net.finmath.montecarlo.model

Interface AbstractModelInterface

All Known Subinterfaces:

LIBORMarketModelInterface

All Known Implementing Classes:

AbstractModel, LIBORMarketModel, LIBORMarketModelStandard, MonteCarloBlackScholesModel, MonteCarloMultiAssetBlackScholesModel

public interface AbstractModelInterface

The interface for a model of a stochastic process X where X = f(Y) 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().
• The value of μ is provided by the method getDrift(int, net.finmath.stochastic.RandomVariableInterface[], net.finmath.stochastic.RandomVariableInterface[]).
• The value λ_j is provided by the method getFactorLoading(int, int, net.finmath.stochastic.RandomVariableInterface[]).
• The function f is provided by the method applyStateSpaceTransform(int, net.finmath.stochastic.RandomVariableInterface).

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.

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[]	getDrift(int timeIndex, RandomVariableInterface[] realizationAtTimeIndex, RandomVariableInterface[] realizationPredictor) This method has to be implemented to return the drift, i.e.
RandomVariableInterface[]	getFactorLoading(int timeIndex, int componentIndex, 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.
int	getNumberOfComponents() Returns the number of components
int	getNumberOfFactors() Returns the number of factors m, i.e., the number of independent Brownian drivers.
RandomVariableInterface	getNumeraire(double time) Return the numeraire at a given time index.
AbstractProcessInterface	getProcess() Get the numerical scheme used to generate the stochastic process.
TimeDiscretizationInterface	getTimeDiscretization() Returns the time discretization of the model parameters.
void	setProcess(AbstractProcessInterface process) Set the numerical scheme used to generate the stochastic process.

Method Detail

getTimeDiscretization

TimeDiscretizationInterface getTimeDiscretization()

Returns the time discretization of the model parameters. It is not necessary that this time discretization agrees with the discretization of the stochactic process used in Abstract Process implementation.

Returns:

The time discretization

getNumberOfComponents

int getNumberOfComponents()

Returns the number of components

Returns:

The number of components

applyStateSpaceTransform

RandomVariableInterface applyStateSpaceTransform(int componentIndex,
                                                 RandomVariableInterface randomVariable)

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

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.

getInitialState

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.

Returns:

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

getNumeraire

RandomVariableInterface getNumeraire(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:

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

RandomVariableInterface[] getDrift(int timeIndex,
                                   RandomVariableInterface[] realizationAtTimeIndex,
                                   RandomVariableInterface[] 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.

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

getNumberOfFactors

int getNumberOfFactors()

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

Returns:

The number of factors.

getFactorLoading

RandomVariableInterface[] getFactorLoading(int timeIndex,
                                           int componentIndex,
                                           RandomVariableInterface[] 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:

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.

setProcess

void setProcess(AbstractProcessInterface process)

Set the numerical scheme used to generate the stochastic process. The model needs the numerical scheme to calculate, e.g., the numeraire.

Parameters:

process - The process.

getProcess

AbstractProcessInterface getProcess()

Get the numerical scheme used to generate the stochastic process. The model needs the numerical scheme to calculate, e.g., the numeraire.

Returns:

the process