net.finmath.montecarlo.process

Class ProcessEulerScheme

java.lang.Object

net.finmath.montecarlo.process.AbstractProcess

net.finmath.montecarlo.process.ProcessEulerScheme

All Implemented Interfaces:

Cloneable, AbstractProcessInterface, ProcessInterface

public class ProcessEulerScheme
extends AbstractProcess

This class implements some numerical schemes for multi-dimensional multi-factor Ito process. It features the standard Euler scheme and the standard predictor-corrector Euler scheme for Y, then applies the state space transform \( X = f(Y) \). For the standard Euler scheme the process Y is discretized as \[ Y(t_{i+1}) = Y(t_{i}) + \mu(t_{i}) \Delta t_{i} + \sigma(t_{i}) \Delta W(t_{i}) \text{.} \] Hence, using the state space transform, it is possible to create a log-Euler scheme, i.e., \[ X(t_{i+1}) = X(t_{i}) \cdot \exp\left( (\mu(t_{i}) - \frac{1}{2} \sigma(t_{i})^2) \Delta t_{i} + \sigma(t_{i}) \Delta W(t_{i}) \right) \text{.} \] The dimension is called numberOfComponents here. The default for numberOfFactors is 1.

Version:

1.4

Author:

Christian Fries

See Also:

The interface definition contains more details.

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	ProcessEulerScheme.Scheme

Constructor Summary

Constructors

Constructor and Description
ProcessEulerScheme(IndependentIncrementsInterface stochasticDriver) Create an Euler discretization scheme.
ProcessEulerScheme(IndependentIncrementsInterface stochasticDriver, ProcessEulerScheme.Scheme scheme) Create an Euler discretization scheme.

Method Summary

Modifier and Type	Method and Description
ProcessEulerScheme	clone() Create and return a clone of this process.
BrownianMotionInterface	getBrownianMotion()
AbstractProcessInterface	getCloneWithModifiedData(Map<String,Object> dataModified) Returns a clone of this model where the specified properties have been modified.
Object	getCloneWithModifiedSeed(int seed)
RandomVariableInterface	getMonteCarloWeights(int timeIndex) This method returns the weights of a weighted Monte Carlo method (the probability density).
int	getNumberOfFactors()
int	getNumberOfPaths()
RandomVariableInterface	getProcessValue(int timeIndex, int componentIndex) This method returns the realization of the process at a certain time index.
ProcessEulerScheme.Scheme	getScheme()
IndependentIncrementsInterface	getStochasticDriver()
String	toString()

Methods inherited from class net.finmath.montecarlo.process.AbstractProcess

applyStateSpaceTransform, getDrift, getFactorLoading, getInitialState, getNumberOfComponents, getTime, getTimeDiscretization, getTimeIndex, setModel

Methods inherited from class java.lang.Object

equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

ProcessEulerScheme

public ProcessEulerScheme(IndependentIncrementsInterface stochasticDriver,
                          ProcessEulerScheme.Scheme scheme)

Create an Euler discretization scheme.

Parameters:

stochasticDriver - The stochastic driver of the process (e.g. a Brownian motion).

scheme - The scheme to use. See ProcessEulerScheme.Scheme.

ProcessEulerScheme

public ProcessEulerScheme(IndependentIncrementsInterface stochasticDriver)

Create an Euler discretization scheme.

Parameters:

stochasticDriver - The stochastic driver of the process (e.g. a Brownian motion).

Method Detail

getProcessValue

public RandomVariableInterface getProcessValue(int timeIndex,
                                               int componentIndex)

This method returns the realization of the process at a certain time index.

Parameters:

timeIndex - Time index at which the process should be observed

componentIndex - Component index of the process

Returns:

A vector of process realizations (on path)

getMonteCarloWeights

public RandomVariableInterface getMonteCarloWeights(int timeIndex)

This method returns the weights of a weighted Monte Carlo method (the probability density).

Parameters:

timeIndex - Time index at which the process should be observed

Returns:

A vector of positive weights

getNumberOfPaths

public int getNumberOfPaths()

Returns:

Returns the numberOfPaths.

getNumberOfFactors

public int getNumberOfFactors()

Returns:

Returns the numberOfFactors.

getStochasticDriver

public IndependentIncrementsInterface getStochasticDriver()

Returns:

Returns the independent increments interface used in the generation of the process

getBrownianMotion

public BrownianMotionInterface getBrownianMotion()

Returns:

Returns the Brownian motion used in the generation of the process

getScheme

public ProcessEulerScheme.Scheme getScheme()

Returns:

Returns the scheme.

clone

public ProcessEulerScheme clone()

Description copied from interface: AbstractProcessInterface

Create and return a clone of this process. The clone is not tied to any model, but has the same process specification, that is, if the model is the same, it would generate the same paths.

Specified by:

clone in interface AbstractProcessInterface

Specified by:

clone in interface ProcessInterface

Specified by:

clone in class AbstractProcess

Returns:

Clone of the process

getCloneWithModifiedData

public AbstractProcessInterface getCloneWithModifiedData(Map<String,Object> dataModified)

Description copied from interface: AbstractProcessInterface

Returns a clone of this model where the specified properties have been modified. Note that there is no guarantee that a model reacts on a specification of a properties in the parameter map dataModified. If data is provided which is ignored by the model no exception may be thrown.

Parameters:

dataModified - Key-value-map of parameters to modify.

Returns:

A clone of this model (or this model if no parameter was modified).

getCloneWithModifiedSeed

public Object getCloneWithModifiedSeed(int seed)

Specified by:

getCloneWithModifiedSeed in class AbstractProcess

toString

public String toString()

Overrides:

toString in class Object