net.finmath.montecarlo.interestrate.models

Class LIBORMarketModelFromCovarianceModel

java.lang.Object

net.finmath.montecarlo.model.AbstractProcessModel

net.finmath.montecarlo.interestrate.models.LIBORMarketModelFromCovarianceModel

All Implemented Interfaces:

Serializable, IndependentModelParameterProvider, LIBORMarketModel, LIBORModel, TermStructureModel, ProcessModel

public class LIBORMarketModelFromCovarianceModel
extends AbstractProcessModel
implements LIBORMarketModel, Serializable

Implements a (generalized) LIBOR market model with generic covariance structure (lognormal, normal, displaced or stochastic volatility) with some drift approximation methods.

In its default case the class specifies a multi-factor LIBOR market model in its log-normal formulation, that is L_j = exp(Y_j) where \[ dY_{j} = \mu_{j} dt + \lambda_{1,j} dW_{1} + \ldots + \lambda_{m,j} dW_{m} \]
The model uses an LIBORCovarianceModel for the specification of (λ_1,j,...,λ_m,j) as a covariance model. See ProcessModel for details on the implemented interface

However, the class is more general:

• The model may be log-normal or normal specification with a given local volatility.
• The class implements different measure(drift) / numeraire pairs: terminal measure and spot measure.
• The class allows to configure a discounting curve (e.g. for "OIS discounting") using a simple deterministic zero spread. In this case, the numeraire \( N(t) \) is adjusted by \( \exp( \int_0^t -\lambda(\tau) d\tau ) \).

The class specifies a LIBOR market model, that is L_j = f(Y_j) where

• f is f(x) = exp(x) (default, log-normal LIBOR Market Model) or
• f is f(x) = x (normal model, used if property.set("stateSpace","NORMAL"))

and
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 as a covariance model. If the covariance model is of type AbstractLIBORCovarianceModelParametric a calibration to swaptions can be performed.
Note that λ may still depend on L, hence generating a log-normal dynamic for L even if the stateSpace property has been set to NORMAL.
The map properties allows to configure the model. The following keys may be used:

• measure: Possible values:
  • SPOT: Simulate under spot measure. In this case, the single curve numeraire is \( N(T_{i}) = \prod_{j=0}^{i-1} (1 + L(T_{j},T_{j+1};T_{j}) (T_{j+1}-T_{j})) \).
  • TERMINAL: Simulate under terminal measure. In this case, the single curve numeraire is \( N(T_{i}) = P(T_{n};T_{i}) = \prod_{j=i}^{n-1} (1 + L(T_{j},T_{j+1};T_{i}) (T_{j+1}-T_{j}))^{-1} \).
• stateSpace: Possible values:
  • LOGNORMAL: The state space transform is set to exp, i.e., L = exp(Y). When the covariance model is deterministic, then this is the classical lognormal LIBOR market model. Note that the covariance model may still provide a local volatility function.
  • NORMAL: The state space transform is set to identity, i.e., L = Y. When the covariance model is deterministic, then this is a normal LIBOR market model. Note that the covariance model may still provide a local volatility function.
• liborCap: An optional Double value applied as a cap to the LIBOR rates. May be used to limit the simulated valued to prevent values attaining POSITIVE_INFINITY and numerical problems. To disable the cap, set liborCap to Double.POSITIVE_INFINITY.

The main task of this class is to calculate the risk-neutral drift and the corresponding numeraire given the covariance model. The calibration of the covariance structure is not part of this class. For the calibration of parametric models of the instantaneous covariance see AbstractLIBORCovarianceModelParametric.getCloneCalibrated(LIBORMarketModel, CalibrationProduct[], Map).

Version:

1.2

Author:

Christian Fries

See Also:

The interface for numerical schemes., The interface for models provinding parameters to numerical schemes., The abstract covariance model plug ins., A parametic covariance model including a generic calibration algorithm., Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	LIBORMarketModelFromCovarianceModel.Driftapproximation
static class	LIBORMarketModelFromCovarianceModel.InterpolationMethod
static class	LIBORMarketModelFromCovarianceModel.Measure
static class	LIBORMarketModelFromCovarianceModel.StateSpace

