net.finmath.montecarlo

Class BrownianBridge

java.lang.Object

net.finmath.montecarlo.BrownianBridge

All Implemented Interfaces:

BrownianMotion, IndependentIncrements

public class BrownianBridge
extends Object
implements BrownianMotion

This class implements a Brownian bridge, i.e., samples of realizations of a Brownian motion conditional to a given start and end value.

A Brownian bridge is a conditional Brownian motion, i.e. for given random variables X and Y the Brownian bridge is
(W(t) | W(s) = X , W(T) = Y),
where W is a Brownian motion and s ≤ t ≤ T.

The samples of the Brownian bridge are generated by a Brownian motion which will be used to fill the gap between start and end. It is important that this Browninan motion is independent from the one which generated start and end, i.e. here: it should have a different seed.

The class implements the BrownianMotion, i.e., it only provides the increments of the Brownian bridge (however, in most application, like refinement of an Euler-scheme, this is exactly the desired object).

Note: The number of paths needs to be specified, because the start and the end point may be not stochastic, i.e. it is not possible to infer this quantity from the specified start and end.

Version:

1.0

Author:

Christian Fries

Date:

24.11.2013

Constructor Summary

Constructors

Constructor and Description
BrownianBridge(TimeDiscretization timeDiscretization, int numberOfPaths, int seed, RandomVariable[] start, RandomVariable[] end) Construct a Brownian bridge, bridging from a given start to a given end.
BrownianBridge(TimeDiscretization timeDiscretization, int numberOfPaths, int seed, RandomVariable start, RandomVariable end) Construct a Brownian bridge, bridging from a given start to a given end.

Method Summary

Modifier and Type	Method and 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) Return the increment for a given timeIndex.
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.
String	toString()

Methods inherited from class java.lang.Object

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

Constructor Detail

BrownianBridge

public BrownianBridge(TimeDiscretization timeDiscretization,
                      int numberOfPaths,
                      int seed,
                      RandomVariable[] start,
                      RandomVariable[] end)

Construct a Brownian bridge, bridging from a given start to a given end.

Parameters:

timeDiscretization - The time discretization used for the Brownian increments.

numberOfPaths - Number of paths to simulate.

seed - The seed of the random number generator.

start - Start value of the Brownian bridge.

end - End value of the Brownian bridge.

BrownianBridge

public BrownianBridge(TimeDiscretization timeDiscretization,
                      int numberOfPaths,
                      int seed,
                      RandomVariable start,
                      RandomVariable end)

Construct a Brownian bridge, bridging from a given start to a given end.

Parameters:

timeDiscretization - The time discretization used for the Brownian increments.

numberOfPaths - Number of paths to simulate.

seed - The seed of the random number generator.

start - Start value of the Brownian bridge.

end - End value of the Brownian bridge.

Method Detail

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)

Description copied from interface: IndependentIncrements

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

Specified by:

getIncrement in interface IndependentIncrements

Parameters:

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

Returns:

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

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)

toString

public String toString()

Overrides:

toString in class Object