stochasticprocess.hpp

/* -*- 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.
*/
 
#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 {
 
 
    class StochasticProcess : public Observer, public Observable {
      public:
        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;
 
 
        virtual Size size() const = 0;
        virtual Size factors() const;
        virtual Array initialValues() const = 0;
        virtual Array drift(Time t,
                            const Array& x) const = 0;
        virtual Matrix diffusion(Time t,
                                 const Array& x) const = 0;
        virtual Array expectation(Time t0,
                                  const Array& x0,
                                  Time dt) const;
        virtual Matrix stdDeviation(Time t0,
                                    const Array& x0,
                                    Time dt) const;
        virtual Matrix covariance(Time t0,
                                  const Array& x0,
                                  Time dt) const;
        virtual Array evolve(Time t0,
                             const Array& x0,
                             Time dt,
                             const Array& dw) const;
        virtual Array apply(const Array& x0,
                            const Array& dx) const;
 
 
 
        virtual Time time(const Date&) const;
 
 
        void update() override;
      protected:
        StochasticProcess() = default;
        explicit StochasticProcess(ext::shared_ptr<discretization>);
        ext::shared_ptr<discretization> discretization_;
    };
 
 
 
    class StochasticProcess1D : public StochasticProcess {
      public:
        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;
        };
 
 
        virtual Real x0() const = 0;
        virtual Real drift(Time t, Real x) const = 0;
        virtual Real diffusion(Time t, Real x) const = 0;
        virtual Real expectation(Time t0, Real x0, Time dt) const;
        virtual Real stdDeviation(Time t0, Real x0, Time dt) const;
        virtual Real variance(Time t0, Real x0, Time dt) const;
        virtual Real evolve(Time t0, Real x0, Time dt, Real dw) const;
        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