Module net.finmath.lib

Package net.finmath.montecarlo.interestrate.models.covariance

Contains covariance models and their calibration as plug-ins for the LIBOR market model and volatility and correlation models which may be used to build a covariance model. Covariance models provide they free parameters via an interface. The class AbstractLIBORCovarianceModelParametric provides a method that implements the generic calibration of the models.

Author:

Christian Fries

Interface Summary

Interface	Description
LIBORCovarianceModel	Interface for covariance models providing a vector of (possibly stochastic) factor loadings.
LIBORCovarianceModelCalibrateable	Interface for covariance models which may perform a calibration by providing the corresponding getCloneCalibrated-method.
ShortRateVolatilityModel	Interface for piecewise constant short rate volatility models with piecewise constant instantaneous short rate volatility \( t \mapsto \sigma(t) \) and piecewise constant short rate mean reversion speed \( t \mapsto a(t) \).
ShortRateVolatilityModelCalibrateable	Interface for covariance models which may perform a calibration by providing the corresponding getCloneCalibrated-method.
ShortRateVolatilityModelParametric	Interface for short rate volatility models which are determined by a vector of parameter.
TermStructureCovarianceModel	A base class and interface description for the instantaneous covariance of an forward rate interest rate model.
TermStructureFactorLoadingsModel	A base class and interface description for the instantaneous covariance of an forward rate interest rate model.
TermStructureFactorLoadingsModelParametric	A base class and interface description for the instantaneous covariance of an forward rate interest rate model.
TermStructureTenorTimeScaling

