StochasticProcess Class Reference

#include <ql/stochasticprocess.hpp>

Inheritance diagram for StochasticProcess:

Inheritance graph
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List of all members.

Detailed Description

multi-dimensional stochastic process class.

This class describes a stochastic process governed by

\[ d\mathrm{x}_t = \mu(t, x_t)\mathrm{d}t + \sigma(t, \mathrm{x}_t) \cdot d\mathrm{W}_t. \]


Public Member Functions

Stochastic process interface
virtual Size size () const=0
 returns the number of dimensions of the stochastic process
virtual Size factors () const
 returns the number of independent factors of the process
virtual Disposable< ArrayinitialValues () const=0
 returns the initial values of the state variables
virtual Disposable< Arraydrift (Time t, const Array &x) const=0
 returns the drift part of the equation, i.e., $ \mu(t, \mathrm{x}_t) $
virtual Disposable< Matrixdiffusion (Time t, const Array &x) const=0
 returns the diffusion part of the equation, i.e. $ \sigma(t, \mathrm{x}_t) $
virtual Disposable< Arrayexpectation (Time t0, const Array &x0, Time dt) const
virtual Disposable< MatrixstdDeviation (Time t0, const Array &x0, Time dt) const
virtual Disposable< Matrixcovariance (Time t0, const Array &x0, Time dt) const
virtual Disposable< Arrayevolve (Time t0, const Array &x0, Time dt, const Array &dw) const
virtual Disposable< Arrayapply (const Array &x0, const Array &dx) const
utilities
virtual Time time (const Date &) const
Observer interface
void update ()

Protected Member Functions

 StochasticProcess (const boost::shared_ptr< discretization > &)

Protected Attributes

boost::shared_ptr< discretizationdiscretization_

Classes

class  discretization
 discretization of a stochastic process over a given time interval More...


Member Function Documentation

virtual Disposable<Array> expectation ( Time  t0,
const Array x0,
Time  dt 
) const [virtual]

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 in G2Process, G2ForwardProcess, and StochasticProcessArray.

virtual Disposable<Matrix> stdDeviation ( Time  t0,
const Array x0,
Time  dt 
) const [virtual]

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 in G2Process, G2ForwardProcess, and StochasticProcessArray.

virtual Disposable<Matrix> covariance ( Time  t0,
const Array x0,
Time  dt 
) const [virtual]

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 in G2Process, G2ForwardProcess, LiborForwardModelProcess, and StochasticProcessArray.

virtual Disposable<Array> evolve ( Time  t0,
const Array x0,
Time  dt,
const Array dw 
) const [virtual]

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 in HestonProcess, LiborForwardModelProcess, and StochasticProcessArray.

virtual Disposable<Array> apply ( const Array x0,
const Array dx 
) const [virtual]

applies a change to the asset value. By default, it returns $ \mathrm{x} + \Delta \mathrm{x} $.

Reimplemented in HestonProcess, LiborForwardModelProcess, and StochasticProcessArray.

virtual Time time ( const Date  )  const [virtual]

returns the time value corresponding to the given date in the reference system of the stochastic process.

Note:
As a number of processes might not need this functionality, a default implementation is given which raises an exception.

Reimplemented in GeneralizedBlackScholesProcess, HestonProcess, Merton76Process, and StochasticProcessArray.

void update (  )  [virtual]

This method must be implemented in derived classes. An instance of Observer does not call this method directly: instead, it will be called by the observables the instance registered with when they need to notify any changes.

Implements Observer.

Reimplemented in GeneralizedBlackScholesProcess, and HestonProcess.