDF(\lambda) \\
n &=& \exp{-\lambda^{2}/2} / \sqrt{2 \pi} \\
q_{2} &=& 1 + \lambda^{2} \\
q_{3} &=& \lambda n + N + \lambda^2 N \\
\sigma^{2}_{2} = 2 + 4 \lambda^{4} \\
\sigma^{2}_{3} = \lambda^{3} n + 5 \lambda n + 3N
+ \lambda^{4} N + 6 \lambda^{2} N -\\lambda^{2} n^{2} - N^{2}
- \lambda^{4} N^{2} - 2 \lambda n N - 2 \lambda^{3} nN
- 2 \lambda^{2} N^{2} \ \
\sigma_{12} = -2 \lambda \\
\sigma_{13} = -2 n - 2 \lambda N \\
\sigma_{23} = 2N + \sigma_{12} \sigma_{13} \\
\end{array}
\f]
\ingroup processes
*/
class GJRGARCHProcess : public StochasticProcess {
public:
enum Discretization { PartialTruncation, FullTruncation,
Reflection};
GJRGARCHProcess(Handle<YieldTermStructure> riskFreeRate,
Handle<YieldTermStructure> dividendYield,
Handle<Quote> s0,
Real v0,
Real omega,
Real alpha,
Real beta,
Real gamma,
Real lambda,
Real daysPerYear = 252.0,
Discretization d = FullTruncation);
Size size() const override;
Array initialValues() const override;
Array drift(Time t, const Array& x) const override;
Matrix diffusion(Time t, const Array& x) const override;
Array apply(const Array& x0, const Array& dx) const override;
Array evolve(Time t0, const Array& x0, Time dt, const Array& dw) const override;
Real v0() const { return v0_; }
Real lambda() const { return lambda_; }
Real omega() const { return omega_; }
Real alpha() const { return alpha_; }
Real beta() const { return beta_; }
Real gamma() const { return gamma_; }
Real daysPerYear() const { return daysPerYear_; }
const Handle<Quote>& s0() const;
const Handle<YieldTermStructure>& dividendYield() const;
const Handle<YieldTermStructure>& riskFreeRate() const;
Time time(const Date&) const override;
private:
Handle<YieldTermStructure> riskFreeRate_, dividendYield_;
Handle<Quote> s0_;
Real v0_, omega_, alpha_, beta_, gamma_, lambda_, daysPerYear_;
Discretization discretization_;
};
}
#endif
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