1-dimensional stochastic process More...
#include <ql/stochasticprocess.hpp>
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 | |
| virtual Real | drift (Time t, Real x) const =0 |
| returns the drift part of the equation, i.e. \( \mu(t, x_t) \) | |
| virtual Real | diffusion (Time t, Real x) const =0 |
| returns the diffusion part of the equation, i.e. \( \sigma(t, x_t) \) | |
| 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 (ext::shared_ptr< discretization >) | |
Additional Inherited Members | |
| Public Types inherited from Observer | |
| typedef set_type::iterator | iterator |
| Public Member Functions inherited from StochasticProcess | |
| virtual Size | factors () const |
| returns the number of independent factors of the process | |
| virtual Time | time (const Date &) const |
| void | update () override |
| Public Member Functions inherited from Observer | |
| Observer (const Observer &) | |
| Observer & | operator= (const 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 | deepUpdate () |
| Public Member Functions inherited from Observable | |
| Observable (const Observable &) | |
| Observable & | operator= (const Observable &) |
| Observable (Observable &&)=delete | |
| Observable & | operator= (Observable &&)=delete |
| void | notifyObservers () |
| StochasticProcess (ext::shared_ptr< discretization >) | |
| ext::shared_ptr< discretization > | discretization_ |
Detailed Description
1-dimensional stochastic process
This class describes a stochastic process governed by
\[ dx_t = \mu(t, x_t)dt + \sigma(t, x_t)dW_t. \]
Member Function Documentation
◆ x0()
|
pure virtual |
returns the initial value of the state variable
Implemented in CoxIngersollRossProcess, ExtendedOrnsteinUhlenbeckProcess, GemanRoncoroniProcess, GeneralizedBlackScholesProcess, GeneralizedOrnsteinUhlenbeckProcess, GeometricBrownianMotionProcess, GsrProcess, HullWhiteForwardProcess, HullWhiteProcess, Merton76Process, MfStateProcess, OrnsteinUhlenbeckProcess, SquareRootProcess, and VarianceGammaProcess.
◆ drift()
returns the drift part of the equation, i.e. \( \mu(t, x_t) \)
Implemented in CoxIngersollRossProcess, ExtendedBlackScholesMertonProcess, ExtendedOrnsteinUhlenbeckProcess, GemanRoncoroniProcess, GeneralizedBlackScholesProcess, GeneralizedOrnsteinUhlenbeckProcess, GeometricBrownianMotionProcess, GsrProcess, HullWhiteForwardProcess, HullWhiteProcess, Merton76Process, MfStateProcess, OrnsteinUhlenbeckProcess, SquareRootProcess, and VarianceGammaProcess.
◆ diffusion()
returns the diffusion part of the equation, i.e. \( \sigma(t, x_t) \)
Implemented in CoxIngersollRossProcess, ExtendedBlackScholesMertonProcess, ExtendedOrnsteinUhlenbeckProcess, GemanRoncoroniProcess, GeneralizedBlackScholesProcess, GeneralizedOrnsteinUhlenbeckProcess, GeometricBrownianMotionProcess, GsrProcess, HullWhiteForwardProcess, HullWhiteProcess, Merton76Process, MfStateProcess, OrnsteinUhlenbeckProcess, SquareRootProcess, VarianceGammaProcess, and VegaStressedBlackScholesProcess.
◆ expectation()
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 CoxIngersollRossProcess, ExtendedOrnsteinUhlenbeckProcess, GeneralizedBlackScholesProcess, GeneralizedOrnsteinUhlenbeckProcess, GsrProcess, HullWhiteForwardProcess, HullWhiteProcess, MfStateProcess, and OrnsteinUhlenbeckProcess.
◆ stdDeviation()
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 CoxIngersollRossProcess, ExtendedOrnsteinUhlenbeckProcess, GemanRoncoroniProcess, GeneralizedBlackScholesProcess, GeneralizedOrnsteinUhlenbeckProcess, GsrProcess, HullWhiteForwardProcess, HullWhiteProcess, MfStateProcess, and OrnsteinUhlenbeckProcess.
◆ 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 CoxIngersollRossProcess, ExtendedOrnsteinUhlenbeckProcess, GeneralizedBlackScholesProcess, GeneralizedOrnsteinUhlenbeckProcess, GsrProcess, HullWhiteForwardProcess, HullWhiteProcess, MfStateProcess, and OrnsteinUhlenbeckProcess.
◆ evolve()
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 CoxIngersollRossProcess, ExtendedBlackScholesMertonProcess, GemanRoncoroniProcess, and GeneralizedBlackScholesProcess.
◆ apply()
applies a change to the asset value. By default, it returns \( x + \Delta x \).
Reimplemented in GeneralizedBlackScholesProcess, and Merton76Process.
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