Module net.finmath.lib
Package net.finmath.montecarlo.interestrate.models.covariance
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
-
ClassDescriptionA base class and interface description for the instantaneous covariance of an forward rate interest rate model.Base class for parametric covariance models, see also
AbstractLIBORCovarianceModel.A base class and interface description for the instantaneous volatility of an short rate model.Base class for parametric volatility models, see alsoAbstractShortRateVolatilityModel.Blended model (or displaced diffusion model) build on top of a standard covariance model.Displaced model build on top of a standard covariance model.Exponential decay model build on top of a given covariance model.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.Abstract base class and interface description of a correlation model (as it is used inLIBORCovarianceModelFromVolatilityAndCorrelation).Simple 1-parametric correlation model given by R, where R is a factor reduced matrix (seeLinearAlgebra.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 seeLIBORCorrelationModelThreeParameterExponentialDecay.Simple correlation model given by R, where R is a factor reduced matrix (seeLinearAlgebra.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}))Interface for covariance models providing a vector of (possibly stochastic) factor loadings.A five parameter covariance model corresponding.Interface for covariance models which may perform a calibration by providing the correspondinggetCloneCalibrated-method.The five parameter covariance model consisting of anLIBORVolatilityModelMaturityDependentFourParameterExponentialFormand anLIBORCorrelationModelExponentialDecay.A covariance model build from a volatility model implementingLIBORVolatilityModeland a correlation model implementingLIBORCorrelationModel.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.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.Abstract base class and interface description of a volatility model (as it is used inLIBORCovarianceModelFromVolatilityAndCorrelation).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 \( \{ t_{j} \} \).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 \[ \left( \sigma^{\text{Black}}_{i}(t_{k}) \right)^2 = \frac{1}{t_{k} \int_{0}^{t_{k}} \left( ( a + b (T_{i}-t) ) exp(-c (T_{i}-t)) + d \right)^{2} \ \mathrm{d}t \text{.} \]Implements a simple volatility model using given piece-wise constant values on a given discretization grid.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.Implements the volatility model σi(tj) = a * exp(-b (Ti-tj))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 \( t \mapsto a(t) \).A short rate volatility model from given volatility and mean reversion.Interface for covariance models which may perform a calibration by providing the correspondinggetCloneCalibrated-method.Interface for short rate volatility models which are determined by a vector of parameter.Short rate volatility model with a piecewise constant volatility and a piecewise constant mean reversion.A base class and interface description for the instantaneous covariance of an forward rate interest rate model.A base class and interface description for the instantaneous covariance of an forward rate interest rate model.A base class and interface description for the instantaneous covariance of an forward rate interest rate model.A base class and interface description for the instantaneous covariance of an forward rate interest rate model.