Constructor Summary

Constructors

Constructor and Description
LIBORMarketModelFromCovarianceModel(TimeDiscretization liborPeriodDiscretization, AnalyticModel analyticModel, ForwardCurve forwardRateCurve, DiscountCurve discountCurve, AbstractRandomVariableFactory randomVariableFactory, LIBORCovarianceModel covarianceModel, CalibrationProduct[] calibrationProducts, Map<String,?> properties) Deprecated. Use LIBORMarketModelFromCovarianceModel.of() instead.
LIBORMarketModelFromCovarianceModel(TimeDiscretization liborPeriodDiscretization, AnalyticModel analyticModel, ForwardCurve forwardRateCurve, DiscountCurve discountCurve, AbstractRandomVariableFactory randomVariableFactory, LIBORCovarianceModel covarianceModel, Map<String,?> properties) Creates a LIBOR Market Model for given covariance.
LIBORMarketModelFromCovarianceModel(TimeDiscretization liborPeriodDiscretization, AnalyticModel analyticModel, ForwardCurve forwardRateCurve, DiscountCurve discountCurve, LIBORCovarianceModel covarianceModel, CalibrationProduct[] calibrationItems, Map<String,?> properties) Deprecated. Use LIBORMarketModelFromCovarianceModel.of() instead.
LIBORMarketModelFromCovarianceModel(TimeDiscretization liborPeriodDiscretization, ForwardCurve forwardRateCurve, DiscountCurve discountCurve, LIBORCovarianceModel covarianceModel) Creates a LIBOR Market Model for given covariance.
LIBORMarketModelFromCovarianceModel(TimeDiscretization liborPeriodDiscretization, ForwardCurve forwardRateCurve, DiscountCurve discountCurve, LIBORCovarianceModel covarianceModel, AbstractSwaptionMarketData swaptionMarketData) Creates a LIBOR Market Model for given covariance.
LIBORMarketModelFromCovarianceModel(TimeDiscretization liborPeriodDiscretization, ForwardCurve forwardRateCurve, DiscountCurve discountCurve, LIBORCovarianceModel covarianceModel, AbstractSwaptionMarketData swaptionMarketData, Map<String,?> properties) Creates a LIBOR Market Model for given covariance.
LIBORMarketModelFromCovarianceModel(TimeDiscretization liborPeriodDiscretization, ForwardCurve forwardRateCurve, DiscountCurve discountCurve, LIBORCovarianceModel covarianceModel, CalibrationProduct[] calibrationItems, Map<String,?> properties) Deprecated. Use LIBORMarketModelFromCovarianceModel.of() instead.
LIBORMarketModelFromCovarianceModel(TimeDiscretization liborPeriodDiscretization, ForwardCurve forwardRateCurve, LIBORCovarianceModel covarianceModel) Creates a LIBOR Market Model for given covariance.
LIBORMarketModelFromCovarianceModel(TimeDiscretization liborPeriodDiscretization, ForwardCurve forwardRateCurve, LIBORCovarianceModel covarianceModel, AbstractSwaptionMarketData 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 and Description
RandomVariable	applyStateSpaceTransform(int componentIndex, RandomVariable randomVariable) Applies the state space transform fi to the given state random variable such that Yi → fi(Yi) =: Xi.
RandomVariable	applyStateSpaceTransformInverse(int componentIndex, RandomVariable randomVariable)
Object	clone()
AnalyticModel	getAnalyticModel() Return the associated analytic model, a collection of market date object like discount curve, forward curve and volatility surfaces.
LIBORMarketModelFromCovarianceModel	getCloneWithModifiedCovarianceModel(LIBORCovarianceModel covarianceModel) Create a new object implementing LIBORMarketModel, using the new covariance model.
LIBORMarketModelFromCovarianceModel	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(int timeIndex, RandomVariable[] realizationAtTimeIndex, RandomVariable[] realizationPredictor) Return the complete vector of the drift for the time index timeIndex, given that current state is realizationAtTimeIndex.
LIBORMarketModelFromCovarianceModel.Driftapproximation	getDriftApproximationMethod()
RandomVariable[]	getFactorLoading(int timeIndex, int componentIndex, RandomVariable[] realizationAtTimeIndex) This method has to be implemented to return the factor loadings, i.e.
RandomVariable	getForwardDiscountBond(double time, double maturity) Returns the time \( t \) forward bond derived from the numeraire, i.e., \( P(T;t) = E( \frac{N(t)}{N(T)} \vert \mathcal{F}_{t} ) \).
ForwardCurve	getForwardRateCurve() Return the initial forward rate curve.
RandomVariable[]	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.
double[][][]	getIntegratedLIBORCovariance() Returns the integrated instantaneous log-forward rate covariance, i.e., \( \int_{0}^{t_i} \mathrm{d} \log(L_{j}) \mathrm{d} \log(L_{k}) \mathrm{d}t \).
LIBORMarketModelFromCovarianceModel.InterpolationMethod	getInterpolationMethod()
RandomVariable	getLIBOR(double time, double periodStart, double periodEnd) Returns the time \( t \) forward rate on the models forward curve.
RandomVariable	getLIBOR(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).
LIBORMarketModelFromCovarianceModel.Measure	getMeasure()
Map<String,RandomVariable>	getModelParameters() Returns a map of independent model parameters of this model.
int	getNumberOfComponents() Returns the number of components
int	getNumberOfLibors() Get the number of LIBORs in the LIBOR discretization.
RandomVariable	getNumeraire(double time) Return the numeraire at a given time.
Map<Double,RandomVariable>	getNumeraireAdjustments()
protected RandomVariable	getNumerairetUnAdjusted(double time)
protected RandomVariable	getNumerairetUnAdjustedAtLIBORIndex(int liborTimeIndex)
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 \( t = 0 \).
AbstractSwaptionMarketData	getSwaptionMarketData() Return the swaption market data used for calibration (if any, may be null).
static LIBORMarketModelFromCovarianceModel	of(TimeDiscretization liborPeriodDiscretization, AnalyticModel analyticModel, ForwardCurve forwardRateCurve, DiscountCurve discountCurve, AbstractRandomVariableFactory randomVariableFactory, LIBORCovarianceModel covarianceModel, CalibrationProduct[] calibrationProducts, Map<String,?> properties) Creates a LIBOR Market Model for given covariance with a calibration (if calibration items are given).
String	toString()

