Module net.finmath.lib

Package net.finmath.montecarlo.assetderivativevaluation

Class MonteCarloMultiAssetBlackScholesModel

java.lang.Object

net.finmath.montecarlo.model.AbstractProcessModel

net.finmath.montecarlo.assetderivativevaluation.MonteCarloMultiAssetBlackScholesModel

All Implemented Interfaces:

Model, AssetModelMonteCarloSimulationModel, ProcessModel, MonteCarloSimulationModel

public class MonteCarloMultiAssetBlackScholesModel
extends AbstractProcessModel
implements AssetModelMonteCarloSimulationModel

This class implements a multi-asset Black Schole Model as Monte-Carlo simulation implementing AssetModelMonteCarloSimulationModel. The model is \[ dS_{i} = r S_{i} dt + \sigma_{i} S_{i} dW_{i}, \quad S_{i}(0) = S_{i,0}, \] \[ dN = r N dt, \quad N(0) = N_{0}, \] \[ dW_{i} dW_{j} = \rho_{i,j} dt, \] The class provides the model of \( S_{i} \) to an MonteCarloProcess via the specification of \( f = exp \), \( \mu_{i} = r - \frac{1}{2} \sigma_{i}^2 \), \( \lambda_{i,j} = \sigma_{i} g_{i,j} \), i.e., of the SDE \[ dX_{i} = \mu_{i} dt + \lambda_{i,j} dW, \quad X_{i}(0) = \log(S_{i,0}), \] with \( S = f(X) \). See MonteCarloProcess for the notation.

Version:

1.1

Author:

Christian Fries, Roland Bachl

See Also:

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

Constructor Summary

Constructors

Constructor	Description
MonteCarloMultiAssetBlackScholesModel(BrownianMotion brownianMotion, double[] initialValues, double riskFreeRate, double[] volatilities, double[][] correlations)	Create a Monte-Carlo simulation using given time discretization.
MonteCarloMultiAssetBlackScholesModel(RandomVariableFactory randomVariableFactory, BrownianMotion brownianMotion, double[] initialValues, double riskFreeRate, double[][] factorLoadings)	Create a Monte-Carlo simulation using given time discretization.
MonteCarloMultiAssetBlackScholesModel(TimeDiscretization timeDiscretization, int numberOfPaths, double[] initialValues, double riskFreeRate, double[] volatilities, double[][] correlations)	Create a Monte-Carlo simulation using given time discretization.
MonteCarloMultiAssetBlackScholesModel(TimeDiscretization timeDiscretization, int numberOfPaths, int seed, double[] initialValues, double riskFreeRate, double[] volatilities, double[][] correlations)	Create a Monte-Carlo simulation using given time discretization.

Method Summary

Modifier and Type	Method	Description
RandomVariable	applyStateSpaceTransform(MonteCarloProcess process, int timeIndex, int componentIndex, RandomVariable randomVariable)	Applies the state space transform fi to the given state random variable such that Yi → fi(Yi) =: Xi.
RandomVariable	applyStateSpaceTransformInverse(MonteCarloProcess process, int timeIndex, int componentIndex, RandomVariable randomVariable)	Applies the inverse state space transform f-1i to the given random variable such that Xi → f-1i(Xi) =: Yi.
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.
MonteCarloMultiAssetBlackScholesModel	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.
double[][]	getCorrelations()	Returns the volatility parameters of this model.
RandomVariable[]	getDrift(MonteCarloProcess process, int timeIndex, RandomVariable[] realizationAtTimeIndex, RandomVariable[] realizationPredictor)	This method has to be implemented to return the drift, i.e.
RandomVariable[]	getFactorLoading(MonteCarloProcess process, int timeIndex, int component, RandomVariable[] realizationAtTimeIndex)	This method has to be implemented to return the factor loadings, i.e.
double[][]	getFactorLoadings()	Returns the factorLoadings parameters of this model.
RandomVariable[]	getInitialState(MonteCarloProcess process)	Returns the initial value of the state variable of the process Y, not to be confused with the initial value of the model X (which is the state space transform applied to this state value.
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	getNumberOfComponents()	Returns the number of components
int	getNumberOfFactors()	Returns the number of factors m, i.e., the number of independent Brownian drivers.
int	getNumberOfPaths()	Returns the number of paths.
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	getNumeraire(MonteCarloProcess process, double time)	Return the numeraire at a given time index.
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.
double	getRiskFreeRate()	Returns the risk free rate parameter of this model.
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.
double[]	getVolatilities()	Returns the volatility parameters of this model.
String	toString()

