net.finmath.montecarlo.assetderivativevaluation

Class MonteCarloBlackScholesModel

java.lang.Object

net.finmath.montecarlo.model.AbstractModel

net.finmath.montecarlo.assetderivativevaluation.MonteCarloBlackScholesModel

All Implemented Interfaces:

AssetModelMonteCarloSimulationInterface, AbstractModelInterface, MonteCarloSimulationInterface

public class MonteCarloBlackScholesModel
extends AbstractModel
implements AssetModelMonteCarloSimulationInterface

This class glues together a BlackScholeModel and a Monte-Carlo implementation of a AbstractProcess and forms a Monte-Carlo implementation of the Black-Scholes Model by implementing AssetModelMonteCarloSimulationInterface. 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 AbstractProcessInterface 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 AbstractProcessInterface for the notation.

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, AbstractProcess process) Create a Monte-Carlo simulation using given process discretization scheme.
MonteCarloBlackScholesModel(TimeDiscretizationInterface 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
RandomVariableInterface	applyStateSpaceTransform(int componentIndex, RandomVariableInterface randomVariable) Applied the state space transform fi to the given state random variable such that Yi → fi(Yi) =: Xi.
RandomVariableInterface	getAssetValue(double time, int assetIndex) Returns the random variable representing the asset's value at a given time for a given asset.
RandomVariableInterface	getAssetValue(int timeIndex, int assetIndex) Returns the random variable representing the asset's value at a given time for a given asset.
AssetModelMonteCarloSimulationInterface	getCloneWithModifiedData(java.util.Map<java.lang.String,java.lang.Object> dataModified) Create a clone of this simulation modifying some of its properties (if any).
AssetModelMonteCarloSimulationInterface	getCloneWithModifiedSeed(int seed) Create a clone of the object implementing AssetModelMonteCarloSimulationInterface using a different Monte-Carlo seed.
RandomVariableInterface[]	getDrift(int timeIndex, RandomVariableInterface[] realizationAtTimeIndex, RandomVariableInterface[] realizationPredictor) This method has to be implemented to return the drift, i.e.
RandomVariableInterface[]	getFactorLoading(int timeIndex, int component, RandomVariableInterface[] realizationAtTimeIndex) This method has to be implemented to return the factor loadings, i.e.
RandomVariableInterface[]	getInitialState() 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.
RandomVariableInterface	getMonteCarloWeights(double time) 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	getNumberOfPaths() Returns the numberOfPaths.
RandomVariableInterface	getNumeraire(double time) Returns the numeraire associated with the valuation measure used by this model.
RandomVariableInterface	getNumeraire(int timeIndex) Returns the numeraire associated with the valuation measure used by this model.
RandomVariableInterface	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 MonteCarloSimulationInterface.
double	getRiskFreeRate() Returns the risk free rate parameter of this model.
double	getVolatility() Returns the volatility parameter of this model.
java.lang.String	toString()

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

getInitialValue, getMonteCarloWeights, getNumberOfFactors, getProcess, getProcessValue, getTime, getTimeDiscretization, getTimeIndex, setProcess

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface net.finmath.montecarlo.MonteCarloSimulationInterface

getMonteCarloWeights, getTime, getTimeDiscretization, getTimeIndex

Constructor Detail

MonteCarloBlackScholesModel

public MonteCarloBlackScholesModel(TimeDiscretizationInterface 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,
                                   AbstractProcess 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

getInitialState

public RandomVariableInterface[] getInitialState()

Description copied from interface: AbstractModelInterface

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 AbstractModelInterface

Returns:

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

getDrift

public RandomVariableInterface[] getDrift(int timeIndex,
                                          RandomVariableInterface[] realizationAtTimeIndex,
                                          RandomVariableInterface[] realizationPredictor)

Description copied from interface: AbstractModelInterface

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.

Specified by:

getDrift in interface AbstractModelInterface

Parameters:

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 of no predictor is available.

