| 1 | /* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */ |
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| 2 | |
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| 3 | /* |
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| 4 | Copyright (C) 2003 Ferdinando Ametrano |
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| 5 | Copyright (C) 2001, 2002, 2003 Sadruddin Rejeb |
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| 6 | Copyright (C) 2004, 2005 StatPro Italia srl |
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| 7 | |
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| 8 | This file is part of QuantLib, a free-software/open-source library |
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| 9 | for financial quantitative analysts and developers - http://quantlib.org/ |
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| 10 | |
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| 11 | QuantLib is free software: you can redistribute it and/or modify it |
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| 12 | under the terms of the QuantLib license. You should have received a |
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| 13 | copy of the license along with this program; if not, please email |
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| 14 | <quantlib-dev@lists.sf.net>. The license is also available online at |
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| 15 | <http://quantlib.org/license.shtml>. |
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| 16 | |
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| 17 | This program is distributed in the hope that it will be useful, but WITHOUT |
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| 18 | ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS |
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| 19 | FOR A PARTICULAR PURPOSE. See the license for more details. |
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| 20 | */ |
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| 21 | |
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| 22 | /*! \file stochasticprocess.hpp |
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| 23 | \brief stochastic processes |
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| 24 | */ |
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| 25 | |
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| 26 | #ifndef quantlib_stochastic_process_hpp |
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| 27 | #define quantlib_stochastic_process_hpp |
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| 28 | |
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| 29 | #include <ql/time/date.hpp> |
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| 30 | #include <ql/patterns/observable.hpp> |
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| 31 | #include <ql/math/matrix.hpp> |
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| 32 | |
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| 33 | namespace QuantLib { |
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| 34 | |
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| 35 | //! multi-dimensional stochastic process class. |
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| 36 | /*! This class describes a stochastic process governed by |
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| 37 | \f[ |
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| 38 | d\mathrm{x}_t = \mu(t, x_t)\mathrm{d}t |
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| 39 | + \sigma(t, \mathrm{x}_t) \cdot d\mathrm{W}_t. |
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| 40 | \f] |
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| 41 | */ |
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| 42 | class StochasticProcess : public Observer, public Observable { |
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| 43 | public: |
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| 44 | //! discretization of a stochastic process over a given time interval |
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| 45 | class discretization { |
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| 46 | public: |
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| 47 | virtual ~discretization() = default; |
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| 48 | virtual Array drift(const StochasticProcess&, |
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| 49 | Time t0, |
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| 50 | const Array& x0, |
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| 51 | Time dt) const = 0; |
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| 52 | virtual Matrix diffusion(const StochasticProcess&, |
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| 53 | Time t0, |
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| 54 | const Array& x0, |
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| 55 | Time dt) const = 0; |
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| 56 | virtual Matrix covariance(const StochasticProcess&, |
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| 57 | Time t0, |
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| 58 | const Array& x0, |
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| 59 | Time dt) const = 0; |
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| 60 | }; |
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| 61 | ~StochasticProcess() override = default; |
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| 62 | //! \name Stochastic process interface |
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| 63 | //@{ |
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| 64 | //! returns the number of dimensions of the stochastic process |
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| 65 | virtual Size size() const = 0; |
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| 66 | //! returns the number of independent factors of the process |
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| 67 | virtual Size factors() const; |
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| 68 | //! returns the initial values of the state variables |
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| 69 | virtual Array initialValues() const = 0; |
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| 70 | /*! \brief returns the drift part of the equation, i.e., |
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| 71 | \f$ \mu(t, \mathrm{x}_t) \f$ |
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| 72 | */ |
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| 73 | virtual Array drift(Time t, |
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| 74 | const Array& x) const = 0; |
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| 75 | /*! \brief returns the diffusion part of the equation, i.e. |
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| 76 | \f$ \sigma(t, \mathrm{x}_t) \f$ |
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| 77 | */ |
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| 78 | virtual Matrix diffusion(Time t, |
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| 79 | const Array& x) const = 0; |
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| 80 | /*! returns the expectation |
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| 81 | \f$ E(\mathrm{x}_{t_0 + \Delta t} |