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

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

Methods inherited from class java.lang.Object

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

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

getNumberOfFactors, getProcess, getTimeDiscretization, setProcess

Constructor Detail

LIBORMarketModelFromCovarianceModel

public LIBORMarketModelFromCovarianceModel(TimeDiscretization liborPeriodDiscretization,
                                           AnalyticModel analyticModel,
                                           ForwardCurve forwardRateCurve,
                                           DiscountCurve discountCurve,
                                           AbstractRandomVariableFactory randomVariableFactory,
                                           LIBORCovarianceModel covarianceModel,
                                           Map<String,?> properties)
                                    throws CalculationException

Creates a LIBOR Market Model for given covariance. The map properties allows to configure the model. The following keys may be used:

• measure: Possible values:
  • SPOT (String): Simulate under spot measure.
  • TERMINAL (String): Simulate under terminal measure.
• stateSpace: Possible values:
  • LOGNORMAL (String): Simulate L = exp(Y).
  • NORMAL (String): Simulate L = Y.
• liborCap: An optional Double value applied as a cap to the LIBOR rates. May be used to limit the simulated valued to prevent values attaining POSITIVE_INFINITY and numerical problems. To disable the cap, set liborCap to Double.POSITIVE_INFINITY.
• calibrationParameters: Possible values:
  • Map<String,Object> a parameter map with the following key/value pairs:
    • accuracy: Double specifying the required solver accuracy.
    • maxIterations: Integer specifying the maximum iterations for the solver.

Parameters:

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

analyticModel - The associated analytic model of this model (containing the associated market data objects like curve).

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.

randomVariableFactory - The random variable factory used to create the inital values of the model.

covarianceModel - The covariance model to use.

properties - Key value map specifying properties like measure and stateSpace.

Throws:

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

LIBORMarketModelFromCovarianceModel

@Deprecated
public LIBORMarketModelFromCovarianceModel(TimeDiscretization liborPeriodDiscretization,
                                                       AnalyticModel analyticModel,
                                                       ForwardCurve forwardRateCurve,
                                                       DiscountCurve discountCurve,
                                                       AbstractRandomVariableFactory randomVariableFactory,
                                                       LIBORCovarianceModel covarianceModel,
                                                       CalibrationProduct[] calibrationProducts,
                                                       Map<String,?> properties)
                                                throws CalculationException

Deprecated. Use LIBORMarketModelFromCovarianceModel.of() instead.

