/src/quantlib/ql/stochasticprocess.hpp

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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */

/*
 Copyright (C) 2003 Ferdinando Ametrano
 Copyright (C) 2001, 2002, 2003 Sadruddin Rejeb
 Copyright (C) 2004, 2005 StatPro Italia srl

 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 stochasticprocess.hpp
    \brief stochastic processes
*/

#ifndef quantlib_stochastic_process_hpp
#define quantlib_stochastic_process_hpp

#include <ql/time/date.hpp>
#include <ql/patterns/observable.hpp>
#include <ql/math/matrix.hpp>

namespace QuantLib {

    //! multi-dimensional stochastic process class.
    /*! This class describes a stochastic process governed by
        \f[
        d\mathrm{x}_t = \mu(t, x_t)\mathrm{d}t
                      + \sigma(t, \mathrm{x}_t) \cdot d\mathrm{W}_t.
        \f]
    */
    class StochasticProcess : public Observer, public Observable {
      public:
        //! discretization of a stochastic process over a given time interval
        class discretization {
          public:
            virtual ~discretization() = default;
            virtual Array drift(const StochasticProcess&,
                                Time t0,
                                const Array& x0,
                                Time dt) const = 0;
            virtual Matrix diffusion(const StochasticProcess&,
                                     Time t0,
                                     const Array& x0,
                                     Time dt) const = 0;
            virtual Matrix covariance(const StochasticProcess&,
                                      Time t0,
                                      const Array& x0,
                                      Time dt) const = 0;
        };
        ~StochasticProcess() override = default;
        //! \name Stochastic process interface
        //@{
        //! returns the number of dimensions of the stochastic process
        virtual Size size() const = 0;
        //! returns the number of independent factors of the process
        virtual Size factors() const;
        //! returns the initial values of the state variables
        virtual Array initialValues() const = 0;
        /*! \brief returns the drift part of the equation, i.e.,
                   \f$ \mu(t, \mathrm{x}_t) \f$
        */
        virtual Array drift(Time t,
                            const Array& x) const = 0;
        /*! \brief returns the diffusion part of the equation, i.e.
                   \f$ \sigma(t, \mathrm{x}_t) \f$
        */
        virtual Matrix diffusion(Time t,
                                 const Array& x) const = 0;
        /*! returns the expectation
            \f$ E(\mathrm{x}_{t_0 + \Delta t}
                | \mathrm{x}_{t_0} = \mathrm{x}_0) \f$
            of the process after a time interval \f$ \Delta t \f$
            according to the given discretization. This method can be
            overridden in derived classes which want to hard-code a
            particular discretization.
        */
        virtual Array expectation(Time t0,
                                  const Array& x0,
                                  Time dt) const;
        /*! returns the standard deviation
            \f$ S(\mathrm{x}_{t_0 + \Delta t}
                | \mathrm{x}_{t_0} = \mathrm{x}_0) \f$
            of the process after a time interval \f$ \Delta t \f$
            according to the given discretization. This method can be
            overridden in derived classes which want to hard-code a
            particular discretization.
        */
        virtual Matrix stdDeviation(Time t0,
                                    const Array& x0,
                                    Time dt) const;
        /*! returns the covariance
            \f$ V(\mathrm{x}_{t_0 + \Delta t}
                | \mathrm{x}_{t_0} = \mathrm{x}_0) \f$
            of the process after a time interval \f$ \Delta t \f$
            according to the given discretization. This method can be
            overridden in derived classes which want to hard-code a
            particular discretization.
        */
        virtual Matrix covariance(Time t0,
                                  const Array& x0,
                                  Time dt) const;
        /*! returns the asset value after a time interval \f$ \Delta t
            \f$ according to the given discretization. By default, it
            returns
            \f[
            E(\mathrm{x}_0,t_0,\Delta t) +
            S(\mathrm{x}_0,t_0,\Delta t) \cdot \Delta \mathrm{w}
            \f]
            where \f$ E \f$ is the expectation and \f$ S \f$ the
            standard deviation.
        */
        virtual Array evolve(Time t0,
                             const Array& x0,
                             Time dt,
                             const Array& dw) const;
        /*! applies a change to the asset value. By default, it
            returns \f$ \mathrm{x} + \Delta \mathrm{x} \f$.
        */
        virtual Array apply(const Array& x0,
                            const Array& dx) const;
        //@}

        //! \name utilities
        //@{
        /*! returns the time value corresponding to the given date
            in the reference system of the stochastic process.