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| 82 | | \mathrm{x}_{t_0} = \mathrm{x}_0) \f$ |
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| 83 | of the process after a time interval \f$ \Delta t \f$ |
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| 84 | according to the given discretization. This method can be |
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| 85 | overridden in derived classes which want to hard-code a |
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| 86 | particular discretization. |
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| 87 | */ |
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| 88 | virtual Array expectation(Time t0, |
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| 89 | const Array& x0, |
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| 90 | Time dt) const; |
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| 91 | /*! returns the standard deviation |
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| 92 | \f$ S(\mathrm{x}_{t_0 + \Delta t} |
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| 93 | | \mathrm{x}_{t_0} = \mathrm{x}_0) \f$ |
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| 94 | of the process after a time interval \f$ \Delta t \f$ |
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| 95 | according to the given discretization. This method can be |
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| 96 | overridden in derived classes which want to hard-code a |
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| 97 | particular discretization. |
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| 98 | */ |
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| 99 | virtual Matrix stdDeviation(Time t0, |
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| 100 | const Array& x0, |
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| 101 | Time dt) const; |
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| 102 | /*! returns the covariance |
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| 103 | \f$ V(\mathrm{x}_{t_0 + \Delta t} |
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| 104 | | \mathrm{x}_{t_0} = \mathrm{x}_0) \f$ |
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| 105 | of the process after a time interval \f$ \Delta t \f$ |
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| 106 | according to the given discretization. This method can be |
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| 107 | overridden in derived classes which want to hard-code a |
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| 108 | particular discretization. |
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| 109 | */ |
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| 110 | virtual Matrix covariance(Time t0, |
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| 111 | const Array& x0, |
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| 112 | Time dt) const; |
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| 113 | /*! returns the asset value after a time interval \f$ \Delta t |
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| 114 | \f$ according to the given discretization. By default, it |
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| 115 | returns |
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| 116 | \f[ |
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| 117 | E(\mathrm{x}_0,t_0,\Delta t) + |
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| 118 | S(\mathrm{x}_0,t_0,\Delta t) \cdot \Delta \mathrm{w} |
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| 119 | \f] |
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| 120 | where \f$ E \f$ is the expectation and \f$ S \f$ the |
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| 121 | standard deviation. |
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| 122 | */ |
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| 123 | virtual Array evolve(Time t0, |
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| 124 | const Array& x0, |
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| 125 | Time dt, |
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| 126 | const Array& dw) const; |
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| 127 | /*! applies a change to the asset value. By default, it |
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| 128 | returns \f$ \mathrm{x} + \Delta \mathrm{x} \f$. |
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| 129 | */ |
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| 130 | virtual Array apply(const Array& x0, |
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| 131 | const Array& dx) const; |
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| 132 | //@} |
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| 133 | |
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| 134 | //! \name utilities |
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| 135 | //@{ |
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| 136 | /*! returns the time value corresponding to the given date |
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| 137 | in the reference system of the stochastic process. |
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| 138 | |
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| 139 | \note As a number of processes might not need this |
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| 140 | functionality, a default implementation is given |
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| 141 | which raises an exception. |
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| 142 | */ |
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| 143 | virtual Time time(const Date&) const; |
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| 144 | //@} |
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| 145 | |
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| 146 | //! \name Observer interface |
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| 147 | //@{ |
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| 148 | void update() override; |
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| 149 | //@} |
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| 150 | protected: |
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| 151 | StochasticProcess() = default; |
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| 152 | explicit StochasticProcess(ext::shared_ptr<discretization>); |
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| 153 | ext::shared_ptr<discretization> discretization_; |
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| 154 | }; |
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| 155 | |
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| 156 | |
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| 157 | //! 1-dimensional stochastic process |
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| 158 | /*! This class describes a stochastic process governed by |
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| 159 | \f[ |
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| 160 | dx_t = \mu(t, x_t)dt + \sigma(t, x_t)dW_t. |
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| 161 | \f] |
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| 162 | */ |
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| 163 | class StochasticProcess1D : public StochasticProcess { |
