Module net.finmath.lib

Package net.finmath.montecarlo

Class CorrelatedBrownianMotion

java.lang.Object

net.finmath.montecarlo.CorrelatedBrownianMotion

All Implemented Interfaces:

BrownianMotion, IndependentIncrements

public class CorrelatedBrownianMotion
extends Object
implements BrownianMotion

Provides a correlated Brownian motion from given (independent) increments and a given matrix of factor loadings. The i-th factor of this BrownianMotionLazyInit is dW_i where dW_i = f_i,1 dU₁ + ... + f_i,m dU_m for i = 1, ..., n. Here f_i,j are the factor loadings, an n × m-matrix. If dU_j are independent, then dW_i dW_k = ρ_i,k dt where ρ_i,k = f_i · f_j. Note: It is possible to create this class with a Brownian motion U which is already correlated. The factors loadings will be applied accordingly.

Version:

1.0

Author:

Christian Fries

Constructor Summary

Constructors

Constructor	Description
CorrelatedBrownianMotion(BrownianMotion uncollelatedFactors, double[][] factorLoadings)	Create a correlated Brownian motion from given independent increments and a given matrix of factor loadings.

Method Summary

Modifier and Type	Method	Description
RandomVariable	getBrownianIncrement(int timeIndex, int factor)	Return the Brownian increment for a given timeIndex.
BrownianMotion	getCloneWithModifiedSeed(int seed)	Return a new object implementing BrownianMotion having the same specifications as this object but a different seed for the random number generator.
BrownianMotion	getCloneWithModifiedTimeDiscretization(TimeDiscretization newTimeDiscretization)	Return a new object implementing BrownianMotion having the same specifications as this object but a different time discretization.
RandomVariable	getIncrement(int timeIndex, int factor)	Return the increment for a given timeIndex and given factor.
int	getNumberOfFactors()	Returns the number of factors.
int	getNumberOfPaths()	Returns the number of paths.
RandomVariable	getRandomVariableForConstant(double value)	Returns a random variable which is initialized to a constant, but has exactly the same number of paths or discretization points as the ones used by this BrownianMotion.
TimeDiscretization	getTimeDiscretization()	Returns the time discretization used for this set of time-discrete Brownian increments.

Methods inherited from class java.lang.Object

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

Methods inherited from interface net.finmath.montecarlo.BrownianMotion

getBrownianIncrement

Methods inherited from interface net.finmath.montecarlo.IndependentIncrements

getIncrement

Constructor Details

CorrelatedBrownianMotion

public CorrelatedBrownianMotion(BrownianMotion uncollelatedFactors, double[][] factorLoadings)

Create a correlated Brownian motion from given independent increments and a given matrix of factor loadings. The i-th factor of this BrownianMotionLazyInit is dW_i where dW_i = f_i,1 dU₁ + ... + f_i,m dU_m for i = 1, ..., n. Here f_i,j are the factor loadings, an n × m-matrix. If dU_j are independent, then dW_i dW_k = ρ_i,k dt where ρ_i,k = f_i · f_j.

Parameters:

uncollelatedFactors - The Brownian motion providing the (uncorrelated) factors dU_j.

factorLoadings - The factor loadings f_i,j.

Method Details

getBrownianIncrement

public RandomVariable getBrownianIncrement(int timeIndex, int factor)

Description copied from interface: BrownianMotion

Return the Brownian increment for a given timeIndex. The method returns the random variable Δ W_j(t_i) := W_j(t_i+1)-W(t_i) for the given time index i and a given factor (index) j

Specified by:

getBrownianIncrement in interface BrownianMotion

Parameters:

timeIndex - The time index (corresponding to the this class's time discretization).

factor - The index of the factor (independent scalar Brownian increment).

Returns:

The factor (component) of the Brownian increments (a random variable).

getTimeDiscretization

public TimeDiscretization getTimeDiscretization()

Description copied from interface: BrownianMotion

Returns the time discretization used for this set of time-discrete Brownian increments.

Specified by:

getTimeDiscretization in interface BrownianMotion

Specified by:

getTimeDiscretization in interface IndependentIncrements

Returns:

The time discretization used for this set of time-discrete Brownian increments.

getNumberOfFactors

public int getNumberOfFactors()

Description copied from interface: BrownianMotion

Returns the number of factors.

Specified by:

getNumberOfFactors in interface BrownianMotion

Specified by:

getNumberOfFactors in interface IndependentIncrements

Returns:

The number of factors.

getNumberOfPaths

public int getNumberOfPaths()

Description copied from interface: BrownianMotion

Returns the number of paths.

Specified by:

getNumberOfPaths in interface BrownianMotion

Specified by:

getNumberOfPaths in interface IndependentIncrements

Returns:

The number of paths.

getRandomVariableForConstant

public RandomVariable getRandomVariableForConstant(double value)

Description copied from interface: BrownianMotion

Returns a random variable which is initialized to a constant, but has exactly the same number of paths or discretization points as the ones used by this BrownianMotion.

Specified by:

getRandomVariableForConstant in interface BrownianMotion

Specified by:

getRandomVariableForConstant in interface IndependentIncrements

Parameters:

value - The constant value to be used for initialized the random variable.

Returns:

A new random variable.

getCloneWithModifiedSeed

public BrownianMotion getCloneWithModifiedSeed(int seed)

Description copied from interface: BrownianMotion

Return a new object implementing BrownianMotion having the same specifications as this object but a different seed for the random number generator. This method is useful if you like to make Monte-Carlo samplings by changing the seed.

Specified by:

getCloneWithModifiedSeed in interface BrownianMotion

Specified by:

getCloneWithModifiedSeed in interface IndependentIncrements

Parameters:

seed - New value for the seed.

Returns:

New object implementing BrownianMotion.

getCloneWithModifiedTimeDiscretization

public BrownianMotion getCloneWithModifiedTimeDiscretization(TimeDiscretization newTimeDiscretization)

Description copied from interface: BrownianMotion

Return a new object implementing BrownianMotion having the same specifications as this object but a different time discretization.

Specified by:

getCloneWithModifiedTimeDiscretization in interface BrownianMotion

Specified by:

getCloneWithModifiedTimeDiscretization in interface IndependentIncrements

Parameters:

newTimeDiscretization - New time discretization

Returns:

New object implementing BrownianMotion.

getIncrement

public RandomVariable getIncrement(int timeIndex, int factor)

Description copied from interface: IndependentIncrements

Return the increment for a given timeIndex and given factor. The method returns the random variable Δ X_j(t_i) := X_j(t_i+1)-X(t_i) for the given time index i and a given factor (index) j

Specified by:

getIncrement in interface IndependentIncrements

Parameters:

timeIndex - The time index (corresponding to the this class's time discretization)

factor - The index of the factor (independent scalar increment)

Returns:

The factor (component) of the increments (a random variable)