net.finmath.montecarlo.assetderivativevaluation

Class MonteCarloBlackScholesModel

java.lang.Object

net.finmath.montecarlo.assetderivativevaluation.MonteCarloBlackScholesModel

All Implemented Interfaces:

Model, AssetModelMonteCarloSimulationModel, MonteCarloSimulationModel

public class MonteCarloBlackScholesModel
extends Object
implements AssetModelMonteCarloSimulationModel

This class glues together a BlackScholeModel and a Monte-Carlo implementation of a MonteCarloProcessFromProcessModel and forms a Monte-Carlo implementation of the Black-Scholes Model by implementing AssetModelMonteCarloSimulationModel. The model is \[ dS = r S dt + \sigma S dW, \quad S(0) = S_{0}, \] \[ dN = r N dt, \quad N(0) = N_{0}, \] The class provides the model of S to an MonteCarloProcess via the specification of \( f = exp \), \( \mu = r - \frac{1}{2} \sigma^2 \), \( \lambda_{1,1} = \sigma \), i.e., of the SDE \[ dX = \mu dt + \lambda_{1,1} dW, \quad X(0) = \log(S_{0}), \] with \( S = f(X) \). See MonteCarloProcess for the notation.

Version:

1.0

Author:

Christian Fries

See Also:

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

Constructor Summary

Constructors

Constructor and Description
MonteCarloBlackScholesModel(double initialValue, double riskFreeRate, double volatility, MonteCarloProcessFromProcessModel process) Create a Monte-Carlo simulation using given process discretization scheme.
MonteCarloBlackScholesModel(TimeDiscretization timeDiscretization, int numberOfPaths, double initialValue, double riskFreeRate, double volatility) Create a Monte-Carlo simulation using given time discretization.

Method Summary

Modifier and Type	Method and 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.
BlackScholesModel	getModel() Returns the AbstractProcessModel used for this Monte-Carlo simulation.
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

MonteCarloBlackScholesModel

public MonteCarloBlackScholesModel(TimeDiscretization timeDiscretization,
                                   int numberOfPaths,
                                   double initialValue,
                                   double riskFreeRate,
                                   double volatility)

Create a Monte-Carlo simulation using given time discretization.

Parameters:

timeDiscretization - The time discretization.

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

initialValue - Spot value.

riskFreeRate - The risk free rate.

volatility - The log volatility.

MonteCarloBlackScholesModel

public MonteCarloBlackScholesModel(double initialValue,
                                   double riskFreeRate,
                                   double volatility,
                                   MonteCarloProcessFromProcessModel process)

Create a Monte-Carlo simulation using given process discretization scheme.

Parameters:

initialValue - Spot value

riskFreeRate - The risk free rate

volatility - The log volatility

process - The process discretization scheme which should be used for the simulation.

Method Detail

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.

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 \( t = 0 \).

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.

getModel

public BlackScholesModel getModel()

Returns the AbstractProcessModel used for this Monte-Carlo simulation.

Returns:

the model