AbstractLIBORCovarianceModel |
A base class and interface description for the instantaneous covariance of
an forward rate interest rate model.
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AbstractLIBORCovarianceModelParametric |
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AbstractShortRateVolatilityModel |
A base class and interface description for the instantaneous volatility of
an short rate model.
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AbstractShortRateVolatilityModelParametric |
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LIBORCorrelationModel |
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LIBORCorrelationModelExponentialDecay |
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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}))
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LIBORCovarianceModel |
Interface for covariance models providing a vector of (possibly stochastic) factor loadings.
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LIBORCovarianceModelCalibrateable |
Interface for covariance models which may perform a calibration by providing the corresponding getCloneCalibrated -method.
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LIBORVolatilityModel |
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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 \( \{ t_{j} \} \).
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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
\[
\left( \sigma^{\text{Black}}_{i}(t_{k}) \right)^2 = \frac{1}{t_{k} \int_{0}^{t_{k}} \left( ( a + b (T_{i}-t) ) exp(-c (T_{i}-t)) + d \right)^{2} \ \mathrm{d}t \text{.}
\]
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LIBORVolatilityModelFromGivenMatrix |
Implements a simple volatility model using given piece-wise constant values on
a given discretization grid.
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LIBORVolatilityModelMaturityDependentFourParameterExponentialForm |
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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.
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LIBORVolatilityModelTwoParameterExponentialForm |
Implements the volatility model σi(tj) = a * exp(-b (Ti-tj))
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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 \( t \mapsto a(t) \).
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ShortRateVolatilityModelCalibrateable |
Interface for covariance models which may perform a calibration by providing the corresponding getCloneCalibrated -method.
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ShortRateVolatilityModelParametric |
Interface for short rate volatility models which are determined by a vector of parameter.
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TermStructureCovarianceModelInterface |
A base class and interface description for the instantaneous covariance of
an forward rate interest rate model.
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TermStructureCovarianceModelParametric |
A base class and interface description for the instantaneous covariance of
an forward rate interest rate model.
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TermStructureFactorLoadingsModelInterface |
A base class and interface description for the instantaneous covariance of
an forward rate interest rate model.
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TermStructureFactorLoadingsModelParametricInterface |
A base class and interface description for the instantaneous covariance of
an forward rate interest rate model.
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TermStructureTenorTimeScalingInterface |
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