Methods inherited from class net.finmath.montecarlo.model.AbstractProcessModel

getInitialValue, getReferenceDate

Methods inherited from class java.lang.Object

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

Methods inherited from interface net.finmath.montecarlo.MonteCarloSimulationModel

getReferenceDate

Constructor Detail

MonteCarloMultiAssetBlackScholesModel

public MonteCarloMultiAssetBlackScholesModel(RandomVariableFactory randomVariableFactory,
                                             BrownianMotion brownianMotion,
                                             double[] initialValues,
                                             double riskFreeRate,
                                             double[][] factorLoadings)

Create a Monte-Carlo simulation using given time discretization.

Parameters:

randomVariableFactory - The RandomVariableFactory used to construct model parameters as random variables.

brownianMotion - The Brownian motion to be used for the numerical scheme.

initialValues - Spot values.

riskFreeRate - The risk free rate.

factorLoadings - The matrix of factor loadings, where factorLoadings[underlyingIndex][factorIndex] is the coefficient of the Brownian driver factorIndex used for the underlying underlyingIndex.

MonteCarloMultiAssetBlackScholesModel

public MonteCarloMultiAssetBlackScholesModel(BrownianMotion brownianMotion,
                                             double[] initialValues,
                                             double riskFreeRate,
                                             double[] volatilities,
                                             double[][] correlations)

Create a Monte-Carlo simulation using given time discretization.

Parameters:

brownianMotion - The Brownian motion to be used for the numerical scheme.

initialValues - Spot values.

riskFreeRate - The risk free rate.

volatilities - The log volatilities.

correlations - A correlation matrix.

MonteCarloMultiAssetBlackScholesModel

public MonteCarloMultiAssetBlackScholesModel(TimeDiscretization timeDiscretization,
                                             int numberOfPaths,
                                             double[] initialValues,
                                             double riskFreeRate,
                                             double[] volatilities,
                                             double[][] correlations)

Create a Monte-Carlo simulation using given time discretization.

Parameters:

timeDiscretization - The time discretization.

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

initialValues - Spot values.

riskFreeRate - The risk free rate.

volatilities - The log volatilities.

correlations - A correlation matrix.

MonteCarloMultiAssetBlackScholesModel

public MonteCarloMultiAssetBlackScholesModel(TimeDiscretization timeDiscretization,
                                             int numberOfPaths,
                                             int seed,
                                             double[] initialValues,
                                             double riskFreeRate,
                                             double[] volatilities,
                                             double[][] correlations)

Create a Monte-Carlo simulation using given time discretization.

Parameters:

timeDiscretization - The time discretization.

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

seed - The seed to be used.

initialValues - Spot values.

riskFreeRate - The risk free rate.

volatilities - The log volatilities.

correlations - A correlation matrix.

Method Detail

getInitialState

public RandomVariable[] getInitialState(MonteCarloProcess process)

Description copied from interface: ProcessModel

Returns the initial value of the state variable of the process Y, not to be confused with the initial value of the model X (which is the state space transform applied to this state value.

Specified by:

getInitialState in interface ProcessModel

Parameters:

process - The discretization process generating this model. The process provides call backs for TimeDiscretization and allows calls to getProcessValue for timeIndices less or equal the given one.

Returns:

The initial value of the state variable of the process Y(t=0).

getDrift

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

Description copied from interface: ProcessModel

This method has to be implemented to return the drift, i.e. the coefficient vector
μ = (μ₁, ..., μ_n) such that X = f(Y) and
dY_j = μ_j dt + λ_1,j dW₁ + ... + λ_m,j dW_m
in an m-factor model. Here j denotes index of the component of the resulting process. Since the model is provided only on a time discretization, the method may also (should try to) return the drift as \( \frac{1}{t_{i+1}-t_{i}} \int_{t_{i}}^{t_{i+1}} \mu(\tau) \mathrm{d}\tau \).

Specified by:

getDrift in interface ProcessModel

Parameters:

process - The discretization process generating this model. The process provides call backs for TimeDiscretization and allows calls to getProcessValue for timeIndices less or equal the given one.

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 if no predictor is available.

