Module net.finmath.lib

Package net.finmath.montecarlo.assetderivativevaluation

Class MonteCarloMertonModel

java.lang.Object

net.finmath.montecarlo.assetderivativevaluation.MonteCarloMertonModel

All Implemented Interfaces:

Model, AssetModelMonteCarloSimulationModel, MonteCarloSimulationModel

public class MonteCarloMertonModel
extends Object
implements AssetModelMonteCarloSimulationModel

This class glues together a MertonModel and a Monte-Carlo implementation of a MonteCarloProcessFromProcessModel, namely EulerSchemeFromProcessModel, and forms a Monte-Carlo implementation of the Merton model by implementing AssetModelMonteCarloSimulationModel. The model is \[ dS = \mu S dt + \sigma S dW + S dJ, \quad S(0) = S_{0}, \] \[ dN = r N dt, \quad N(0) = N_{0}, \] where \( W \) is Brownian motion and \( J \) is a jump process (compound Poisson process). The process \( J \) is given by \( J(t) = \sum_{i=1}^{N(t)} (Y_{i}-1) \), where \( \log(Y_{i}) \) are i.i.d. normals with mean \( a - \frac{1}{2} b^{2} \) and standard deviation \( b \). Here \( a \) is the jump size mean and \( b \) is the jump size std. dev. For details on the construction of the model see MertonModel.

Version:

1.0

Author:

Christian Fries

See Also:

MertonModel, The interface for numerical schemes., The interface for models provinding parameters to numerical schemes.

Constructor Summary

Constructors

Constructor	Description
MonteCarloMertonModel(TimeDiscretization timeDiscretization, int numberOfPaths, int seed, double initialValue, double riskFreeRate, double volatility, double jumpIntensity, double jumpSizeMean, double jumpSizeStDev)	Create a Monte-Carlo simulation using given time discretization and given parameters.

Method Summary

Modifier and Type	Method	Description
RandomVariable	getAssetValue(double time, int assetIndex)	Returns the random variable representing the asset's value at a given time for a given asset.
RandomVariable	getAssetValue(int timeIndex, int assetIndex)	Returns the random variable representing the asset's value at a given time for a given asset.
AssetModelMonteCarloSimulationModel	getCloneWithModifiedData(Map<String,Object> dataModified)	Create a clone of this simulation modifying some of its properties (if any).
AssetModelMonteCarloSimulationModel	getCloneWithModifiedSeed(int seed)	Create a clone of the object implementing AssetModelMonteCarloSimulationModel using a different Monte-Carlo seed.
RandomVariable	getMonteCarloWeights(double time)	This method returns the weights of a weighted Monte Carlo method (the probability density).
RandomVariable	getMonteCarloWeights(int timeIndex)	This method returns the weights of a weighted Monte Carlo method (the probability density).
int	getNumberOfAssets()	Returns the number of asset price processes.
int	getNumberOfPaths()	Returns the numberOfPaths.
RandomVariable	getNumeraire(double time)	Returns the numeraire associated with the valuation measure used by this model.
RandomVariable	getNumeraire(int timeIndex)	Returns the numeraire associated with the valuation measure used by this model.
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 MonteCarloSimulationModel.
LocalDateTime	getReferenceDate()	Returns the model's date corresponding to the time discretization's \( t = 0 \).
double	getTime(int timeIndex)	Returns the time for a given time index.
TimeDiscretization	getTimeDiscretization()	Returns the timeDiscretizationFromArray.
int	getTimeIndex(double time)	Returns the time index for a given time.

Methods inherited from class java.lang.Object

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

Constructor Detail

MonteCarloMertonModel

public MonteCarloMertonModel(TimeDiscretization timeDiscretization,
                             int numberOfPaths,
                             int seed,
                             double initialValue,
                             double riskFreeRate,
                             double volatility,
                             double jumpIntensity,
                             double jumpSizeMean,
                             double jumpSizeStDev)

Create a Monte-Carlo simulation using given time discretization and given parameters.

Parameters:

timeDiscretization - The time discretization.

numberOfPaths - The number of Monte-Carlo path to be used.

seed - The seed used for the random number generator.

initialValue - Spot value.

riskFreeRate - The risk free rate.

volatility - The log volatility.

jumpIntensity - The intensity parameter lambda of the compound Poisson process.

jumpSizeMean - The mean jump size of the normal distributes jump sizes of the compound Poisson process.

jumpSizeStDev - The standard deviation of the normal distributes jump sizes of the compound Poisson process.

Method Detail

getReferenceDate

public LocalDateTime getReferenceDate()

Description copied from interface: MonteCarloSimulationModel

Returns the model's date corresponding to the time discretization's \( t = 0 \).

Specified by:

getReferenceDate in interface MonteCarloSimulationModel

Returns:

The model's date corresponding to the time discretization's \( t = 0 \).

getAssetValue

public RandomVariable getAssetValue(double time,
                                    int assetIndex)
                             throws CalculationException

Description copied from interface: AssetModelMonteCarloSimulationModel

Returns the random variable representing the asset's value at a given time for a given asset.

