Module net.finmath.lib

Package net.finmath.montecarlo.model

Interface ProcessModel

All Known Subinterfaces:

LIBORMarketModel, LIBORModel, TermStructureModel

All Known Implementing Classes:

AbstractProcessModel, BachelierModel, BlackScholesModel, BlackScholesModelWithCurves, DisplacedLognomalModel, HestonModel, HullWhiteModel, HullWhiteModelWithConstantCoeff, HullWhiteModelWithDirectSimulation, HullWhiteModelWithShiftExtension, InhomogeneousDisplacedLognomalModel, InhomogenousBachelierModel, LIBORMarketModelFromCovarianceModel, LIBORMarketModelStandard, LIBORMarketModelWithTenorRefinement, MertonModel, MonteCarloMultiAssetBlackScholesModel, MultiAssetBlackScholesModel, VarianceGammaModel

public interface ProcessModel

The interface for a model of a stochastic process X where X(t) = f(t,Y(t)) and
\[ dY_{j} = \mu_{j} dt + \lambda_{1,j} dW_{1} + \ldots + \lambda_{m,j} dW_{m} \]

• The value of Y(0) is provided by the method getInitialState(net.finmath.montecarlo.process.MonteCarloProcess).
• The value of μ is provided by the method getDrift(net.finmath.montecarlo.process.MonteCarloProcess, int, net.finmath.stochastic.RandomVariable[], net.finmath.stochastic.RandomVariable[]).
• The value λ_j is provided by the method getFactorLoading(net.finmath.montecarlo.process.MonteCarloProcess, int, int, net.finmath.stochastic.RandomVariable[]).
• The function f is provided by the method applyStateSpaceTransform(net.finmath.montecarlo.process.MonteCarloProcess, int, int, net.finmath.stochastic.RandomVariable).

Here, μ and λ_j may depend on X, which allows to implement stochastic drifts (like in a LIBOR market model) of local volatility models.
Examples:

• The Black Scholes model can be modeled by S = X = Y (i.e. f is the identity) and μ₁ = r S and λ_1,1 = σ S.
• Alternatively, the Black Scholes model can be modeled by S = X = exp(Y) (i.e. f is exp) and μ₁ = r - 0.5 σ σ and λ_1,1 = σ.

Version:

2.0

Author:

Christian Fries

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.
default 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.
ProcessModel	getCloneWithModifiedData(Map<String,Object> dataModified)	Returns a clone of this model where the specified properties have been modified.
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 componentIndex, RandomVariable[] realizationAtTimeIndex)	This method has to be implemented to return the factor loadings, i.e.
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.
int	getNumberOfComponents()	Returns the number of components
int	getNumberOfFactors()	Returns the number of factors m, i.e., the number of independent Brownian drivers.
RandomVariable	getNumeraire(MonteCarloProcess process, double time)	Return the numeraire at a given time index.
RandomVariable	getRandomVariableForConstant(double value)	Return a random variable initialized with a constant using the models random variable factory.
LocalDateTime	getReferenceDate()	Returns the model's date corresponding to the time discretization's \( t = 0 \).

Method Detail

getReferenceDate

LocalDateTime getReferenceDate()

Returns the model's date corresponding to the time discretization's \( t = 0 \). Note: Currently not all models provide a reference date. This will change in future versions.

Returns:

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

getNumberOfComponents

int getNumberOfComponents()

Returns the number of components

Returns:

The number of components

applyStateSpaceTransform

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

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

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

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

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.

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.

getInitialState

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.

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).

getNumeraire

RandomVariable getNumeraire(MonteCarloProcess process,
                            double time)
                     throws CalculationException

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

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

Throws:

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

getDrift

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

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 \( \frac{1}{t_{i+1}-t_{i}} \int_{t_{i}}^{t_{i+1}} \mu(\tau) \mathrm{d}\tau \).

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).

getNumberOfFactors

int getNumberOfFactors()

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

Returns:

The number of factors.

getFactorLoading

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

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.

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 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.

getRandomVariableForConstant

RandomVariable getRandomVariableForConstant(double value)

Return a random variable initialized with a constant using the models random variable factory.

Parameters:

value - The constant value.

Returns:

A new random variable initialized with a constant value.

getCloneWithModifiedData

ProcessModel getCloneWithModifiedData(Map<String,Object> dataModified)
                               throws CalculationException

Returns a clone of this model where the specified properties have been modified. Note that there is no guarantee that a model reacts on a specification of a properties in the parameter map dataModified. If data is provided which is ignored by the model no exception may be thrown.

Parameters:

dataModified - Key-value-map of parameters to modify.

Returns:

A clone of this model (or this model if no parameter was modified).

Throws:

CalculationException - Thrown when the model could not be created.