            \note As a number of processes might not need this
                  functionality, a default implementation is given
                  which raises an exception.
        */
        virtual Time time(const Date&) const;
        //@}

        //! \name Observer interface
        //@{
        void update() override;
        //@}
      protected:
        StochasticProcess() = default;
        explicit StochasticProcess(ext::shared_ptr<discretization>);
        ext::shared_ptr<discretization> discretization_;
    };


    //! 1-dimensional stochastic process
    /*! This class describes a stochastic process governed by
        \f[
            dx_t = \mu(t, x_t)dt + \sigma(t, x_t)dW_t.
        \f]
    */
    class StochasticProcess1D : public StochasticProcess {
      public:
        //! discretization of a 1-D stochastic process
        class discretization {
          public:
            virtual ~discretization() = default;
            virtual Real drift(const StochasticProcess1D&,
                               Time t0, Real x0, Time dt) const = 0;
            virtual Real diffusion(const StochasticProcess1D&,
                                   Time t0, Real x0, Time dt) const = 0;
            virtual Real variance(const StochasticProcess1D&,
                                  Time t0, Real x0, Time dt) const = 0;
        };
        //! \name 1-D stochastic process interface
        //@{
        //! returns the initial value of the state variable
        virtual Real x0() const = 0;
        //! returns the drift part of the equation, i.e. \f$ \mu(t, x_t) \f$
        virtual Real drift(Time t, Real x) const = 0;
        /*! \brief returns the diffusion part of the equation, i.e.
            \f$ \sigma(t, x_t) \f$
        */
        virtual Real diffusion(Time t, Real x) const = 0;
        /*! returns the expectation
            \f$ E(x_{t_0 + \Delta t} | x_{t_0} = x_0) \f$
            of the process after a time interval \f$ \Delta t \f$
            according to the given discretization. This method can be
            overridden in derived classes which want to hard-code a
            particular discretization.
        */
        virtual Real expectation(Time t0, Real x0, Time dt) const;
        /*! returns the standard deviation
            \f$ S(x_{t_0 + \Delta t} | x_{t_0} = x_0) \f$
            of the process after a time interval \f$ \Delta t \f$
            according to the given discretization. This method can be
            overridden in derived classes which want to hard-code a
            particular discretization.
        */
        virtual Real stdDeviation(Time t0, Real x0, Time dt) const;
        /*! returns the variance
            \f$ V(x_{t_0 + \Delta t} | x_{t_0} = x_0) \f$
            of the process after a time interval \f$ \Delta t \f$
            according to the given discretization. This method can be
            overridden in derived classes which want to hard-code a
            particular discretization.
        */
        virtual Real variance(Time t0, Real x0, Time dt) const;
        /*! returns the asset value after a time interval \f$ \Delta t
            \f$ according to the given discretization. By default, it
            returns
            \f[
            E(x_0,t_0,\Delta t) + S(x_0,t_0,\Delta t) \cdot \Delta w
            \f]
            where \f$ E \f$ is the expectation and \f$ S \f$ the
            standard deviation.
        */
        virtual Real evolve(Time t0, Real x0, Time dt, Real dw) const;
        /*! applies a change to the asset value. By default, it
            returns \f$ x + \Delta x \f$.
        */
        virtual Real apply(Real x0, Real dx) const;
        //@}
      protected:
        StochasticProcess1D() = default;
        explicit StochasticProcess1D(ext::shared_ptr<discretization>);
        ext::shared_ptr<discretization> discretization_;
      private:
        // StochasticProcess interface implementation
        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 expectation(Time t0, const Array& x0, Time dt) const override;
        Matrix stdDeviation(Time t0, const Array& x0, Time dt) const override;
        Matrix covariance(Time t0, const Array& x0, Time dt) const override;
        Array evolve(Time t0, const Array& x0, Time dt, const Array& dw) const override;
        Array apply(const Array& x0, const Array& dx) const override;
    };


