1-dimensional stochastic process More...
#include <ql/stochasticprocess.hpp>
 Inheritance diagram for StochasticProcess1D:
 Inheritance diagram for StochasticProcess1D:| Classes | |
| class | discretization | 
| discretization of a 1-D stochastic process  More... | |
| Public Member Functions | |
| 1-D stochastic process interface | |
| 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 | 
|  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 () | 
|  Public Member Functions inherited from Observer | |
| Observer (const Observer &) | |
| Observer & | operator= (const Observer &) | 
| std::pair< iterator, bool > | registerWith (const boost::shared_ptr< Observable > &) | 
| void | registerWithObservables (const boost::shared_ptr< Observer > &) | 
| Size | unregisterWith (const boost::shared_ptr< Observable > &) | 
| void | unregisterWithAll () | 
| virtual void | deepUpdate () | 
|  Public Member Functions inherited from Observable | |
| Observable (const Observable &) | |
| Observable & | operator= (const Observable &) | 
| void | notifyObservers () | 
| Protected Member Functions | |
| StochasticProcess1D (const boost::shared_ptr< discretization > &) | |
|  Protected Member Functions inherited from StochasticProcess | |
| StochasticProcess (const boost::shared_ptr< discretization > &) | |
| Protected Attributes | |
| boost::shared_ptr< discretization > | discretization_ | 
|  Protected Attributes inherited from StochasticProcess | |
| boost::shared_ptr< discretization > | discretization_ | 
| Additional Inherited Members | |
|  Public Types inherited from Observer | |
| typedef std::set< boost::shared_ptr< Observable > > | set_type | 
| typedef set_type::iterator | iterator | 
1-dimensional stochastic process
This class describes a stochastic process governed by
\[ dx_t = \mu(t, x_t)dt + \sigma(t, x_t)dW_t. \]
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 GeneralizedBlackScholesProcess, HullWhiteForwardProcess, ExtendedOrnsteinUhlenbeckProcess, GeneralizedOrnsteinUhlenbeckProcess, OrnsteinUhlenbeckProcess, GsrProcess, HullWhiteProcess, and MfStateProcess.
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 GeneralizedBlackScholesProcess, HullWhiteForwardProcess, ExtendedOrnsteinUhlenbeckProcess, GemanRoncoroniProcess, GeneralizedOrnsteinUhlenbeckProcess, OrnsteinUhlenbeckProcess, GsrProcess, HullWhiteProcess, and MfStateProcess.
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 GeneralizedBlackScholesProcess, HullWhiteForwardProcess, OrnsteinUhlenbeckProcess, ExtendedOrnsteinUhlenbeckProcess, GeneralizedOrnsteinUhlenbeckProcess, GsrProcess, HullWhiteProcess, and MfStateProcess.
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 GeneralizedBlackScholesProcess, GemanRoncoroniProcess, and ExtendedBlackScholesMertonProcess.
applies a change to the asset value. By default, it returns \( x + \Delta x \).
Reimplemented in GeneralizedBlackScholesProcess, and Merton76Process.