Creates a LIBOR Market Model for given covariance.
If calibrationItems in non-empty and the covariance model is a parametric model, the covariance will be replaced by a calibrate version of the same model, i.e., the LIBOR Market Model will be calibrated.
The map properties allows to configure the model. The following keys may be used:

• measure: Possible values:
  • SPOT (String): Simulate under spot measure.
  • TERMINAL (String): Simulate under terminal measure.
• stateSpace: Possible values:
  • LOGNORMAL (String): Simulate L = exp(Y).
  • NORMAL (String): Simulate L = Y.
• liborCap: An optional Double value applied as a cap to the LIBOR rates. May be used to limit the simulated valued to prevent values attaining POSITIVE_INFINITY and numerical problems. To disable the cap, set liborCap to Double.POSITIVE_INFINITY.
• calibrationParameters: Possible values:
  • Map<String,Object> a parameter map with the following key/value pairs:
    • accuracy: Double specifying the required solver accuracy.
    • maxIterations: Integer specifying the maximum iterations for the solver.

Parameters:

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

analyticModel - The associated analytic model of this model (containing the associated market data objects like curve).

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.

randomVariableFactory - The random variable factory used to create the inital values of the model.

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).

properties - Key value map specifying properties like measure and stateSpace.

Throws:

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

LIBORMarketModelFromCovarianceModel

@Deprecated
public LIBORMarketModelFromCovarianceModel(TimeDiscretization liborPeriodDiscretization,
                                                       AnalyticModel analyticModel,
                                                       ForwardCurve forwardRateCurve,
                                                       DiscountCurve discountCurve,
                                                       LIBORCovarianceModel covarianceModel,
                                                       CalibrationProduct[] calibrationItems,
                                                       Map<String,?> properties)
                                                throws CalculationException

Deprecated. Use LIBORMarketModelFromCovarianceModel.of() instead.

Creates a LIBOR Market Model for given covariance.
If calibrationItems in non-empty and the covariance model is a parametric model, the covariance will be replaced by a calibrate version of the same model, i.e., the LIBOR Market Model will be calibrated.
The map properties allows to configure the model. The following keys may be used:

• measure: Possible values:
  • SPOT (String): Simulate under spot measure.
  • TERMINAL (String): Simulate under terminal measure.
• stateSpace: Possible values:
  • LOGNORMAL (String): Simulate L = exp(Y).
  • NORMAL (String): Simulate L = Y.
• liborCap: An optional Double value applied as a cap to the LIBOR rates. May be used to limit the simulated valued to prevent values attaining POSITIVE_INFINITY and numerical problems. To disable the cap, set liborCap to Double.POSITIVE_INFINITY.
• calibrationParameters: Possible values:
  • Map<String,Object> a parameter map with the following key/value pairs:
    • accuracy: Double specifying the required solver accuracy.
    • maxIterations: Integer specifying the maximum iterations for the solver.

Parameters:

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

analyticModel - The associated analytic model of this model (containing the associated market data objects like curve).

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.

calibrationItems - 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).

properties - Key value map specifying properties like measure and stateSpace.

Throws:

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

LIBORMarketModelFromCovarianceModel

public LIBORMarketModelFromCovarianceModel(TimeDiscretization liborPeriodDiscretization,
                                           ForwardCurve forwardRateCurve,
                                           LIBORCovarianceModel covarianceModel)
                                    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.

covarianceModel - The covariance model to use.

Throws:

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

LIBORMarketModelFromCovarianceModel

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

Throws:

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

LIBORMarketModelFromCovarianceModel

public LIBORMarketModelFromCovarianceModel(TimeDiscretization liborPeriodDiscretization,
                                           ForwardCurve forwardRateCurve,
                                           LIBORCovarianceModel covarianceModel,
                                           AbstractSwaptionMarketData 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.

LIBORMarketModelFromCovarianceModel

public LIBORMarketModelFromCovarianceModel(TimeDiscretization liborPeriodDiscretization,
                                           ForwardCurve forwardRateCurve,
                                           DiscountCurve discountCurve,
                                           LIBORCovarianceModel covarianceModel,
                                           AbstractSwaptionMarketData 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.

LIBORMarketModelFromCovarianceModel

public LIBORMarketModelFromCovarianceModel(TimeDiscretization liborPeriodDiscretization,
                                           ForwardCurve forwardRateCurve,
                                           DiscountCurve discountCurve,
                                           LIBORCovarianceModel covarianceModel,
                                           AbstractSwaptionMarketData swaptionMarketData,
                                           Map<String,?> properties)
                                    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.

properties - Key value map specifying properties like measure and stateSpace.