    // inline definitions

    inline Size StochasticProcess1D::size() const {
        return 1;
    }

    inline Array StochasticProcess1D::initialValues() const {
        Array a(1, x0());
        return a;
    }

    inline Array StochasticProcess1D::drift(Time t, const Array& x) const {
        #if defined(QL_EXTRA_SAFETY_CHECKS)
        QL_REQUIRE(x.size() == 1, "1-D array required");
        #endif
        Array a(1, drift(t, x[0]));
        return a;
    }

    inline Matrix StochasticProcess1D::diffusion(Time t, const Array& x) const {
        #if defined(QL_EXTRA_SAFETY_CHECKS)
        QL_REQUIRE(x.size() == 1, "1-D array required");
        #endif
        Matrix m(1, 1, diffusion(t, x[0]));
        return m;
    }

    inline Array StochasticProcess1D::expectation(
                                    Time t0, const Array& x0, Time dt) const {
        #if defined(QL_EXTRA_SAFETY_CHECKS)
        QL_REQUIRE(x0.size() == 1, "1-D array required");
        #endif
        Array a(1, expectation(t0, x0[0], dt));
        return a;
    }

    inline Matrix StochasticProcess1D::stdDeviation(
                                    Time t0, const Array& x0, Time dt) const {
        #if defined(QL_EXTRA_SAFETY_CHECKS)
        QL_REQUIRE(x0.size() == 1, "1-D array required");
        #endif
        Matrix m(1, 1, stdDeviation(t0, x0[0], dt));
        return m;
    }

    inline Matrix StochasticProcess1D::covariance(
                                    Time t0, const Array& x0, Time dt) const {
        #if defined(QL_EXTRA_SAFETY_CHECKS)
        QL_REQUIRE(x0.size() == 1, "1-D array required");
        #endif
        Matrix m(1, 1, variance(t0, x0[0], dt));
        return m;
    }

    inline Array StochasticProcess1D::evolve(Time t0, const Array& x0,
                                             Time dt, const Array& dw) const {
        #if defined(QL_EXTRA_SAFETY_CHECKS)
        QL_REQUIRE(x0.size() == 1, "1-D array required");
        QL_REQUIRE(dw.size() == 1, "1-D array required");
        #endif
        Array a(1, evolve(t0,x0[0],dt,dw[0]));
        return a;
    }

    inline Array StochasticProcess1D::apply(const Array& x0,
                                            const Array& dx) const {
        #if defined(QL_EXTRA_SAFETY_CHECKS)
        QL_REQUIRE(x0.size() == 1, "1-D array required");
        QL_REQUIRE(dx.size() == 1, "1-D array required");
        #endif
        Array a(1, apply(x0[0],dx[0]));
        return a;
    }

