Module net.finmath.lib

Package net.finmath.montecarlo.interestrate.models

Class LIBORMarketModelStandard

java.lang.Object

net.finmath.montecarlo.model.AbstractProcessModel

net.finmath.montecarlo.interestrate.models.LIBORMarketModelStandard

All Implemented Interfaces:

IndependentModelParameterProvider, LIBORMarketModel, LIBORModel, TermStructureModel, ProcessModel

public class LIBORMarketModelStandard
extends AbstractProcessModel
implements LIBORMarketModel

Implements a basic LIBOR market model with some drift approximation methods.
The class implements different measure(drift) / numeraire pairs (terminal and spot).
The class specifies a LIBOR market model in its log-normal formulation, that is L_j = exp(Y_j) where
dY_j = μ_j dt + λ_1,j dW₁ + ... + λ_m,j dW_m
see ProcessModel for details on the implemented interface.
The model uses an AbstractLIBORCovarianceModel for the specification of (λ_1,j,...,λ_m,j) as a covariance model, which may have the ability to calibrate to swaptions.

Version:

1.1

Author:

Christian Fries

See Also:

• AbstractLIBORCovarianceModel

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static enum	LIBORMarketModelStandard.Driftapproximation
static enum	LIBORMarketModelStandard.Measure

Constructor Summary

Constructors

Constructor	Description
LIBORMarketModelStandard(TimeDiscretization liborPeriodDiscretization, ForwardCurve forwardRateCurve, DiscountCurve discountCurve, LIBORCovarianceModel covarianceModel)	Creates a LIBOR Market Model for given covariance.
LIBORMarketModelStandard(TimeDiscretization liborPeriodDiscretization, ForwardCurve forwardRateCurve, DiscountCurve discountCurve, LIBORCovarianceModel covarianceModel, SwaptionMarketData swaptionMarketData)	Creates a LIBOR Market Model for given covariance.
LIBORMarketModelStandard(TimeDiscretization liborPeriodDiscretization, ForwardCurve forwardRateCurve, DiscountCurve discountCurve, LIBORCovarianceModel covarianceModel, CalibrationProduct[] calibrationProducts)	Creates a LIBOR Market Model for given covariance.
LIBORMarketModelStandard(TimeDiscretization liborPeriodDiscretization, ForwardCurve forwardRateCurve, LIBORCovarianceModel covarianceModel)	Creates a LIBOR Market Model for given covariance.
LIBORMarketModelStandard(TimeDiscretization liborPeriodDiscretization, ForwardCurve forwardRateCurve, LIBORCovarianceModel covarianceModel, SwaptionMarketData swaptionMarketData)	Creates a LIBOR Market Model using a given covariance model and calibrating this model to given swaption volatility data.

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.
Object	clone()
AnalyticModel	getAnalyticModel()	Return the associated analytic model, a collection of market date object like discount curve, forward curve and volatility surfaces.
LIBORMarketModelStandard	getCloneWithModifiedCovarianceModel(LIBORCovarianceModel covarianceModel)	Create a new object implementing LIBORMarketModel, using the new covariance model.
LIBORMarketModelStandard	getCloneWithModifiedData(Map<String,Object> dataModified)	Create a new object implementing LIBORModel, using the new data.
LIBORCovarianceModel	getCovarianceModel()	Return the forward rate (LIBOR) covariance model.
DiscountCurve	getDiscountCurve()	Return the discount curve associated the forwards.
RandomVariable[]	getDrift(MonteCarloProcess process, int timeIndex, RandomVariable[] realizationAtTimeIndex, RandomVariable[] realizationPredictor)	Return the complete vector of the drift for the time index timeIndex, given that current state is realizationAtTimeIndex.
LIBORMarketModelStandard.Driftapproximation	getDriftApproximationMethod()
protected RandomVariable	getDriftEuler(MonteCarloProcess process, int timeIndex, int componentIndex, RandomVariable[] liborVectorStart)
RandomVariable[]	getFactorLoading(MonteCarloProcess process, int timeIndex, int componentIndex, RandomVariable[] realizationAtTimeIndex)	This method has to be implemented to return the factor loadings, i.e.
RandomVariable	getForwardRate(MonteCarloProcess process, double time, double periodStart, double periodEnd)	Returns the time \( t \) forward rate on the models forward curve.
ForwardCurve	getForwardRateCurve()	Return the initial forward rate curve.
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.
double[][][]	getIntegratedLIBORCovariance(TimeDiscretization simulationTimeDiscretization)	Returns the integrated instantaneous log-forward rate covariance, i.e., \( \int_{0}^{t_i} \mathrm{d} \log(L_{j}) \mathrm{d} \log(L_{k}) \mathrm{d}t \).
RandomVariable	getLIBOR(MonteCarloProcess process, int timeIndex, int liborIndex)	Return the forward rate at a given timeIndex and for a given liborIndex.
double	getLiborPeriod(int timeIndex)	The period start corresponding to a given forward rate discretization index.
TimeDiscretization	getLiborPeriodDiscretization()	The tenor time discretization of the forward rate curve.
int	getLiborPeriodIndex(double time)	Same as java.util.Arrays.binarySearch(liborPeriodDiscretization,time).
LIBORMarketModelStandard.Measure	getMeasure()
Map<String,RandomVariable>	getModelParameters()	Returns a map of independent model parameters of this model.
int	getNumberOfComponents()	This method is just a synonym to getNumberOfLibors
int	getNumberOfFactors()	Returns the number of factors m, i.e., the number of independent Brownian drivers.
int	getNumberOfLibors()	Get the number of LIBORs in the LIBOR discretization.
RandomVariable	getNumeraire(MonteCarloProcess process, double time)	Return the numeraire at a given time.
RandomVariable	getRandomVariableForConstant(double value)	Return a random variable initialized with a constant using the models random variable factory.
SwaptionMarketData	getSwaptionMarketData()	Return the swaption market data used for calibration (if any, may be null).
void	setDriftApproximationMethod(LIBORMarketModelStandard.Driftapproximation driftApproximationMethod)
void	setMeasure(LIBORMarketModelStandard.Measure measure)