Returns:

The drift or average drift from timeIndex to timeIndex+1, i.e. \( \frac{1}{t_{i+1}-t_{i}} \int_{t_{i}}^{t_{i+1}} \mu(\tau) \mathrm{d}\tau \) (or a suitable approximation).

getFactorLoading

public RandomVariable[] getFactorLoading(MonteCarloProcess process,
                                         int timeIndex,
                                         int component,
                                         RandomVariable[] realizationAtTimeIndex)

Description copied from interface: ProcessModel

This method has to be implemented to return the factor loadings, i.e. the coefficient vector
λ_j = (λ_1,j, ..., λ_m,j) such that X = f(Y) and
dY_j = μ_j dt + λ_1,j dW₁ + ... + λ_m,j dW_m
in an m-factor model. Here j denotes index of the component of the resulting process.

Specified by:

getFactorLoading in interface ProcessModel

Parameters:

process - The discretization process generating this model. The process provides call backs for TimeDiscretization and allows calls to getProcessValue for timeIndices less or equal the given one.

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

component - The index j of the driven component.

realizationAtTimeIndex - The realization of X at the time corresponding to timeIndex (in order to implement local and stochastic volatlity models).

Returns:

The factor loading for given factor and component.

applyStateSpaceTransform

public RandomVariable applyStateSpaceTransform(MonteCarloProcess process,
                                               int timeIndex,
                                               int componentIndex,
                                               RandomVariable randomVariable)

Description copied from interface: ProcessModel

Applies the state space transform f_i to the given state random variable such that Y_i → f_i(Y_i) =: X_i.

Specified by:

applyStateSpaceTransform in interface ProcessModel

Parameters:

process - The discretization process generating this model. The process provides call backs for TimeDiscretization and allows calls to getProcessValue for timeIndices less or equal the given one.

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

componentIndex - The component index i.

randomVariable - The state random variable Y_i.

Returns:

New random variable holding the result of the state space transformation.

applyStateSpaceTransformInverse

public RandomVariable applyStateSpaceTransformInverse(MonteCarloProcess process,
                                                      int timeIndex,
                                                      int componentIndex,
                                                      RandomVariable randomVariable)

Description copied from interface: ProcessModel

Applies the inverse state space transform f^-1_i to the given random variable such that X_i → f^-1_i(X_i) =: Y_i.

Specified by:

applyStateSpaceTransformInverse in interface ProcessModel

Parameters:

process - The discretization process generating this model. The process provides call backs for TimeDiscretization and allows calls to getProcessValue for timeIndices less or equal the given one.

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

componentIndex - The component index i.

randomVariable - The state random variable X_i.

Returns:

New random variable holding the result of the state space transformation.

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.

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.

getNumeraire

public RandomVariable getNumeraire(MonteCarloProcess process,
                                   double time)

Description copied from interface: ProcessModel

Return the numeraire at a given time index. Note: The random variable returned is a defensive copy and may be modified.

Specified by:

getNumeraire in interface ProcessModel

Parameters:

process - The discretization process generating this model. The process provides call backs for TimeDiscretization and allows calls to getProcessValue for timeIndices less or equal the given one.

time - The time t for which the numeraire N(t) should be returned.

Returns:

The numeraire at the specified time as RandomVariable

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.

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

Specified by:

getRandomVariableForConstant in interface ProcessModel

Parameters:

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

Returns:

A new random variable.

getNumberOfComponents

public int getNumberOfComponents()

Description copied from interface: ProcessModel

Returns the number of components

Specified by:

getNumberOfComponents in interface ProcessModel

Returns:

The number of components

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

toString

public String toString()

Overrides:

toString in class Object

getRiskFreeRate

public double getRiskFreeRate()

Returns the risk free rate parameter of this model.

Returns:

Returns the riskFreeRate.

getFactorLoadings

public double[][] getFactorLoadings()

Returns the factorLoadings parameters of this model.

Returns:

Returns the factorLoadings.

getVolatilities

public double[] getVolatilities()

Returns the volatility parameters of this model.

Returns:

Returns the volatilities.

getCorrelations

public double[][] getCorrelations()

Returns the volatility parameters of this model.

Returns:

Returns the volatilities.

getNumberOfPaths

public int getNumberOfPaths()

Returns the number of paths.

Specified by:

getNumberOfPaths in interface MonteCarloSimulationModel

Returns:

The number of paths.

See Also:

MonteCarloProcess.getNumberOfPaths()

getCloneWithModifiedData

public MonteCarloMultiAssetBlackScholesModel 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

Specified by:

getCloneWithModifiedData in interface ProcessModel

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.

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.

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.

getNumberOfFactors

public int getNumberOfFactors()

Description copied from interface: ProcessModel

Returns the number of factors m, i.e., the number of independent Brownian drivers.

Specified by:

getNumberOfFactors in interface ProcessModel

Returns:

The number of factors.