1/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
2
3/*
4 Copyright (C) 2005, 2007, 2009, 2014 Klaus Spanderen
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 hestonprocess.hpp
21 \brief Heston stochastic process
22*/
23
24#ifndef quantlib_heston_process_hpp
25#define quantlib_heston_process_hpp
26
27#include <ql/stochasticprocess.hpp>
28#include <ql/termstructures/yieldtermstructure.hpp>
29#include <ql/quote.hpp>
30
31namespace QuantLib {
32
33 //! Square-root stochastic-volatility Heston process
34 /*! This class describes the square root stochastic volatility
35 process governed by
36 \f[
37 \begin{array}{rcl}
38 dS(t, S) &=& \mu S dt + \sqrt{v} S dW_1 \\
39 dv(t, S) &=& \kappa (\theta - v) dt + \sigma \sqrt{v} dW_2 \\
40 dW_1 dW_2 &=& \rho dt
41 \end{array}
42 \f]
43
44 \ingroup processes
45 */
46 class HestonProcess : public StochasticProcess {
47 public:
48 enum Discretization { PartialTruncation,
49 FullTruncation,
50 Reflection,
51 NonCentralChiSquareVariance,
52 QuadraticExponential,
53 QuadraticExponentialMartingale,
54 BroadieKayaExactSchemeLobatto,
55 BroadieKayaExactSchemeLaguerre,
56 BroadieKayaExactSchemeTrapezoidal };
57
58 HestonProcess(Handle<YieldTermStructure> riskFreeRate,
59 Handle<YieldTermStructure> dividendYield,
60 Handle<Quote> s0,
61 Real v0,
62 Real kappa,
63 Real theta,
64 Real sigma,
65 Real rho,
66 Discretization d = QuadraticExponentialMartingale);
67
68 Size size() const override;
69 Size factors() const override;
70
71 Array initialValues() const override;
72 Array drift(Time t, const Array& x) const override;
73 Matrix diffusion(Time t, const Array& x) const override;
74 Array apply(const Array& x0, const Array& dx) const override;
75 Array evolve(Time t0, const Array& x0, Time dt, const Array& dw) const override;
76
77 Real v0() const { return v0_; }
78 Real rho() const { return rho_; }
79 Real kappa() const { return kappa_; }
80 Real theta() const { return theta_; }
81 Real sigma() const { return sigma_; }
82
83 const Handle<Quote>& s0() const;
84 const Handle<YieldTermStructure>& dividendYield() const;
85 const Handle<YieldTermStructure>& riskFreeRate() const;
86
87 Time time(const Date&) const override;
88
89 // probability densitiy function,
90 // semi-analytical solution of the Fokker-Planck equation in x=ln(s)
91 Real pdf(Real x, Real v, Time t, Real eps=1e-3) const;
92
93 private:
94 Real varianceDistribution(Real v, Real dw, Time dt) const;
95
96 Handle<YieldTermStructure> riskFreeRate_, dividendYield_;
97 Handle<Quote> s0_;
98 Real v0_, kappa_, theta_, sigma_, rho_;
99 Discretization discretization_;
100 };
101}
102#endif
103

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