Throws:

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

LIBORMarketModelFromCovarianceModel

@Deprecated
public LIBORMarketModelFromCovarianceModel(TimeDiscretization liborPeriodDiscretization,
                                                       ForwardCurve forwardRateCurve,
                                                       DiscountCurve discountCurve,
                                                       LIBORCovarianceModel covarianceModel,
                                                       CalibrationProduct[] calibrationItems,
                                                       Map<String,?> properties)
                                                throws CalculationException

Deprecated. Use LIBORMarketModelFromCovarianceModel.of() instead.

Creates a LIBOR Market Model for given covariance.
If calibrationItems in non-empty and the covariance model is a parametric model, the covariance will be replaced by a calibrate version of the same model, i.e., the LIBOR Market Model will be calibrated.
The map properties allows to configure the model. The following keys may be used:

• measure: Possible values:
  • SPOT (String): Simulate under spot measure.
  • TERMINAL (String): Simulate under terminal measure.
• stateSpace: Possible values:
  • LOGNORMAL (String): Simulate L = exp(Y).
  • NORMAL (String): Simulate L = Y.
• calibrationParameters: Possible values:
  • Map<String,Object> a parameter map with the following key/value pairs:
    • accuracy: Double specifying the required solver accuracy.
    • maxIterations: Integer specifying the maximum iterations for the solver.

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.

calibrationItems - 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).

properties - Key value map specifying properties like measure and stateSpace.

Throws:

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

Method Detail

of

public static LIBORMarketModelFromCovarianceModel of(TimeDiscretization liborPeriodDiscretization,
                                                     AnalyticModel analyticModel,
                                                     ForwardCurve forwardRateCurve,
                                                     DiscountCurve discountCurve,
                                                     AbstractRandomVariableFactory randomVariableFactory,
                                                     LIBORCovarianceModel covarianceModel,
                                                     CalibrationProduct[] calibrationProducts,
                                                     Map<String,?> properties)
                                              throws CalculationException

Creates a LIBOR Market Model for given covariance with a calibration (if calibration items are given).
If calibrationItems in non-empty and the covariance model is a parametric model, the covariance will be replaced by a calibrate version of the same model, i.e., the LIBOR Market Model will be calibrated. Note: Calibration is not lazy.
The map properties allows to configure the model. The following keys may be used:

• measure: Possible values:
  • SPOT (String): Simulate under spot measure.
  • TERMINAL (String): Simulate under terminal measure.
• stateSpace: Possible values:
  • LOGNORMAL (String): Simulate L = exp(Y).
  • NORMAL (String): Simulate L = Y.
• liborCap: An optional Double value applied as a cap to the LIBOR rates. May be used to limit the simulated valued to prevent values attaining POSITIVE_INFINITY and numerical problems. To disable the cap, set liborCap to Double.POSITIVE_INFINITY.
• calibrationParameters: Possible values:
  • Map<String,Object> a parameter map with the following key/value pairs:
    • accuracy: Double specifying the required solver accuracy.
    • maxIterations: Integer specifying the maximum iterations for the solver.

Parameters:

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

analyticModel - The associated analytic model of this model (containing the associated market data objects like curve).

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.

randomVariableFactory - The random variable factory used to create the inital values of the model.

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).

properties - Key value map specifying properties like measure and stateSpace.

Returns:

A new instance of LIBORMarketModelFromCovarianceModel, possibly calibrated.

Throws:

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

getReferenceDate

public LocalDateTime getReferenceDate()

Description copied from interface: ProcessModel

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.

Specified by:

getReferenceDate in interface ProcessModel

Overrides:

getReferenceDate in class AbstractProcessModel

Returns:

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

getNumeraire

public RandomVariable getNumeraire(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:

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

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.

getForwardDiscountBond

public RandomVariable getForwardDiscountBond(double time,
                                             double maturity)
                                      throws CalculationException

Description copied from interface: TermStructureModel

Returns the time \( t \) forward bond derived from the numeraire, i.e., \( P(T;t) = E( \frac{N(t)}{N(T)} \vert \mathcal{F}_{t} ) \). Note: It is guaranteed that the random variabble returned by this method is \( \mathcal{F}_{t} ) \)-measurable.

Specified by:

getForwardDiscountBond in interface TermStructureModel

Parameters:

time - The evaluation time.

maturity - The maturity.

Returns:

The forward bond P(T;t).