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| 164 | public: |
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| 165 | //! discretization of a 1-D stochastic process |
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| 166 | class discretization { |
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| 167 | public: |
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| 168 | virtual ~discretization() = default; |
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| 169 | virtual Real drift(const StochasticProcess1D&, |
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| 170 | Time t0, Real x0, Time dt) const = 0; |
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| 171 | virtual Real diffusion(const StochasticProcess1D&, |
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| 172 | Time t0, Real x0, Time dt) const = 0; |
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| 173 | virtual Real variance(const StochasticProcess1D&, |
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| 174 | Time t0, Real x0, Time dt) const = 0; |
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| 175 | }; |
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| 176 | //! \name 1-D stochastic process interface |
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| 177 | //@{ |
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| 178 | //! returns the initial value of the state variable |
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| 179 | virtual Real x0() const = 0; |
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| 180 | //! returns the drift part of the equation, i.e. \f$ \mu(t, x_t) \f$ |
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| 181 | virtual Real drift(Time t, Real x) const = 0; |
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| 182 | /*! \brief returns the diffusion part of the equation, i.e. |
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| 183 | \f$ \sigma(t, x_t) \f$ |
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| 184 | */ |
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| 185 | virtual Real diffusion(Time t, Real x) const = 0; |
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| 186 | /*! returns the expectation |
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| 187 | \f$ E(x_{t_0 + \Delta t} | x_{t_0} = x_0) \f$ |
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| 188 | of the process after a time interval \f$ \Delta t \f$ |
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| 189 | according to the given discretization. This method can be |
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| 190 | overridden in derived classes which want to hard-code a |
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| 191 | particular discretization. |
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| 192 | */ |
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| 193 | virtual Real expectation(Time t0, Real x0, Time dt) const; |
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| 194 | /*! returns the standard deviation |
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| 195 | \f$ S(x_{t_0 + \Delta t} | x_{t_0} = x_0) \f$ |
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| 196 | of the process after a time interval \f$ \Delta t \f$ |
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| 197 | according to the given discretization. This method can be |
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| 198 | overridden in derived classes which want to hard-code a |
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| 199 | particular discretization. |
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| 200 | */ |
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| 201 | virtual Real stdDeviation(Time t0, Real x0, Time dt) const; |
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| 202 | /*! returns the variance |
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| 203 | \f$ V(x_{t_0 + \Delta t} | x_{t_0} = x_0) \f$ |
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| 204 | of the process after a time interval \f$ \Delta t \f$ |
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| 205 | according to the given discretization. This method can be |
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| 206 | overridden in derived classes which want to hard-code a |
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| 207 | particular discretization. |
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| 208 | */ |
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| 209 | virtual Real variance(Time t0, Real x0, Time dt) const; |
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| 210 | /*! returns the asset value after a time interval \f$ \Delta t |
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| 211 | \f$ according to the given discretization. By default, it |
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| 212 | returns |
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| 213 | \f[ |
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| 214 | E(x_0,t_0,\Delta t) + S(x_0,t_0,\Delta t) \cdot \Delta w |
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| 215 | \f] |
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| 216 | where \f$ E \f$ is the expectation and \f$ S \f$ the |
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| 217 | standard deviation. |
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| 218 | */ |
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| 219 | virtual Real evolve(Time t0, Real x0, Time dt, Real dw) const; |
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| 220 | /*! applies a change to the asset value. By default, it |
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| 221 | returns \f$ x + \Delta x \f$. |
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| 222 | */ |
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| 223 | virtual Real apply(Real x0, Real dx) const; |
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| 224 | //@} |
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| 225 | protected: |
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| 226 | StochasticProcess1D() = default; |
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| 227 | explicit StochasticProcess1D(ext::shared_ptr<discretization>); |
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| 228 | ext::shared_ptr<discretization> discretization_; |
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| 229 | private: |
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| 230 | // StochasticProcess interface implementation |
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| 231 | Size size() const override; |
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| 232 | Array initialValues() const override; |
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| 233 | Array drift(Time t, const Array& x) const override; |
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| 234 | Matrix diffusion(Time t, const Array& x) const override; |
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| 235 | Array expectation(Time t0, const Array& x0, Time dt) const override; |
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| 236 | Matrix stdDeviation(Time t0, const Array& x0, Time dt) const override; |
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| 237 | Matrix covariance(Time t0, const Array& x0, Time dt) const override; |
