StochasticProcess Class Reference

#include <ql/stochasticprocess.hpp>

Inheritance diagram for StochasticProcess:

Inheritance graph
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List of all members.

Detailed Description

Stochastic process class.

This class describes a stochastic process governed by

\[ dx_t = \mu(t, x_t)dt + \sigma(t, x_t)dW_t. \]


Public Member Functions

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 variance (Time t0, Real x0, Time dt) const
virtual Real evolve (Real change, Real currentValue) 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 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 OrnsteinUhlenbeckProcess.

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 OrnsteinUhlenbeckProcess.

virtual Real evolve Real  change,
Real  currentValue
const [virtual]
 

applies a change to the asset value. By default; it returns $ x + \Delta x $ .

Reimplemented in BlackScholesProcess, and Merton76Process.

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 BlackScholesProcess, and Merton76Process.

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 BlackScholesProcess.


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