net.finmath.montecarlo.interestrate.models

Class LIBORMarketModelWithTenorRefinement

java.lang.Object

net.finmath.montecarlo.model.AbstractProcessModel

net.finmath.montecarlo.interestrate.models.LIBORMarketModelWithTenorRefinement

All Implemented Interfaces:

TermStructureModel, ProcessModel

public class LIBORMarketModelWithTenorRefinement
extends AbstractProcessModel
implements TermStructureModel

Implements a discretized Heath-Jarrow-Morton model / LIBOR market model with dynamic tenor refinement, see https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2884699.

In its default case the class specifies a multi-factor LIBOR market model, that is \( L_{j} = \frac{1}{T_{j+1}-T_{j}} ( exp(Y_{j}) - 1 ) \), where \[ dY_{j} = \mu_{j} dt + \lambda_{1,j} dW_{1} + \ldots + \lambda_{m,j} dW_{m} \]
The model uses an AbstractLIBORCovarianceModel for the specification of (λ_1,j,...,λ_m,j) as a covariance model. 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 (through a local volatility model).
The simulation is performed under spot measure, that is, the numeraire is \( N(T_{i}) = \prod_{j=0}^{i-1} (1 + L(T_{j},T_{j+1};T_{j}) (T_{j+1}-T_{j})) \). The map properties allows to configure the model. The following keys may be used:

• 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.

Version:

1.2

Author:

Christian Fries

See Also:

The interface for numerical schemes., The interface for models provinding parameters to numerical schemes., https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2884699

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	LIBORMarketModelWithTenorRefinement.Driftapproximation

Constructor Summary

Constructors

Constructor and Description
LIBORMarketModelWithTenorRefinement(TimeDiscretization[] liborPeriodDiscretizations, Integer[] numberOfDiscretizationIntervalls, AnalyticModel analyticModel, ForwardCurve forwardRateCurve, DiscountCurve discountCurve, TermStructureCovarianceModelInterface covarianceModel, CalibrationProduct[] calibrationProducts, Map<String,?> properties) Creates a model for given covariance.

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.
TermStructureModel	getCloneWithModifiedData(Map<String,Object> dataModified) Create a new object implementing TermStructureModel, using the new data.
TermStructureCovarianceModelInterface	getCovarianceModel() Returns the term structure 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.
RandomVariable[]	getFactorLoading(int timeIndex, int componentIndex, RandomVariable[] realizationAtTimeIndex) This method has to be implemented to return the factor loadings, i.e.
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.
RandomVariable	getLIBOR(double time, double periodStart, double periodEnd) Returns the time \( t \) forward rate on the models forward curve.
RandomVariable	getLIBOR(int timeIndex, double periodStart, double periodEnd)
RandomVariable	getLIBORForStateVariable(TimeDiscretization liborPeriodDiscretization, RandomVariable[] stateVariables, double periodStart, double periodEnd)
int	getNumberOfComponents() Returns the number of components
int	getNumberOfLibors()
RandomVariable	getNumeraire(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.
RandomVariable	getStateVariable(int timeIndex, double periodStart, double periodEnd)
RandomVariable	getStateVariableForPeriod(TimeDiscretization liborPeriodDiscretization, RandomVariable[] stateVariables, double periodStart, double periodEnd)

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

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

Methods inherited from class java.lang.Object

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

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

getForwardDiscountBond

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

getNumberOfFactors, getProcess, getReferenceDate, getTimeDiscretization, setProcess

Constructor Detail

LIBORMarketModelWithTenorRefinement

public LIBORMarketModelWithTenorRefinement(TimeDiscretization[] liborPeriodDiscretizations,
                                           Integer[] numberOfDiscretizationIntervalls,
                                           AnalyticModel analyticModel,
                                           ForwardCurve forwardRateCurve,
                                           DiscountCurve discountCurve,
                                           TermStructureCovarianceModelInterface covarianceModel,
                                           CalibrationProduct[] calibrationProducts,
                                           Map<String,?> properties)
                                    throws CalculationException

Creates a model for given covariance. Creates a discretized Heath-Jarrow-Morton model / LIBOR market model with dynamic tenor refinement, see https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2884699.
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:

• 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:

liborPeriodDiscretizations - A vector of tenor discretizations of the interest rate curve into forward rates (tenor structure), finest first.

numberOfDiscretizationIntervalls - A vector of number of periods to be taken from the liborPeriodDiscretizations.

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.

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.

Method Detail

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.

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.

getStateVariableForPeriod

public RandomVariable getStateVariableForPeriod(TimeDiscretization liborPeriodDiscretization,
                                                RandomVariable[] stateVariables,
                                                double periodStart,
                                                double periodEnd)

getLIBORForStateVariable

public RandomVariable getLIBORForStateVariable(TimeDiscretization liborPeriodDiscretization,
                                               RandomVariable[] stateVariables,
                                               double periodStart,
                                               double periodEnd)

getStateVariable

public RandomVariable getStateVariable(int timeIndex,
                                       double periodStart,
                                       double periodEnd)

getLIBOR

public RandomVariable getLIBOR(double time,
                               double periodStart,
                               double periodEnd)

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.

getLIBOR

public RandomVariable getLIBOR(int timeIndex,
                               double periodStart,
                               double periodEnd)

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()

clone

public Object clone()

Overrides:

clone in class Object

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

getCloneWithModifiedData

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

Description copied from interface: TermStructureModel

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

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 TermStructureModel, using the new data.

Throws:

CalculationException - Thrown when the model could not be created.

getCovarianceModel

public TermStructureCovarianceModelInterface getCovarianceModel()

Returns the term structure covariance model.

Returns:

the term structure covariance model.