Specified by:

getAssetValue in interface AssetModelMonteCarloSimulationModel

Parameters:

time - Simulation time

assetIndex - Index of the asset (0 for a single asset model)

Returns:

The asset process as seen on simulation time

Throws:

CalculationException - Thrown if the valuation fails, specific cause may be available via the cause() method.

getAssetValue

public RandomVariable getAssetValue(int timeIndex,
                                    int assetIndex)
                             throws CalculationException

Description copied from interface: AssetModelMonteCarloSimulationModel

Returns the random variable representing the asset's value at a given time for a given asset.

Specified by:

getAssetValue in interface AssetModelMonteCarloSimulationModel

Parameters:

timeIndex - Index of simulation time

assetIndex - Index of the asset (0 for a single asset model)

Returns:

The asset process as seen on simulation time

Throws:

CalculationException - Thrown if the valuation fails, specific cause may be available via the cause() method.

getNumeraire

public RandomVariable getNumeraire(int timeIndex)
                            throws CalculationException

Description copied from interface: AssetModelMonteCarloSimulationModel

Returns the numeraire associated with the valuation measure used by this model.

Specified by:

getNumeraire in interface AssetModelMonteCarloSimulationModel

Parameters:

timeIndex - The time index (associated with this models time discretization).

Returns:

The numeraire associated with the valuation measure used by this model.

Throws:

CalculationException - Thrown if calculation of numeraire fails.

getNumeraire

public RandomVariable getNumeraire(double time)
                            throws CalculationException

Description copied from interface: AssetModelMonteCarloSimulationModel

Returns the numeraire associated with the valuation measure used by this model.

Specified by:

getNumeraire in interface AssetModelMonteCarloSimulationModel

Parameters:

time - The time for which the numeraire is requested.

Returns:

The numeraire associated with the valuation measure used by this model.

Throws:

CalculationException - Thrown if calculation of numeraire fails.

getMonteCarloWeights

public RandomVariable getMonteCarloWeights(double time)
                                    throws CalculationException

Description copied from interface: MonteCarloSimulationModel

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

Specified by:

getMonteCarloWeights in interface MonteCarloSimulationModel

Parameters:

time - Time at which the process should be observed

Returns:

A vector of positive weights which sums up to one

Throws:

CalculationException - Thrown if the valuation fails, specific cause may be available via the cause() method.

getNumberOfAssets

public int getNumberOfAssets()

Description copied from interface: AssetModelMonteCarloSimulationModel

Returns the number of asset price processes.

Specified by:

getNumberOfAssets in interface AssetModelMonteCarloSimulationModel

Returns:

The number of asset price processes

getCloneWithModifiedData

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

Description copied from interface: AssetModelMonteCarloSimulationModel

Create a clone of this simulation modifying some of its properties (if any).

Specified by:

getCloneWithModifiedData in interface AssetModelMonteCarloSimulationModel

Specified by:

getCloneWithModifiedData in interface MonteCarloSimulationModel

Parameters:

dataModified - The data which should be changed in the new model

Returns:

Returns a clone of this model, with some data modified (then it is no longer a clone :-)

getCloneWithModifiedSeed

public AssetModelMonteCarloSimulationModel getCloneWithModifiedSeed(int seed)

Description copied from interface: AssetModelMonteCarloSimulationModel

Create a clone of the object implementing AssetModelMonteCarloSimulationModel using a different Monte-Carlo seed.

Specified by:

getCloneWithModifiedSeed in interface AssetModelMonteCarloSimulationModel

Parameters:

seed - The seed of the underlying random number generator.

Returns:

Returns a clone of this model except for a modified Monte-Carlo seed.

getNumberOfPaths

public int getNumberOfPaths()

Description copied from interface: MonteCarloSimulationModel

Returns the numberOfPaths.

Specified by:

getNumberOfPaths in interface MonteCarloSimulationModel

Returns:

Returns the numberOfPaths.

getTimeDiscretization

public TimeDiscretization getTimeDiscretization()

Description copied from interface: MonteCarloSimulationModel

Returns the timeDiscretizationFromArray.

Specified by:

getTimeDiscretization in interface MonteCarloSimulationModel

Returns:

Returns the timeDiscretizationFromArray.

getTime

public double getTime(int timeIndex)

Description copied from interface: MonteCarloSimulationModel

Returns the time for a given time index.

Specified by:

getTime in interface MonteCarloSimulationModel

Parameters:

timeIndex - Time index

Returns:

Returns the time for a given time index.

getTimeIndex

public int getTimeIndex(double time)

Description copied from interface: MonteCarloSimulationModel

Returns the time index for a given time.

Specified by:

getTimeIndex in interface MonteCarloSimulationModel

Parameters:

time - The time.

Returns:

Returns the time index for a given time.

getRandomVariableForConstant

public RandomVariable getRandomVariableForConstant(double value)

Description copied from interface: MonteCarloSimulationModel

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 MonteCarloSimulationModel.

Specified by:

getRandomVariableForConstant in interface MonteCarloSimulationModel

Parameters:

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

Returns:

A new random variable.

getMonteCarloWeights

public RandomVariable getMonteCarloWeights(int timeIndex)
                                    throws CalculationException

Description copied from interface: MonteCarloSimulationModel

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

Specified by:

getMonteCarloWeights in interface MonteCarloSimulationModel

Parameters:

timeIndex - Time index at which the process should be observed

Returns:

A vector of positive weights which sums up to one

Throws:

CalculationException - Thrown if the valuation fails, specific cause may be available via the cause() method.