Class Summary

Class	Description
AbstractLIBORCovarianceModel	A base class and interface description for the instantaneous covariance of an forward rate interest rate model.
AbstractLIBORCovarianceModelParametric	Base class for parametric covariance models, see also AbstractLIBORCovarianceModel.
AbstractShortRateVolatilityModel	A base class and interface description for the instantaneous volatility of an short rate model.
AbstractShortRateVolatilityModelParametric	Base class for parametric volatility models, see also AbstractShortRateVolatilityModel.
BlendedLocalVolatilityModel	Blended model (or displaced diffusion model) build on top of a standard covariance model.
DisplacedLocalVolatilityModel	Displaced model build on top of a standard covariance model.
ExponentialDecayLocalVolatilityModel	Exponential decay model build on top of a given covariance model.
HullWhiteLocalVolatilityModel	Special variant of a blended model (or displaced diffusion model) build on top of a standard covariance model using the special function corresponding to the Hull-White local volatility.
LIBORCorrelationModel	Abstract base class and interface description of a correlation model (as it is used in LIBORCovarianceModelFromVolatilityAndCorrelation).
LIBORCorrelationModelExponentialDecay	Simple 1-parametric correlation model given by R, where R is a factor reduced matrix (see LinearAlgebra.factorReduction(double[][], int)) created from the \( n \) Eigenvectors of \( \tilde{R} \) belonging to the \( n \) largest non-negative Eigenvalues, where \( \tilde{R} = \tilde{\rho}_{i,j} \) and \[ \tilde{\rho}_{i,j} = \exp( -\max(a,0) | T_{i}-T_{j} | ) \] For a more general model featuring three parameters see LIBORCorrelationModelThreeParameterExponentialDecay.
LIBORCorrelationModelThreeParameterExponentialDecay	Simple correlation model given by R, where R is a factor reduced matrix (see LinearAlgebra.factorReduction(double[][], int)) created from the \( n \) Eigenvectors of \( \tilde{R} \) belonging to the \( n \) largest non-negative Eigenvalues, where \( \tilde{R} = \tilde{\rho}_{i,j} \) and \[ \tilde{\rho}_{i,j} = b + (1-b) * \exp(-a |T_{i} - T_{j}| - c \max(T_{i},T_{j}))
LIBORCovarianceModelBH	A five parameter covariance model corresponding.
LIBORCovarianceModelExponentialForm5Param	The five parameter covariance model consisting of an LIBORVolatilityModelMaturityDependentFourParameterExponentialForm and an LIBORCorrelationModelExponentialDecay.
LIBORCovarianceModelExponentialForm7Param
LIBORCovarianceModelFromVolatilityAndCorrelation	A covariance model build from a volatility model implementing LIBORVolatilityModel and a correlation model implementing LIBORCorrelationModel.
LIBORCovarianceModelStochasticHestonVolatility	As Heston like stochastic volatility model, using a process \( \lambda(t) = \sqrt(V(t)) \) \[ dV(t) = \kappa ( \theta - V(t) ) dt + \xi \sqrt{V(t)} dW_{1}(t), \quad V(0) = 1.0, \] where \( \lambda(0) = 1 \) to scale all factor loadings \( f_{i} \) returned by a given covariance model.
LIBORCovarianceModelStochasticVolatility	Simple stochastic volatility model, using a process \[ d\lambda(t) = \nu \lambda(t) \left( \rho \mathrm{d} W_{1}(t) + \sqrt{1-\rho^{2}} \mathrm{d} W_{2}(t) \right) \text{,} \] where \( \lambda(0) = 1 \) to scale all factor loadings \( f_{i} \) returned by a given covariance model.
LIBORVolatilityModel	Abstract base class and interface description of a volatility model (as it is used in LIBORCovarianceModelFromVolatilityAndCorrelation).
LIBORVolatilityModelFourParameterExponentialForm	Implements the volatility model \[ \sigma_{i}(t_{j}) = ( a + b (T_{i}-t_{j}) ) exp(-c (T_{i}-t_{j})) + d \text{.} \] The parameters here have some interpretation: The parameter a: an initial volatility level. The parameter b: the slope at the short end (shortly before maturity). The parameter c: exponential decay of the volatility in time-to-maturity. The parameter d: if c > 0 this is the very long term volatility level. Note that this model results in a terminal (Black 76) volatility which is given by \[ \left( \sigma^{\text{Black}}_{i}(t_{k}) \right)^2 = \frac{1}{t_{k}} \sum_{j=0}^{k-1} \left( ( a + b (T_{i}-t_{j}) ) exp(-c (T_{i}-t_{j})) + d \right)^{2} (t_{j+1}-t_{j}) \] i.e., the instantaneous volatility is given by the picewise constant approximation of the function \[ \sigma_{i}(t) = ( a + b (T_{i}-t) ) exp(-c (T_{i}-t)) + d \] on the time discretization \( \{ t_{j} \} \).
LIBORVolatilityModelFourParameterExponentialFormIntegrated	Implements the volatility model \[ \sigma_{i}(t_{j}) = \sqrt{ \frac{1}{t_{j+1}-t_{j}} \int_{t_{j}}^{t_{j+1}} \left( ( a + b (T_{i}-t) ) exp(-c (T_{i}-t)) + d \right)^{2} \ \mathrm{d}t } \text{.} \] The parameters here have some interpretation: The parameter a: an initial volatility level. The parameter b: the slope at the short end (shortly before maturity). The parameter c: exponential decay of the volatility in time-to-maturity. The parameter d: if c > 0 this is the very long term volatility level. Note that this model results in a terminal (Black 76) volatility which is given by \[ \left( \sigma^{\text{Black}}_{i}(t_{k}) \right)^2 = \frac{1}{t_{k} \int_{0}^{t_{k}} \left( ( a + b (T_{i}-t) ) exp(-c (T_{i}-t)) + d \right)^{2} \ \mathrm{d}t \text{.} \]
LIBORVolatilityModelFromGivenMatrix	Implements a simple volatility model using given piece-wise constant values on a given discretization grid.
LIBORVolatilityModelMaturityDependentFourParameterExponentialForm
LIBORVolatilityModelPiecewiseConstant
LIBORVolatilityModelTimeHomogenousPiecewiseConstant	Implements a piecewise constant volatility model, where \( \sigma(t,T) = sigma_{i} \) where \( i = \max \{ j : \tau_{j} \leq T-t \} \) and \( \tau_{0}, \tau_{1}, \ldots, \tau_{n-1} \) is a given time discretization.
LIBORVolatilityModelTwoParameterExponentialForm	Implements the volatility model σi(tj) = a * exp(-b (Ti-tj))
ShortRateVolatilityModelAsGiven	A short rate volatility model from given volatility and mean reversion.
ShortRateVolatilityModelHoLee
ShortRateVolatilityModelPiecewiseConstant	Short rate volatility model with a piecewise constant volatility and a piecewise constant mean reversion.
TermStructCovarianceModelFromLIBORCovarianceModel
TermStructCovarianceModelFromLIBORCovarianceModelParametric
TermStructureCovarianceModelParametric	A base class and interface description for the instantaneous covariance of an forward rate interest rate model.
TermStructureTenorTimeScalingPicewiseConstant