1/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
2
3/*
4 Copyright (C) 2008 Yee Man Chan
5
6 This file is part of QuantLib, a free-software/open-source library
7 for financial quantitative analysts and developers - http://quantlib.org/
8
9 QuantLib is free software: you can redistribute it and/or modify it
10 under the terms of the QuantLib license. You should have received a
11 copy of the license along with this program; if not, please email
12 <quantlib-dev@lists.sf.net>. The license is also available online at
13 <http://quantlib.org/license.shtml>.
14
15 This program is distributed in the hope that it will be useful, but WITHOUT
16 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
17 FOR A PARTICULAR PURPOSE. See the license for more details.
18*/
19
20/*! \file gjrgarchprocess.hpp
21 \brief GJR-GARCH(1,1) stochastic process
22*/
23
24#ifndef quantlib_gjrgarch_process_hpp
25#define quantlib_gjrgarch_process_hpp
26
27#include <ql/stochasticprocess.hpp>
28#include <ql/termstructures/yieldtermstructure.hpp>
29#include <ql/quote.hpp>
30
31namespace QuantLib {
32
33 //! Stochastic-volatility GJR-GARCH(1,1) process
34 // parameters supplied should be daily constants
35 // they are annualized by setting the parameter daysPerYear
36 /*! This class describes the stochastic volatility
37 process governed by
38 \f[
39 \begin{array}{rcl}
40 dS(t, S) &=& \mu S dt + \sqrt{v} S dW_1 \\
41 dv(t, S) &=& (\omega + (\beta + \alpha * q_{2}
42 + \gamma * q_{3} - 1) v) dt + (\alpha \sigma_{12}
43 + \gamma \sigma_{13}) v dW_1
44 + \sqrt{\alpha^{2} (\sigma^{2}_{2} - \sigma^{2}_{12})
45 + \gamma^{2} (\sigma^{2}_{3} - \sigma^{2}_{13})
46 + 2 \alpha \gamma (\sigma_{23} - \sigma_{12} \sigma_{13})} v dW_2 \ \
47 N = normalCDF(\lambda) \\
48 n &=& \exp{-\lambda^{2}/2} / \sqrt{2 \pi} \\
49 q_{2} &=& 1 + \lambda^{2} \\
50 q_{3} &=& \lambda n + N + \lambda^2 N \\
51 \sigma^{2}_{2} = 2 + 4 \lambda^{4} \\
52 \sigma^{2}_{3} = \lambda^{3} n + 5 \lambda n + 3N
53 + \lambda^{4} N + 6 \lambda^{2} N -\\lambda^{2} n^{2} - N^{2}
54 - \lambda^{4} N^{2} - 2 \lambda n N - 2 \lambda^{3} nN
55 - 2 \lambda^{2} N^{2} \ \
56 \sigma_{12} = -2 \lambda \\
57 \sigma_{13} = -2 n - 2 \lambda N \\
58 \sigma_{23} = 2N + \sigma_{12} \sigma_{13} \\
59 \end{array}
60 \f]
61
62 \ingroup processes
63 */
64 class GJRGARCHProcess : public StochasticProcess {
65 public:
66 enum Discretization { PartialTruncation, FullTruncation,
67 Reflection};
68
69 GJRGARCHProcess(Handle<YieldTermStructure> riskFreeRate,
70 Handle<YieldTermStructure> dividendYield,
71 Handle<Quote> s0,
72 Real v0,
73 Real omega,
74 Real alpha,
75 Real beta,
76 Real gamma,
77 Real lambda,
78 Real daysPerYear = 252.0,
79 Discretization d = FullTruncation);
80
81 Size size() const override;
82 Array initialValues() const override;
83 Array drift(Time t, const Array& x) const override;
84 Matrix diffusion(Time t, const Array& x) const override;
85 Array apply(const Array& x0, const Array& dx) const override;
86 Array evolve(Time t0, const Array& x0, Time dt, const Array& dw) const override;
87
88 Real v0() const { return v0_; }
89 Real lambda() const { return lambda_; }
90 Real omega() const { return omega_; }
91 Real alpha() const { return alpha_; }
92 Real beta() const { return beta_; }
93 Real gamma() const { return gamma_; }
94 Real daysPerYear() const { return daysPerYear_; }
95
96 const Handle<Quote>& s0() const;
97 const Handle<YieldTermStructure>& dividendYield() const;
98 const Handle<YieldTermStructure>& riskFreeRate() const;
99
100 Time time(const Date&) const override;
101
102 private:
103 Handle<YieldTermStructure> riskFreeRate_, dividendYield_;
104 Handle<Quote> s0_;
105 Real v0_, omega_, alpha_, beta_, gamma_, lambda_, daysPerYear_;
106 Discretization discretization_;
107 };
108
109}
110
111
112#endif
113

source code of quantlib/ql/processes/gjrgarchprocess.hpp