1-dimensional stochastic process More...
#include <stochasticprocess.hpp>
Inheritance diagram for StochasticProcess1D:
Collaboration diagram for StochasticProcess1D:
Classes | |
| class | discretization |
| discretization of a 1-D stochastic process More... | |
1-D stochastic process interface | |
| ext::shared_ptr< discretization > | discretization_ |
| virtual Real | x0 () const =0 |
| returns the initial value of the state variable More... | |
| virtual Real | drift (Time t, Real x) const =0 |
| returns the drift part of the equation, i.e. \( \mu(t, x_t) \) More... | |
| virtual Real | diffusion (Time t, Real x) const =0 |
| returns the diffusion part of the equation, i.e. \( \sigma(t, x_t) \) More... | |
| 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 |
| StochasticProcess1D ()=default | |
| StochasticProcess1D (ext::shared_ptr< discretization >) | |
| Size | size () const override |
| returns the number of dimensions of the stochastic process More... | |
| Array | initialValues () const override |
| returns the initial values of the state variables More... | |
| Array | drift (Time t, const Array &x) const override |
| returns the drift part of the equation, i.e., \( \mu(t, \mathrm{x}_t) \) More... | |
| Matrix | diffusion (Time t, const Array &x) const override |
| returns the diffusion part of the equation, i.e. \( \sigma(t, \mathrm{x}_t) \) More... | |
| 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 |
Additional Inherited Members | |
| Public Types inherited from Observer | |
| typedef set_type::iterator | iterator |
| Public Member Functions inherited from StochasticProcess | |
| ~StochasticProcess () override=default | |
| virtual Size | factors () const |
| returns the number of independent factors of the process More... | |
| virtual Time | time (const Date &) const |
| void | update () override |
| Public Member Functions inherited from Observer | |
| Observer ()=default | |
| Observer (const Observer &) | |
| Observer & | operator= (const Observer &) |
| virtual | ~Observer () |
| std::pair< iterator, bool > | registerWith (const ext::shared_ptr< Observable > &) |
| void | registerWithObservables (const ext::shared_ptr< Observer > &) |
| Size | unregisterWith (const ext::shared_ptr< Observable > &) |
| void | unregisterWithAll () |
| virtual void | update ()=0 |
| virtual void | deepUpdate () |
| Public Member Functions inherited from Observable | |
| Observable () | |
| Observable (const Observable &) | |
| Observable & | operator= (const Observable &) |
| Observable (Observable &&)=delete | |
| Observable & | operator= (Observable &&)=delete |
| virtual | ~Observable ()=default |
| void | notifyObservers () |
| Protected Member Functions inherited from StochasticProcess | |
| StochasticProcess ()=default | |
| StochasticProcess (ext::shared_ptr< discretization >) | |
| Protected Attributes inherited from StochasticProcess | |
| ext::shared_ptr< discretization > | discretization_ |
Detailed Description
1-dimensional stochastic process
This class describes a stochastic process governed by
\[ dx_t = \mu(t, x_t)dt + \sigma(t, x_t)dW_t. \]
Definition at line 163 of file stochasticprocess.hpp.
Constructor & Destructor Documentation
◆ StochasticProcess1D() [1/2]
|
protecteddefault |
◆ StochasticProcess1D() [2/2]
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explicitprotected |
Definition at line 75 of file stochasticprocess.cpp.
Member Function Documentation
◆ x0()
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pure virtual |
returns the initial value of the state variable
Implemented in ExtendedOrnsteinUhlenbeckProcess, GemanRoncoroniProcess, GeneralizedOrnsteinUhlenbeckProcess, VarianceGammaProcess, GeneralizedBlackScholesProcess, CoxIngersollRossProcess, GeometricBrownianMotionProcess, GsrProcess, HullWhiteProcess, HullWhiteForwardProcess, Merton76Process, MfStateProcess, OrnsteinUhlenbeckProcess, and SquareRootProcess.
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◆ drift() [1/2]
returns the drift part of the equation, i.e. \( \mu(t, x_t) \)
Implemented in ExtendedBlackScholesMertonProcess, ExtendedOrnsteinUhlenbeckProcess, GemanRoncoroniProcess, GeneralizedOrnsteinUhlenbeckProcess, VarianceGammaProcess, GeneralizedBlackScholesProcess, CoxIngersollRossProcess, GeometricBrownianMotionProcess, GsrProcess, HullWhiteProcess, HullWhiteForwardProcess, MfStateProcess, OrnsteinUhlenbeckProcess, SquareRootProcess, and Merton76Process.
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◆ diffusion() [1/2]
returns the diffusion part of the equation, i.e. \( \sigma(t, x_t) \)
Implemented in ExtendedBlackScholesMertonProcess, ExtendedOrnsteinUhlenbeckProcess, GemanRoncoroniProcess, VegaStressedBlackScholesProcess, GeneralizedOrnsteinUhlenbeckProcess, VarianceGammaProcess, GeneralizedBlackScholesProcess, CoxIngersollRossProcess, GeometricBrownianMotionProcess, HullWhiteProcess, HullWhiteForwardProcess, MfStateProcess, OrnsteinUhlenbeckProcess, SquareRootProcess, GsrProcess, and Merton76Process.