}


#endif

Coverage Report

Created: 2025-08-05 06:45

Line	Count	Source (jump to first uncovered line)
1		/* -- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -- */
2
3		/*
4		Copyright (C) 2003 Ferdinando Ametrano
5		Copyright (C) 2001, 2002, 2003 Sadruddin Rejeb
6		Copyright (C) 2004, 2005 StatPro Italia srl
7
8		This file is part of QuantLib, a free-software/open-source library
9		for financial quantitative analysts and developers - http://quantlib.org/
10
11		QuantLib is free software: you can redistribute it and/or modify it
12		under the terms of the QuantLib license. You should have received a
13		copy of the license along with this program; if not, please email
14		<quantlib-dev@lists.sf.net>. The license is also available online at
15		<http://quantlib.org/license.shtml>.
16
17		This program is distributed in the hope that it will be useful, but WITHOUT
18		ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
19		FOR A PARTICULAR PURPOSE. See the license for more details.
20		*/
21
22		/*! \file stochasticprocess.hpp
23		\brief stochastic processes
24		*/
25
26		#ifndef quantlib_stochastic_process_hpp
27		#define quantlib_stochastic_process_hpp
28
29		#include <ql/time/date.hpp>
30		#include <ql/patterns/observable.hpp>
31		#include <ql/math/matrix.hpp>
32
33		namespace QuantLib {
34
35		//! multi-dimensional stochastic process class.
36		/*! This class describes a stochastic process governed by
37		\f[
38		d\mathrm{x}_t = \mu(t, x_t)\mathrm{d}t
39		+ \sigma(t, \mathrm{x}_t) \cdot d\mathrm{W}_t.
40		\f]
41		*/
42		class StochasticProcess : public Observer, public Observable {
43		public:
44		//! discretization of a stochastic process over a given time interval
45		class discretization {
46		public:
47	1.00k	virtual ~discretization() = default;
48		virtual Array drift(const StochasticProcess&,
49		Time t0,
50		const Array& x0,
51		Time dt) const = 0;
52		virtual Matrix diffusion(const StochasticProcess&,
53		Time t0,
54		const Array& x0,
55		Time dt) const = 0;
56		virtual Matrix covariance(const StochasticProcess&,
57		Time t0,
58		const Array& x0,
59		Time dt) const = 0;
60		};
61	1.00k	~StochasticProcess() override = default;
62		//! \name Stochastic process interface
63		//@{
64		//! returns the number of dimensions of the stochastic process
65		virtual Size size() const = 0;
66		//! returns the number of independent factors of the process
67		virtual Size factors() const;
68		//! returns the initial values of the state variables
69		virtual Array initialValues() const = 0;
70		/*! \brief returns the drift part of the equation, i.e.,
71		\f$ \mu(t, \mathrm{x}_t) \f$
72		*/
73		virtual Array drift(Time t,
74		const Array& x) const = 0;
75		/*! \brief returns the diffusion part of the equation, i.e.
76		\f$ \sigma(t, \mathrm{x}_t) \f$
77		*/
78		virtual Matrix diffusion(Time t,
79		const Array& x) const = 0;
80		/*! returns the expectation
81		\f$ E(\mathrm{x}_{t_0 + \Delta t}
82		\| \mathrm{x}_{t_0} = \mathrm{x}_0) \f$
83		of the process after a time interval \f$ \Delta t \f$
84		according to the given discretization. This method can be
85		overridden in derived classes which want to hard-code a
86		particular discretization.
87		*/
88		virtual Array expectation(Time t0,
89		const Array& x0,
90		Time dt) const;
91		/*! returns the standard deviation
92		\f$ S(\mathrm{x}_{t_0 + \Delta t}
93		\| \mathrm{x}_{t_0} = \mathrm{x}_0) \f$
94		of the process after a time interval \f$ \Delta t \f$
95		according to the given discretization. This method can be
96		overridden in derived classes which want to hard-code a
97		particular discretization.
98		*/
99		virtual Matrix stdDeviation(Time t0,
100		const Array& x0,
101		Time dt) const;
102		/*! returns the covariance
103		\f$ V(\mathrm{x}_{t_0 + \Delta t}