Throws:

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

getNumerairetUnAdjusted

protected RandomVariable getNumerairetUnAdjusted(double time)
                                          throws CalculationException

Throws:

CalculationException

getNumerairetUnAdjustedAtLIBORIndex

protected RandomVariable getNumerairetUnAdjustedAtLIBORIndex(int liborTimeIndex)
                                                      throws CalculationException

Throws:

CalculationException

getNumeraireAdjustments

public Map<Double,RandomVariable> getNumeraireAdjustments()

getInitialState

public RandomVariable[] getInitialState()

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

Returns:

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

getDrift

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

Return the complete vector of the drift for the time index timeIndex, given that current state is realizationAtTimeIndex. The drift will be zero for rates being already fixed. The method currently provides the drift for either Measure.SPOT or Measure.TERMINAL - depending how the model object was constructed. For Measure.TERMINAL the j-th entry of the return value is the random variable \[ \mu_{j}^{\mathbb{Q}^{P(T_{n})}}(t) \ = \ - \mathop{\sum_{l\geq j+1}}_{l\leq n-1} \frac{\delta_{l}}{1+\delta_{l} L_{l}(t)} (\lambda_{j}(t) \cdot \lambda_{l}(t)) \] and for Measure.SPOT the j-th entry of the return value is the random variable \[ \mu_{j}^{\mathbb{Q}^{N}}(t) \ = \ \sum_{m(t) < l\leq j} \frac{\delta_{l}}{1+\delta_{l} L_{l}(t)} (\lambda_{j}(t) \cdot \lambda_{l}(t)) \] where \( \lambda_{j} \) is the vector for factor loadings for the j-th component of the stochastic process (that is, the diffusion part is \( \sum_{k=1}^m \lambda_{j,k} \mathrm{d}W_{k} \)). Note: The scalar product of the factor loadings determines the instantaneous covariance. If the model is written in log-coordinates (using exp as a state space transform), we find \(\lambda_{j} \cdot \lambda_{l} = \sum_{k=1}^m \lambda_{j,k} \lambda_{l,k} = \sigma_{j} \sigma_{l} \rho_{j,l} \). If the model is written without a state space transformation (in its orignial coordinates) then \(\lambda_{j} \cdot \lambda_{l} = \sum_{k=1}^m \lambda_{j,k} \lambda_{l,k} = L_{j} L_{l} \sigma_{j} \sigma_{l} \rho_{j,l} \).

Specified by:

getDrift in interface ProcessModel

Parameters:

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., The factor loading \( \lambda_{j,k} \).

getFactorLoading

public RandomVariable[] getFactorLoading(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:

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(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:

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(int componentIndex,
                                                      RandomVariable randomVariable)

Specified by:

applyStateSpaceTransformInverse in interface ProcessModel

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 LIBORMarketModelFromCovarianceModel.Driftapproximation getDriftApproximationMethod()

Returns:

Returns the driftApproximationMethod.

getLIBOR

public RandomVariable getLIBOR(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:

getLIBOR in interface TermStructureModel

Parameters:

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(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:

timeIndex - The time index (associated with ProcessModel.getTimeDiscretization().

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

Returns:

The forward rate.

Throws:

CalculationException - Thrown if calculation failed.

getNumberOfComponents

public int getNumberOfComponents()

Description copied from interface: ProcessModel

Returns the number of components

Specified by:

getNumberOfComponents in interface ProcessModel

Returns:

The number of components

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.

getInterpolationMethod

public LIBORMarketModelFromCovarianceModel.InterpolationMethod getInterpolationMethod()

Returns:

Returns the LIBOR rates interpolation method. See LIBORMarketModelFromCovarianceModel.InterpolationMethod.

getMeasure

public LIBORMarketModelFromCovarianceModel.Measure getMeasure()

Returns:

Returns the measure. See LIBORMarketModelFromCovarianceModel.Measure.

getIntegratedLIBORCovariance

public double[][][] getIntegratedLIBORCovariance()

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

Returns:

The integrated instantaneous log-LIBOR covariance.

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 AbstractSwaptionMarketData 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.

clone

public Object clone()

Overrides:

clone in class Object

getCloneWithModifiedCovarianceModel

public LIBORMarketModelFromCovarianceModel 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 LIBORMarketModelFromCovarianceModel using the specified covariance model.

getCloneWithModifiedData

public LIBORMarketModelFromCovarianceModel 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 TermStructureModel

Specified by:

getCloneWithModifiedData in interface ProcessModel

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 when the model could not be created.

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.

toString

public String toString()

Overrides:

toString in class Object