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

getInitialValue, getReferenceDate

Methods inherited from class java.lang.Object

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

Methods inherited from interface net.finmath.montecarlo.model.ProcessModel

getReferenceDate

Methods inherited from interface net.finmath.montecarlo.interestrate.TermStructureModel

getForwardDiscountBond, getLIBOR

Constructor Details

LIBORMarketModelStandard

public LIBORMarketModelStandard(TimeDiscretization liborPeriodDiscretization,
 ForwardCurve forwardRateCurve,
 LIBORCovarianceModel covarianceModel)

Creates a LIBOR Market Model for given covariance.

Parameters:

liborPeriodDiscretization - The discretization of the interest rate curve into forward rates (tenor structure).

forwardRateCurve - The initial values for the forward rates.

covarianceModel - The covariance model to use.

LIBORMarketModelStandard

public LIBORMarketModelStandard(TimeDiscretization liborPeriodDiscretization,
 ForwardCurve forwardRateCurve,
 DiscountCurve discountCurve,
 LIBORCovarianceModel covarianceModel)

Creates a LIBOR Market Model for given covariance.

Parameters:

liborPeriodDiscretization - The discretization of the interest rate curve into forward rates (tenor structure).

forwardRateCurve - The initial values for the forward rates.

discountCurve - The discount curve to use. This will create an LMM model with a deterministic zero-spread discounting adjustment.

covarianceModel - The covariance model to use.

LIBORMarketModelStandard

public LIBORMarketModelStandard(TimeDiscretization liborPeriodDiscretization,
 ForwardCurve forwardRateCurve,
 LIBORCovarianceModel covarianceModel,
 SwaptionMarketData swaptionMarketData)
                         throws CalculationException

Creates a LIBOR Market Model using a given covariance model and calibrating this model to given swaption volatility data.

Parameters:

liborPeriodDiscretization - The discretization of the interest rate curve into forward rates (tenor structure).

forwardRateCurve - The initial values for the forward rates.

covarianceModel - The covariance model to use.

swaptionMarketData - The set of swaption values to calibrate to.

Throws:

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

LIBORMarketModelStandard

public LIBORMarketModelStandard(TimeDiscretization liborPeriodDiscretization,
 ForwardCurve forwardRateCurve,
 DiscountCurve discountCurve,
 LIBORCovarianceModel covarianceModel,
 SwaptionMarketData swaptionMarketData)
                         throws CalculationException

Creates a LIBOR Market Model for given covariance.

Parameters:

liborPeriodDiscretization - The discretization of the interest rate curve into forward rates (tenor structure).

forwardRateCurve - The initial values for the forward rates.

discountCurve - The discount curve to use. This will create an LMM model with a deterministic zero-spread discounting adjustment.

covarianceModel - The covariance model to use.

swaptionMarketData - The set of swaption values to calibrate to.

