Extended Ornstein-Uhlenbeck process class. More...
#include <ql/experimental/processes/extendedornsteinuhlenbeckprocess.hpp>
Public Types | |
| enum | Discretization { MidPoint , Trapezodial , GaussLobatto } |
| Public Types inherited from Observer | |
| typedef set_type::iterator | iterator |
Public Member Functions | |
| ExtendedOrnsteinUhlenbeckProcess (Real speed, Volatility sigma, Real x0, std::function< Real(Real)> b, Discretization discretization=MidPoint, Real intEps=1e-4) | |
| virtual Real | evolve (Time t0, Real x0, Time dt, Real dw) const |
| virtual Real | apply (Real x0, Real dx) const |
| 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 interface | |
| Real | x0 () const override |
| returns the initial value of the state variable | |
| Real | speed () const |
| Real | volatility () const |
| Real | drift (Time t, Real x) const override |
| returns the drift part of the equation, i.e. \( \mu(t, x_t) \) | |
| Real | diffusion (Time t, Real x) const override |
| returns the diffusion part of the equation, i.e. \( \sigma(t, x_t) \) | |
| Real | expectation (Time t0, Real x0, Time dt) const override |
| Real | stdDeviation (Time t0, Real x0, Time dt) const override |
| Real | variance (Time t0, Real x0, Time dt) const override |
Additional Inherited Members | |
| StochasticProcess1D (ext::shared_ptr< discretization >) | |
| StochasticProcess (ext::shared_ptr< discretization >) | |
| ext::shared_ptr< discretization > | discretization_ |
| ext::shared_ptr< discretization > | discretization_ |
Detailed Description
Extended Ornstein-Uhlenbeck process class.
This class describes the Ornstein-Uhlenbeck process governed by
\[ dx = a (b(t) - x_t) dt + \sigma dW_t. \]
Member Function Documentation
◆ x0()
|
overridevirtual |
returns the initial value of the state variable
Implements StochasticProcess1D.
◆ drift()
returns the drift part of the equation, i.e. \( \mu(t, x_t) \)
Implements StochasticProcess1D.
◆ diffusion()
returns the diffusion part of the equation, i.e. \( \sigma(t, x_t) \)
Implements StochasticProcess1D.
◆ 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 from StochasticProcess1D.
◆ 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 from StochasticProcess1D.
◆ 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 from StochasticProcess1D.
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