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| 238 | Array evolve(Time t0, const Array& x0, Time dt, const Array& dw) const override; |
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| 239 | Array apply(const Array& x0, const Array& dx) const override; |
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| 240 | }; |
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| 241 | |
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| 242 | |
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| 243 | // inline definitions |
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| 244 | |
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| 245 | inline Size StochasticProcess1D::size() const { |
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| 246 | return 1; |
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| 247 | } |
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| 248 | |
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| 249 | inline Array StochasticProcess1D::initialValues() const { |
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| 250 | Array a(1, x0()); |
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| 251 | return a; |
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| 252 | } |
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| 253 | |
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| 254 | inline Array StochasticProcess1D::drift(Time t, const Array& x) const { |
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| 255 | #if defined(QL_EXTRA_SAFETY_CHECKS) |
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| 256 | QL_REQUIRE(x.size() == 1, "1-D array required" ); |
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| 257 | #endif |
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| 258 | Array a(1, drift(t, x: x[0])); |
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| 259 | return a; |
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| 260 | } |
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| 261 | |
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| 262 | inline Matrix StochasticProcess1D::diffusion(Time t, const Array& x) const { |
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| 263 | #if defined(QL_EXTRA_SAFETY_CHECKS) |
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| 264 | QL_REQUIRE(x.size() == 1, "1-D array required" ); |
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| 265 | #endif |
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| 266 | Matrix m(1, 1, diffusion(t, x: x[0])); |
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| 267 | return m; |
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| 268 | } |
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| 269 | |
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| 270 | inline Array StochasticProcess1D::expectation( |
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| 271 | Time t0, const Array& x0, Time dt) const { |
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| 272 | #if defined(QL_EXTRA_SAFETY_CHECKS) |
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| 273 | QL_REQUIRE(x0.size() == 1, "1-D array required" ); |
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| 274 | #endif |
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| 275 | Array a(1, expectation(t0, x0: x0[0], dt)); |
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| 276 | return a; |
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| 277 | } |
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| 278 | |
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| 279 | inline Matrix StochasticProcess1D::stdDeviation( |
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| 280 | Time t0, const Array& x0, Time dt) const { |
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| 281 | #if defined(QL_EXTRA_SAFETY_CHECKS) |
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| 282 | QL_REQUIRE(x0.size() == 1, "1-D array required" ); |
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| 283 | #endif |
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| 284 | Matrix m(1, 1, stdDeviation(t0, x0: x0[0], dt)); |
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| 285 | return m; |
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| 286 | } |
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| 287 | |
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| 288 | inline Matrix StochasticProcess1D::covariance( |
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| 289 | Time t0, const Array& x0, Time dt) const { |
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| 290 | #if defined(QL_EXTRA_SAFETY_CHECKS) |
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| 291 | QL_REQUIRE(x0.size() == 1, "1-D array required" ); |
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| 292 | #endif |
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| 293 | Matrix m(1, 1, variance(t0, x0: x0[0], dt)); |
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| 294 | return m; |
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| 295 | } |
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| 296 | |
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| 297 | inline Array StochasticProcess1D::evolve(Time t0, const Array& x0, |
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| 298 | Time dt, const Array& dw) const { |
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| 299 | #if defined(QL_EXTRA_SAFETY_CHECKS) |
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| 300 | QL_REQUIRE(x0.size() == 1, "1-D array required" ); |
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| 301 | QL_REQUIRE(dw.size() == 1, "1-D array required" ); |
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| 302 | #endif |
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| 303 | Array a(1, evolve(t0,x0: x0[0],dt,dw: dw[0])); |
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| 304 | return a; |
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| 305 | } |
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| 306 | |
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| 307 | inline Array StochasticProcess1D::apply(const Array& x0, |
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| 308 | const Array& dx) const { |
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| 309 | #if defined(QL_EXTRA_SAFETY_CHECKS) |
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| 310 | QL_REQUIRE(x0.size() == 1, "1-D array required" ); |
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| 311 | QL_REQUIRE(dx.size() == 1, "1-D array required" ); |
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| 312 | #endif |
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| 313 | Array a(1, apply(x0: x0[0],dx: dx[0])); |
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| 314 | return a; |
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| 315 | } |
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| 316 | |
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| 317 | } |
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| 318 | |
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| 319 | |
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| 320 | #endif |
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| 321 | |
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