Returns:

The (average) drift from timeIndex to timeIndex+1

getFactorLoading

public RandomVariableInterface[] getFactorLoading(int timeIndex,
                                                  int component,
                                                  RandomVariableInterface[] realizationAtTimeIndex)

Description copied from interface: AbstractModelInterface

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 AbstractModelInterface

Parameters:

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 RandomVariableInterface applyStateSpaceTransform(int componentIndex,
                                                        RandomVariableInterface randomVariable)

Description copied from interface: AbstractModelInterface

Applied 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 AbstractModelInterface

Parameters:

componentIndex - The component index i.

randomVariable - The state random variable Y_i.

Returns:

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

getAssetValue

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

Description copied from interface: AssetModelMonteCarloSimulationInterface

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

Specified by:

getAssetValue in interface AssetModelMonteCarloSimulationInterface

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 RandomVariableInterface getAssetValue(int timeIndex,
                                             int assetIndex)
                                      throws CalculationException

Description copied from interface: AssetModelMonteCarloSimulationInterface

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

Specified by:

getAssetValue in interface AssetModelMonteCarloSimulationInterface

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 RandomVariableInterface getMonteCarloWeights(double time)
                                             throws CalculationException

Description copied from interface: MonteCarloSimulationInterface

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

Specified by:

getMonteCarloWeights in interface MonteCarloSimulationInterface

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 RandomVariableInterface getNumeraire(int timeIndex)

Description copied from interface: AssetModelMonteCarloSimulationInterface

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

Specified by:

getNumeraire in interface AssetModelMonteCarloSimulationInterface

Parameters:

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

Returns:

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

getNumeraire

public RandomVariableInterface getNumeraire(double time)

Description copied from interface: AssetModelMonteCarloSimulationInterface

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

Specified by:

getNumeraire in interface AssetModelMonteCarloSimulationInterface

Specified by:

getNumeraire in interface AbstractModelInterface

Parameters:

time - The time for which the numeraire is requested.

Returns:

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

getRandomVariableForConstant

public RandomVariableInterface getRandomVariableForConstant(double value)

Description copied from interface: MonteCarloSimulationInterface

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 MonteCarloSimulationInterface.

Specified by:

getRandomVariableForConstant in interface MonteCarloSimulationInterface

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: AbstractModelInterface

Returns the number of components

Specified by:

getNumberOfComponents in interface AbstractModelInterface

Returns:

The number of components

getNumberOfAssets

public int getNumberOfAssets()

Description copied from interface: AssetModelMonteCarloSimulationInterface

Returns the number of asset price processes.

Specified by:

getNumberOfAssets in interface AssetModelMonteCarloSimulationInterface

Returns:

The number of asset price processes

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object

getRiskFreeRate

public double getRiskFreeRate()

Returns the risk free rate parameter of this model.

Returns:

Returns the riskFreeRate.

getVolatility

public double getVolatility()

Returns the volatility parameter of this model.

Returns:

Returns the volatility.

getCloneWithModifiedData

public AssetModelMonteCarloSimulationInterface getCloneWithModifiedData(java.util.Map<java.lang.String,java.lang.Object> dataModified)

Description copied from interface: AssetModelMonteCarloSimulationInterface

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

Specified by:

getCloneWithModifiedData in interface AssetModelMonteCarloSimulationInterface

Specified by:

getCloneWithModifiedData in interface MonteCarloSimulationInterface

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 AssetModelMonteCarloSimulationInterface getCloneWithModifiedSeed(int seed)

Description copied from interface: AssetModelMonteCarloSimulationInterface

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

Specified by:

getCloneWithModifiedSeed in interface AssetModelMonteCarloSimulationInterface

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: MonteCarloSimulationInterface

Returns the numberOfPaths.

Specified by:

getNumberOfPaths in interface MonteCarloSimulationInterface

Returns:

The number of paths.

See Also:

AbstractProcessInterface.getNumberOfPaths()