Throws:

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

LIBORMarketModelStandard

public LIBORMarketModelStandard(TimeDiscretization liborPeriodDiscretization,
 ForwardCurve forwardRateCurve,
 DiscountCurve discountCurve,
 LIBORCovarianceModel covarianceModel,
 CalibrationProduct[] calibrationProducts)
                         throws CalculationException

Creates a LIBOR Market Model for given covariance.

Parameters:

liborPeriodDiscretization - The discretization of the interest rate curve into forward rates (tenor structure).

forwardRateCurve - The initial values for the forward rates.

discountCurve - The discount curve to use. This will create an LMM model with a deterministic zero-spread discounting adjustment.

covarianceModel - The covariance model to use.

calibrationProducts - The vector of calibration items (a union of a product, target value and weight) for the objective function sum weight(i) * (modelValue(i)-targetValue(i).

Throws:

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

Method Details

getNumeraire

public RandomVariable getNumeraire(MonteCarloProcess process,
 double time)
                            throws CalculationException

Return the numeraire at a given time. The numeraire is provided for interpolated points. If requested on points which are not part of the tenor discretization, the numeraire uses a linear interpolation of the reciprocal value. See ISBN 0470047224 for details.

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

Returns:

The numeraire at the specified time as RandomVariableFromDoubleArray

Throws:

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

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)

Return the complete vector of the drift for the time index timeIndex, given that current state is realizationAtTimeIndex. Note: The random variable returned is a defensive copy and may be modified. The drift will be zero for rates being already fixed.

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 - Time index i for which the drift should be returned μ(t_i).

realizationAtTimeIndex - Time current forward rate vector at time index i which should be used in the calculation.

realizationPredictor - The given realization at timeIndex+1 or null if no predictor is available.

Returns:

The drift vector μ(t_i) as RandomVariableFromDoubleArray[]

See Also:

• The calculation of the drift is consistent with the calculation of the numeraire in getNumeraire.

getFactorLoading

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

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.

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.

getRandomVariableForConstant

public RandomVariable getRandomVariableForConstant(double value)

Description copied from interface: ProcessModel

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

Specified by:

getRandomVariableForConstant in interface ProcessModel

Parameters:

value - The constant value.

Returns:

A new random variable initialized with a constant value.

getDriftApproximationMethod

public LIBORMarketModelStandard.Driftapproximation getDriftApproximationMethod()

Returns:

Returns the driftApproximationMethod.

getForwardRate

public RandomVariable getForwardRate(MonteCarloProcess process,
 double time,
 double periodStart,
 double periodEnd)
                              throws CalculationException

Description copied from interface: TermStructureModel

Returns the time \( t \) forward rate on the models forward curve. Note: It is guaranteed that the random variable returned by this method is \( \mathcal{F}_{t} ) \)-measurable.

Specified by:

getForwardRate in interface TermStructureModel

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 evaluation time.

periodStart - The period start of the forward rate.

periodEnd - The period end of the forward rate.

Returns:

The forward rate.

Throws:

CalculationException - Thrown if model fails to calculate the random variable.

getLIBOR

public RandomVariable getLIBOR(MonteCarloProcess process,
 int timeIndex,
 int liborIndex)
                        throws CalculationException

Description copied from interface: LIBORModel

Return the forward rate at a given timeIndex and for a given liborIndex.

Specified by:

getLIBOR in interface LIBORModel

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 (associated with Process.getTimeDiscretization().

liborIndex - The forward rate index (associated with LIBORModel.getLiborPeriodDiscretization().

Returns:

The forward rate.

Throws:

CalculationException - Thrown if calculation failed.

getNumberOfComponents

public int getNumberOfComponents()

This method is just a synonym to getNumberOfLibors

Specified by:

getNumberOfComponents in interface ProcessModel

Returns:

The number of components

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.

getNumberOfLibors

public int getNumberOfLibors()

Description copied from interface: LIBORModel

Get the number of LIBORs in the LIBOR discretization.

Specified by:

getNumberOfLibors in interface LIBORModel

Returns:

The number of LIBORs in the LIBOR discretization

getLiborPeriod

public double getLiborPeriod(int timeIndex)

Description copied from interface: LIBORModel

The period start corresponding to a given forward rate discretization index.

Specified by:

getLiborPeriod in interface LIBORModel

Parameters:

timeIndex - The index corresponding to a given time (interpretation is start of period)

Returns:

The period start corresponding to a given forward rate discretization index.

getLiborPeriodIndex

public int getLiborPeriodIndex(double time)

Description copied from interface: LIBORModel

Same as java.util.Arrays.binarySearch(liborPeriodDiscretization,time). Will return a negative value if the time is not found, but then -index-1 corresponds to the index of the smallest time greater than the given one.