104		\| \mathrm{x}_{t_0} = \mathrm{x}_0) \f$
105		of the process after a time interval \f$ \Delta t \f$
106		according to the given discretization. This method can be
107		overridden in derived classes which want to hard-code a
108		particular discretization.
109		*/
110		virtual Matrix covariance(Time t0,
111		const Array& x0,
112		Time dt) const;
113		/*! returns the asset value after a time interval \f$ \Delta t
114		\f$ according to the given discretization. By default, it
115		returns
116		\f[
117		E(\mathrm{x}_0,t_0,\Delta t) +
118		S(\mathrm{x}_0,t_0,\Delta t) \cdot \Delta \mathrm{w}
119		\f]
120		where \f$ E \f$ is the expectation and \f$ S \f$ the
121		standard deviation.
122		*/
123		virtual Array evolve(Time t0,
124		const Array& x0,
125		Time dt,
126		const Array& dw) const;
127		/*! applies a change to the asset value. By default, it
128		returns \f$ \mathrm{x} + \Delta \mathrm{x} \f$.
129		*/
130		virtual Array apply(const Array& x0,
131		const Array& dx) const;
132		//@}
133
134		//! \name utilities
135		//@{
136		/*! returns the time value corresponding to the given date
137		in the reference system of the stochastic process.
138
139		\note As a number of processes might not need this
140		functionality, a default implementation is given
141		which raises an exception.
142		*/
143		virtual Time time(const Date&) const;
144		//@}
145
146		//! \name Observer interface
147		//@{
148		void update() override;
149		//@}
150		protected:
151	1.00k	StochasticProcess() = default;
152		explicit StochasticProcess(ext::shared_ptr<discretization>);
153		ext::shared_ptr<discretization> discretization_;
154		};
155
156
157		//! 1-dimensional stochastic process
158		/*! This class describes a stochastic process governed by
159		\f[
160		dx_t = \mu(t, x_t)dt + \sigma(t, x_t)dW_t.
161		\f]
162		*/
163		class StochasticProcess1D : public StochasticProcess {
164		public:
165		//! discretization of a 1-D stochastic process
166		class discretization {
167		public:
168	1.00k	virtual ~discretization() = default;
169		virtual Real drift(const StochasticProcess1D&,
170		Time t0, Real x0, Time dt) const = 0;
171		virtual Real diffusion(const StochasticProcess1D&,
172		Time t0, Real x0, Time dt) const = 0;
173		virtual Real variance(const StochasticProcess1D&,
174		Time t0, Real x0, Time dt) const = 0;
175		};
176		//! \name 1-D stochastic process interface
177		//@{
178		//! returns the initial value of the state variable
179		virtual Real x0() const = 0;
180		//! returns the drift part of the equation, i.e. \f$ \mu(t, x_t) \f$
181		virtual Real drift(Time t, Real x) const = 0;
182		/*! \brief returns the diffusion part of the equation, i.e.
183		\f$ \sigma(t, x_t) \f$
184		*/
185		virtual Real diffusion(Time t, Real x) const = 0;
186		/*! returns the expectation
187		\f$ E(x_{t_0 + \Delta t} \| x_{t_0} = x_0) \f$
188		of the process after a time interval \f$ \Delta t \f$
189		according to the given discretization. This method can be
190		overridden in derived classes which want to hard-code a
191		particular discretization.
192		*/
193		virtual Real expectation(Time t0, Real x0, Time dt) const;
194		/*! returns the standard deviation
195		\f$ S(x_{t_0 + \Delta t} \| x_{t_0} = x_0) \f$
196		of the process after a time interval \f$ \Delta t \f$
197		according to the given discretization. This method can be
198		overridden in derived classes which want to hard-code a
199		particular discretization.
200		*/
201		virtual Real stdDeviation(Time t0, Real x0, Time dt) const;
202		/*! returns the variance
203		\f$ V(x_{t_0 + \Delta t} \| x_{t_0} = x_0) \f$
204		of the process after a time interval \f$ \Delta t \f$
205		according to the given discretization. This method can be
206		overridden in derived classes which want to hard-code a
