finMath lib documentation
net.finmath.montecarlo.interestrate

## Class LIBORMarketModel

• All Implemented Interfaces:
LIBORMarketModelInterface, LIBORModelInterface, TermStructureModelInterface, AbstractModelInterface

public class LIBORMarketModel
extends AbstractModel
implements LIBORMarketModelInterface
Implements a (generalized) LIBOR market model 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 Lj = exp(Yj) 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 1,j,...,λm,j) as a covariance model. See AbstractModelInterface 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 Lj = f(Yj) 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
dYj = μj dt + λ1,j dW1 + ... + λm,j dWm

see AbstractModelInterface 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(LIBORMarketModelInterface, AbstractLIBORMonteCarloProduct[], double[], double[], Map).
Version:
1.2
Author:
Christian Fries
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.
• ### Constructor Detail

• #### LIBORMarketModel

public LIBORMarketModel(TimeDiscretizationInterface liborPeriodDiscretization,
AnalyticModelInterface analyticModel,
ForwardCurveInterface forwardRateCurve,
DiscountCurveInterface discountCurve,
AbstractRandomVariableFactory randomVariableFactory,
AbstractLIBORCovarianceModel covarianceModel,
LIBORMarketModel.CalibrationItem[] calibrationItems,
Map<String,?> properties)
throws CalculationException
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.
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.
• #### LIBORMarketModel

public LIBORMarketModel(TimeDiscretizationInterface liborPeriodDiscretization,
AnalyticModelInterface analyticModel,
ForwardCurveInterface forwardRateCurve,
DiscountCurveInterface discountCurve,
AbstractLIBORCovarianceModel covarianceModel,
LIBORMarketModel.CalibrationItem[] calibrationItems,
Map<String,?> properties)
throws CalculationException
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.
• #### LIBORMarketModel

public LIBORMarketModel(TimeDiscretizationInterface liborPeriodDiscretization,
ForwardCurveInterface forwardRateCurve,
AbstractLIBORCovarianceModel 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.
• #### LIBORMarketModel

public LIBORMarketModel(TimeDiscretizationInterface liborPeriodDiscretization,
ForwardCurveInterface forwardRateCurve,
DiscountCurveInterface discountCurve,
AbstractLIBORCovarianceModel 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.
• #### LIBORMarketModel

public LIBORMarketModel(TimeDiscretizationInterface liborPeriodDiscretization,
ForwardCurveInterface forwardRateCurve,
AbstractLIBORCovarianceModel 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.
• #### LIBORMarketModel

public LIBORMarketModel(TimeDiscretizationInterface liborPeriodDiscretization,
ForwardCurveInterface forwardRateCurve,
DiscountCurveInterface discountCurve,
AbstractLIBORCovarianceModel 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.
• #### LIBORMarketModel

public LIBORMarketModel(TimeDiscretizationInterface liborPeriodDiscretization,
ForwardCurveInterface forwardRateCurve,
DiscountCurveInterface discountCurve,
AbstractLIBORCovarianceModel 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.
• #### LIBORMarketModel

public LIBORMarketModel(TimeDiscretizationInterface liborPeriodDiscretization,
ForwardCurveInterface forwardRateCurve,
DiscountCurveInterface discountCurve,
AbstractLIBORCovarianceModel covarianceModel,
LIBORMarketModel.CalibrationItem[] calibrationItems,
Map<String,?> properties)
throws CalculationException
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

• #### getNumeraire

public RandomVariableInterface 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 AbstractModelInterface
Parameters:
time - Time time t for which the numeraire should be returned N(t).
Returns:
The numeraire at the specified time as RandomVariableInterface
Throws:
CalculationException - Thrown if the valuation fails, specific cause may be available via the cause() method.
• #### getInitialState

public RandomVariableInterface[] getInitialState()
Description copied from interface: AbstractModelInterface
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 AbstractModelInterface
Returns:
The initial value of the state variable of the process Y(t=0).
• #### getDrift

public RandomVariableInterface[] getDrift(int timeIndex,
RandomVariableInterface[] realizationAtTimeIndex,
RandomVariableInterface[] 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 AbstractModelInterface
Parameters:
timeIndex - Time index i for which the drift should be returned μ(ti).
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(ti) as RandomVariable[]
The calculation of the drift is consistent with the calculation of the numeraire in getNumeraire., The factor loading $$\lambda_{j,k}$$.

int componentIndex,
RandomVariableInterface[] realizationAtTimeIndex)
Description copied from interface: AbstractModelInterface
This method has to be implemented to return the factor loadings, i.e. the coefficient vector
λj = (λ1,j, ..., λm,j) such that X = f(Y) and
dYj = μj dt + λ1,j dW1 + ... + λm,j dWm
in an m-factor model. Here j denotes index of the component of the resulting process.
Specified by:
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:
• #### applyStateSpaceTransform

public RandomVariableInterface applyStateSpaceTransform(int componentIndex,
RandomVariableInterface randomVariable)
Description copied from interface: AbstractModelInterface
Applies the state space transform fi to the given state random variable such that Yi → fi(Yi) =: Xi.
Specified by:
applyStateSpaceTransform in interface AbstractModelInterface
Parameters:
componentIndex - The component index i.
randomVariable - The state random variable Yi.
Returns:
New random variable holding the result of the state space transformation.
• #### getNumberOfLibors

public int getNumberOfLibors()
Description copied from interface: LIBORModelInterface
Get the number of LIBORs in the LIBOR discretization.
Specified by:
getNumberOfLibors in interface LIBORModelInterface
Returns:
The number of LIBORs in the LIBOR discretization
• #### getLiborPeriod

public double getLiborPeriod(int timeIndex)
Description copied from interface: LIBORModelInterface
The period start corresponding to a given forward rate discretization index.
Specified by:
getLiborPeriod in interface LIBORModelInterface
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: LIBORModelInterface
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 LIBORModelInterface
Parameters:
time - The period start.
Returns:
The index corresponding to a given time (interpretation is start of period)
• #### getIntegratedLIBORCovariance

public double[][][] getIntegratedLIBORCovariance()
Description copied from interface: LIBORMarketModelInterface
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 LIBORMarketModelInterface
Returns:
The integrated instantaneous log-LIBOR covariance.
• #### clone

public Object clone()
Overrides:
clone in class Object
• #### 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).