QuantLib
A free/open-source library for quantitative finance
Reference manual - version 1.6
Classes | Protected Member Functions | Protected Attributes | List of all members
StochasticProcess1D Class Referenceabstract

1-dimensional stochastic process More...

#include <ql/stochasticprocess.hpp>

+ 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 &)
 
Observeroperator= (const Observer &)
 
std::pair< std::set< boost::shared_ptr< Observable > >::iterator, bool > registerWith (const boost::shared_ptr< Observable > &)
 
void registerWithObservables (const boost::shared_ptr< Observer > &)
 
Size unregisterWith (const boost::shared_ptr< Observable > &)
 
void unregisterWithAll ()
 
- Public Member Functions inherited from Observable
 Observable (const Observable &)
 
Observableoperator= (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< discretizationdiscretization_
 
- Protected Attributes inherited from StochasticProcess
boost::shared_ptr< discretizationdiscretization_
 

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

virtual Real expectation ( Time  t0,
Real  x0,
Time  dt 
) const
virtual

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.

virtual Real stdDeviation ( Time  t0,
Real  x0,
Time  dt 
) const
virtual

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 HullWhiteForwardProcess, ExtendedOrnsteinUhlenbeckProcess, GemanRoncoroniProcess, GeneralizedOrnsteinUhlenbeckProcess, OrnsteinUhlenbeckProcess, GsrProcess, HullWhiteProcess, and MfStateProcess.

virtual Real variance ( Time  t0,
Real  x0,
Time  dt 
) const
virtual

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 HullWhiteForwardProcess, OrnsteinUhlenbeckProcess, ExtendedOrnsteinUhlenbeckProcess, GeneralizedOrnsteinUhlenbeckProcess, GsrProcess, HullWhiteProcess, and MfStateProcess.

virtual Real evolve ( Time  t0,
Real  x0,
Time  dt,
Real  dw 
) const
virtual

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.

virtual Real apply ( Real  x0,
Real  dx 
) const
virtual

applies a change to the asset value. By default, it returns \( x + \Delta x \).

Reimplemented in GeneralizedBlackScholesProcess, and Merton76Process.