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◆ expectation() [1/2]
returns the expectation \( E(x_{t_0 + \Delta t} | x_{t_0} = x_0) \) of the process after a time interval \( \Delta t \) according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.
Reimplemented in ExtendedOrnsteinUhlenbeckProcess, GeneralizedOrnsteinUhlenbeckProcess, GeneralizedBlackScholesProcess, CoxIngersollRossProcess, GsrProcess, HullWhiteProcess, HullWhiteForwardProcess, MfStateProcess, and OrnsteinUhlenbeckProcess.
Definition at line 78 of file stochasticprocess.cpp.
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◆ stdDeviation() [1/2]
returns the standard deviation \( S(x_{t_0 + \Delta t} | x_{t_0} = x_0) \) of the process after a time interval \( \Delta t \) according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.
Reimplemented in ExtendedOrnsteinUhlenbeckProcess, GemanRoncoroniProcess, GeneralizedOrnsteinUhlenbeckProcess, GeneralizedBlackScholesProcess, CoxIngersollRossProcess, GsrProcess, HullWhiteProcess, HullWhiteForwardProcess, MfStateProcess, and OrnsteinUhlenbeckProcess.
Definition at line 82 of file stochasticprocess.cpp.
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◆ variance()
returns the variance \( V(x_{t_0 + \Delta t} | x_{t_0} = x_0) \) of the process after a time interval \( \Delta t \) according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.
Reimplemented in ExtendedOrnsteinUhlenbeckProcess, GeneralizedOrnsteinUhlenbeckProcess, GeneralizedBlackScholesProcess, CoxIngersollRossProcess, HullWhiteProcess, HullWhiteForwardProcess, MfStateProcess, OrnsteinUhlenbeckProcess, and GsrProcess.
Definition at line 86 of file stochasticprocess.cpp.
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◆ evolve() [1/2]
returns the asset value after a time interval \( \Delta t \) according to the given discretization. By default, it returns
\[ E(x_0,t_0,\Delta t) + S(x_0,t_0,\Delta t) \cdot \Delta w \]
where \( E \) is the expectation and \( S \) the standard deviation.
Reimplemented in ExtendedBlackScholesMertonProcess, GemanRoncoroniProcess, GeneralizedBlackScholesProcess, and CoxIngersollRossProcess.
Definition at line 90 of file stochasticprocess.cpp.
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◆ apply() [1/2]
applies a change to the asset value. By default, it returns \( x + \Delta x \).
Reimplemented in GeneralizedBlackScholesProcess, and Merton76Process.
Definition at line 95 of file stochasticprocess.cpp.
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◆ size()
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overrideprivatevirtual |
returns the number of dimensions of the stochastic process
Implements StochasticProcess.
Definition at line 245 of file stochasticprocess.hpp.
◆ initialValues()
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overrideprivatevirtual |
returns the initial values of the state variables
Implements StochasticProcess.
Definition at line 249 of file stochasticprocess.hpp.
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◆ drift() [2/2]
returns the drift part of the equation, i.e., \( \mu(t, \mathrm{x}_t) \)
Implements StochasticProcess.
Definition at line 254 of file stochasticprocess.hpp.
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◆ diffusion() [2/2]
returns the diffusion part of the equation, i.e. \( \sigma(t, \mathrm{x}_t) \)
Implements StochasticProcess.
Definition at line 262 of file stochasticprocess.hpp.
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◆ expectation() [2/2]
returns the expectation \( E(\mathrm{x}_{t_0 + \Delta t} | \mathrm{x}_{t_0} = \mathrm{x}_0) \) of the process after a time interval \( \Delta t \) according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.
Reimplemented from StochasticProcess.
Definition at line 270 of file stochasticprocess.hpp.
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◆ stdDeviation() [2/2]
returns the standard deviation \( S(\mathrm{x}_{t_0 + \Delta t} | \mathrm{x}_{t_0} = \mathrm{x}_0) \) of the process after a time interval \( \Delta t \) according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.
Reimplemented from StochasticProcess.
Definition at line 279 of file stochasticprocess.hpp.
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◆ covariance()
returns the covariance \( V(\mathrm{x}_{t_0 + \Delta t} | \mathrm{x}_{t_0} = \mathrm{x}_0) \) of the process after a time interval \( \Delta t \) according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.
Reimplemented from StochasticProcess.
Definition at line 288 of file stochasticprocess.hpp.
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◆ evolve() [2/2]
returns the asset value after a time interval \( \Delta t \) according to the given discretization. By default, it returns
\[ E(\mathrm{x}_0,t_0,\Delta t) + S(\mathrm{x}_0,t_0,\Delta t) \cdot \Delta \mathrm{w} \]
where \( E \) is the expectation and \( S \) the standard deviation.
Reimplemented from StochasticProcess.
Reimplemented in GemanRoncoroniProcess.
Definition at line 297 of file stochasticprocess.hpp.
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◆ apply() [2/2]
applies a change to the asset value. By default, it returns \( \mathrm{x} + \Delta \mathrm{x} \).
Reimplemented from StochasticProcess.
Definition at line 307 of file stochasticprocess.hpp.
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Member Data Documentation
◆ discretization_
|
protected |
Definition at line 228 of file stochasticprocess.hpp.