207		particular discretization.
208		*/
209		virtual Real variance(Time t0, Real x0, Time dt) const;
210		/*! returns the asset value after a time interval \f$ \Delta t
211		\f$ according to the given discretization. By default, it
212		returns
213		\f[
214		E(x_0,t_0,\Delta t) + S(x_0,t_0,\Delta t) \cdot \Delta w
215		\f]
216		where \f$ E \f$ is the expectation and \f$ S \f$ the
217		standard deviation.
218		*/
219		virtual Real evolve(Time t0, Real x0, Time dt, Real dw) const;
220		/*! applies a change to the asset value. By default, it
221		returns \f$ x + \Delta x \f$.
222		*/
223		virtual Real apply(Real x0, Real dx) const;
224		//@}
225		protected:
226	0	StochasticProcess1D() = default;
227		explicit StochasticProcess1D(ext::shared_ptr<discretization>);
228		ext::shared_ptr<discretization> discretization_;
229		private:
230		// StochasticProcess interface implementation
231		Size size() const override;
232		Array initialValues() const override;
233		Array drift(Time t, const Array& x) const override;
234		Matrix diffusion(Time t, const Array& x) const override;
235		Array expectation(Time t0, const Array& x0, Time dt) const override;
236		Matrix stdDeviation(Time t0, const Array& x0, Time dt) const override;
237		Matrix covariance(Time t0, const Array& x0, Time dt) const override;
238		Array evolve(Time t0, const Array& x0, Time dt, const Array& dw) const override;
239		Array apply(const Array& x0, const Array& dx) const override;
240		};
241
242
243		// inline definitions
244
245	0	inline Size StochasticProcess1D::size() const {
246	0	return 1;
247	0	}
248
249	0	inline Array StochasticProcess1D::initialValues() const {
250	0	Array a(1, x0());
251	0	return a;
252	0	}
253
254	0	inline Array StochasticProcess1D::drift(Time t, const Array& x) const {
255	0	#if defined(QL_EXTRA_SAFETY_CHECKS)
256	0	QL_REQUIRE(x.size() == 1, "1-D array required");
257	0	#endif
258	0	Array a(1, drift(t, x[0]));
259	0	return a;
260	0	}
261
262	0	inline Matrix StochasticProcess1D::diffusion(Time t, const Array& x) const {
263	0	#if defined(QL_EXTRA_SAFETY_CHECKS)
264	0	QL_REQUIRE(x.size() == 1, "1-D array required");
265	0	#endif
266	0	Matrix m(1, 1, diffusion(t, x[0]));
267	0	return m;
268	0	}
269
270		inline Array StochasticProcess1D::expectation(
271	0	Time t0, const Array& x0, Time dt) const {
272	0	#if defined(QL_EXTRA_SAFETY_CHECKS)
273	0	QL_REQUIRE(x0.size() == 1, "1-D array required");
274	0	#endif
275	0	Array a(1, expectation(t0, x0[0], dt));
276	0	return a;
277	0	}
278
279		inline Matrix StochasticProcess1D::stdDeviation(
280	0	Time t0, const Array& x0, Time dt) const {
281	0	#if defined(QL_EXTRA_SAFETY_CHECKS)
282	0	QL_REQUIRE(x0.size() == 1, "1-D array required");
283	0	#endif
284	0	Matrix m(1, 1, stdDeviation(t0, x0[0], dt));
285	0	return m;
286	0	}
287
288		inline Matrix StochasticProcess1D::covariance(
289	0	Time t0, const Array& x0, Time dt) const {
290	0	#if defined(QL_EXTRA_SAFETY_CHECKS)
291	0	QL_REQUIRE(x0.size() == 1, "1-D array required");
292	0	#endif
293	0	Matrix m(1, 1, variance(t0, x0[0], dt));
294	0	return m;
295	0	}
296
297		inline Array StochasticProcess1D::evolve(Time t0, const Array& x0,
298	0	Time dt, const Array& dw) const {
299	0	#if defined(QL_EXTRA_SAFETY_CHECKS)
300	0	QL_REQUIRE(x0.size() == 1, "1-D array required");
301	0	QL_REQUIRE(dw.size() == 1, "1-D array required");
302	0	#endif
303	0	Array a(1, evolve(t0,x0[0],dt,dw[0]));
304	0	return a;
305	0	}
306
307		inline Array StochasticProcess1D::apply(const Array& x0,
308	0	const Array& dx) const {
309	0	#if defined(QL_EXTRA_SAFETY_CHECKS)
310	0	QL_REQUIRE(x0.size() == 1, "1-D array required");
311	0	QL_REQUIRE(dx.size() == 1, "1-D array required");
312	0	#endif
313	0	Array a(1, apply(x0[0],dx[0]));
314	0	return a;
315	0	}
316
317		}
318
319
320		#endif