net.finmath.montecarlo.templatemethoddesign

Class LogNormalProcess

java.lang.Object

net.finmath.montecarlo.templatemethoddesign.LogNormalProcess

Direct Known Subclasses:

MonteCarloBlackScholesModel2

public abstract class LogNormalProcess
extends Object

This class is an abstract base class to implement an Euler scheme of a multi-dimensional multi-factor log-normal Ito process. The dimension is called numberOfComponents here. The default for numberOfFactors is 1.

Version:

1.5

Author:

Christian Fries

Date:

19.04.2008

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	LogNormalProcess.Scheme

Constructor Summary

Constructors

Constructor and Description
LogNormalProcess(int numberOfComponents, BrownianMotion brownianMotion) Create a log normal process.
LogNormalProcess(TimeDiscretization timeDiscretization, int numberOfComponents, int numberOfPaths) Create a simulation of log normal process.
LogNormalProcess(TimeDiscretization timeDiscretization, int numberOfComponents, int numberOfFactors, int numberOfPaths, int seed) Create a simulation of log normal process.

Method Summary

Modifier and Type	Method and Description
BrownianMotion	getBrownianMotion()
abstract RandomVariable	getDrift(int timeIndex, int componentIndex, RandomVariable[] realizationAtTimeIndex, RandomVariable[] realizationPredictor)
RandomVariable[]	getDrift(int timeIndex, RandomVariable[] realizationAtTimeIndex, RandomVariable[] realizationPredictor) Get the the drift.
abstract RandomVariable	getFactorLoading(int timeIndex, int factor, int component, RandomVariable[] realizationAtTimeIndex) This method should be overwritten and return the factor loading, i.e.
abstract RandomVariable[]	getInitialValue()
RandomVariable	getMonteCarloWeights(int timeIndex) This method returns the weights of a weighted Monte Carlo method (the probability density).
int	getNumberOfComponents()
int	getNumberOfFactors()
int	getNumberOfPaths()
RandomVariable[]	getProcessValue(int timeIndex) This method returns the realization of the process at a certain time index.
RandomVariable	getProcessValue(int timeIndex, int componentIndex) This method returns the realization of the process at a certain time index.
LogNormalProcess.Scheme	getScheme()
double	getTime(int timeIndex) Returns the time for a given simulation time index.
TimeDiscretization	getTimeDiscretization()
int	getTimeIndex(double time) Returns the time index for a given simulation time.
protected void	setBrownianMotion(BrownianMotion brownianMotion) A derived class may change the Brownian motion.
void	setScheme(LogNormalProcess.Scheme scheme)

Methods inherited from class java.lang.Object

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

Constructor Detail

LogNormalProcess

public LogNormalProcess(int numberOfComponents,
                        BrownianMotion brownianMotion)

Create a log normal process.

Parameters:

numberOfComponents - The number of components (scalar processes).

brownianMotion - A Brownian motion

LogNormalProcess

public LogNormalProcess(TimeDiscretization timeDiscretization,
                        int numberOfComponents,
                        int numberOfPaths)

Create a simulation of log normal process.

Parameters:

timeDiscretization - The time discretization of the process.

numberOfComponents - The number of components (the dimension of the process).

numberOfPaths - The number of path of the simulation.

LogNormalProcess

public LogNormalProcess(TimeDiscretization timeDiscretization,
                        int numberOfComponents,
                        int numberOfFactors,
                        int numberOfPaths,
                        int seed)

Create a simulation of log normal process.

Parameters:

timeDiscretization - The time discretization of the process.

numberOfComponents - The number of components (the dimension of the process).

numberOfFactors - The number of factors of the process.

numberOfPaths - The number of path of the simulation.

seed - The seed of the underlying random number generator.

Method Detail

getInitialValue

public abstract RandomVariable[] getInitialValue()

getDrift

public abstract RandomVariable getDrift(int timeIndex,
                                        int componentIndex,
                                        RandomVariable[] realizationAtTimeIndex,
                                        RandomVariable[] realizationPredictor)

getDrift

public RandomVariable[] getDrift(int timeIndex,
                                 RandomVariable[] realizationAtTimeIndex,
                                 RandomVariable[] realizationPredictor)

Get the the drift.

Parameters:

timeIndex - The time index (related to the model times discretization).

realizationAtTimeIndex - The given realization at timeIndex

realizationPredictor - The given realization at timeIndex+1 or null of no predictor is available.

Returns:

The (average) drift from timeIndex to timeIndex+1

getFactorLoading

public abstract RandomVariable getFactorLoading(int timeIndex,
                                                int factor,
                                                int component,
                                                RandomVariable[] realizationAtTimeIndex)

This method should be overwritten and return the factor loading, i.e. the coeffient λ(i,j) such that
dS(j) = (...) dt + S(j) * (λ(1,j) dW(1) + ... + λ(m,j) dW(m))
in an m-factor model. Here j denotes index of the component of the resulting log-normal process and i denotes the index of the factor.

Overwrite this method if you would like to implement a multi factor model.

Parameters:

timeIndex - The time index of the simulation time discretization.

factor - The factor index.

component - The component index.

realizationAtTimeIndex - The realization at the current time index.

Returns:

factor loading for given factor and component

getProcessValue

public RandomVariable[] getProcessValue(int timeIndex)

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

Parameters:

timeIndex - Time index at which the process should be observed

Returns:

A vector of process realizations (on path)

getProcessValue

public RandomVariable 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 of the process vector

Returns:

A vector of process realizations (on path)

getMonteCarloWeights

public RandomVariable 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 which sums up to one

getNumberOfComponents

public int getNumberOfComponents()

Returns:

Returns the numberOfComponents.

getNumberOfPaths

public int getNumberOfPaths()

Returns:

Returns the numberOfPaths.

getNumberOfFactors

public int getNumberOfFactors()

Returns:

Returns the numberOfFactors.

getTimeDiscretization

public TimeDiscretization getTimeDiscretization()

Returns:

Returns the timeDiscretizationFromArray.

getTime

public double getTime(int timeIndex)

Returns the time for a given simulation time index.

Parameters:

timeIndex - Time index

Returns:

Returns the time for a given time index.

getTimeIndex

public int getTimeIndex(double time)

Returns the time index for a given simulation time.

Parameters:

time - A simulation time

Returns:

Returns the time index for a given time.

getBrownianMotion

public BrownianMotion getBrownianMotion()

Returns:

Returns the Brownian motion used in the generation of the process

getScheme

public LogNormalProcess.Scheme getScheme()

Returns:

Returns the scheme.

setBrownianMotion

protected void setBrownianMotion(BrownianMotion brownianMotion)

A derived class may change the Brownian motion. This is only allowed prior to lazy initialization. The method should be used only while constructing new object. Do not use in flight.

Parameters:

brownianMotion - The brownianMotion to set.

setScheme

public void setScheme(LogNormalProcess.Scheme scheme)

Parameters:

scheme - The scheme to set.