Specified by:

getLiborPeriodIndex in interface LIBORModel

Parameters:

time - The period start.

Returns:

The index corresponding to a given time (interpretation is start of period)

getLiborPeriodDiscretization

public TimeDiscretization getLiborPeriodDiscretization()

Description copied from interface: LIBORModel

The tenor time discretization of the forward rate curve.

Specified by:

getLiborPeriodDiscretization in interface LIBORModel

Returns:

The tenor time discretization of the forward rate curve.

getDriftEuler

protected RandomVariable getDriftEuler(MonteCarloProcess process,
 int timeIndex,
 int componentIndex,
 RandomVariable[] liborVectorStart)

getMeasure

public LIBORMarketModelStandard.Measure getMeasure()

Returns:

Returns the measure.

getIntegratedLIBORCovariance

public double[][][] getIntegratedLIBORCovariance(TimeDiscretization simulationTimeDiscretization)

Description copied from interface: LIBORMarketModel

Returns the integrated instantaneous log-forward rate covariance, i.e., \( \int_{0}^{t_i} \mathrm{d} \log(L_{j}) \mathrm{d} \log(L_{k}) \mathrm{d}t \). The array returned has the parametrization [i][j][k], i.e., integratedLIBORCovariance[timeIndex][componentIndex1][componentIndex2].

Specified by:

getIntegratedLIBORCovariance in interface LIBORMarketModel

Parameters:

simulationTimeDiscretization - The timeDiscretization used for the integration.

Returns:

The integrated instantaneous log-LIBOR covariance.

clone

public Object clone()

Overrides:

clone in class Object

setDriftApproximationMethod

public void setDriftApproximationMethod(LIBORMarketModelStandard.Driftapproximation driftApproximationMethod)

Parameters:

driftApproximationMethod - The driftApproximationMethod to set.

setMeasure

public void setMeasure(LIBORMarketModelStandard.Measure measure)

Parameters:

measure - The measure to set.

getAnalyticModel

public AnalyticModel getAnalyticModel()

Description copied from interface: TermStructureModel

Return the associated analytic model, a collection of market date object like discount curve, forward curve and volatility surfaces.

Specified by:

getAnalyticModel in interface TermStructureModel

Returns:

The associated analytic model.

getDiscountCurve

public DiscountCurve getDiscountCurve()

Description copied from interface: TermStructureModel

Return the discount curve associated the forwards.

Specified by:

getDiscountCurve in interface TermStructureModel

Returns:

the discount curve associated the forwards.

getForwardRateCurve

public ForwardCurve getForwardRateCurve()

Description copied from interface: TermStructureModel

Return the initial forward rate curve.

Specified by:

getForwardRateCurve in interface TermStructureModel

Returns:

the forward rate curve

getSwaptionMarketData

public SwaptionMarketData getSwaptionMarketData()

Return the swaption market data used for calibration (if any, may be null).

Returns:

The swaption market data used for calibration (if any, may be null).

getCovarianceModel

public LIBORCovarianceModel getCovarianceModel()

Description copied from interface: LIBORMarketModel

Return the forward rate (LIBOR) covariance model.

Specified by:

getCovarianceModel in interface LIBORMarketModel

Returns:

The covariance model.

getCloneWithModifiedCovarianceModel

public LIBORMarketModelStandard getCloneWithModifiedCovarianceModel(LIBORCovarianceModel covarianceModel)

Description copied from interface: LIBORMarketModel

Create a new object implementing LIBORMarketModel, using the new covariance model.

Specified by:

getCloneWithModifiedCovarianceModel in interface LIBORMarketModel

Parameters:

covarianceModel - A covariance model

Returns:

A new LIBORMarketModelStandard using the specified covariance model.

getCloneWithModifiedData

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

Description copied from interface: LIBORModel

Create a new object implementing LIBORModel, using the new data.

Specified by:

getCloneWithModifiedData in interface LIBORModel

Specified by:

getCloneWithModifiedData in interface ProcessModel

Specified by:

getCloneWithModifiedData in interface TermStructureModel

Parameters:

dataModified - A map with values to be used in constructions (keys are identical to parameter names of the constructors).

Returns:

A new object implementing LIBORModel, using the new data.

Throws:

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

getModelParameters

public Map<String,RandomVariable> getModelParameters()

Description copied from interface: IndependentModelParameterProvider

Returns a map of independent model parameters of this model.

Specified by:

getModelParameters in interface IndependentModelParameterProvider

Returns:

Map of independent model parameters of this model.