Package net.finmath.montecarlo.interestrate.modelplugins

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.

See: Description

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.
BlendedLocalVolatilityModel	Blended model (or displaced diffusion model) build on top of a standard covariance model.
LIBORCorrelationModel	Abstract base class and interface description of a correlation model (as it is used in LIBORCovarianceModelFromVolatilityAndCorrelation).
LIBORCorrelationModelExponentialDecay	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 \[ \tilde{\rho}_{i,j} = \exp( -\max(a,0) | T_{i}-T_{j} | ) \] 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}))
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.
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
LIBORVolatilityModelTwoParameterExponentialForm	Implements the volatility model σi(tj) = a * exp(-b (Ti-tj))

Package net.finmath.montecarlo.interestrate.modelplugins Description

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.