Class LIBORVolatilityModelFourParameterExponentialFormIntegrated

  • All Implemented Interfaces:
    Serializable

    public class LIBORVolatilityModelFourParameterExponentialFormIntegrated
    extends LIBORVolatilityModel
    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 \[ \left( \sigma^{\text{Black}}_{i}(t_{k}) \right)^2 = \frac{1}{t_{k} \int_{0}^{t_{k}} \left( ( a + b (T_{i}-t) ) exp(-c (T_{i}-t)) + d \right)^{2} \ \mathrm{d}t \text{.} \]
    Version:
    1.1
    Author:
    Christian Fries
    See Also:
    Serialized Form
    • Constructor Detail

      • LIBORVolatilityModelFourParameterExponentialFormIntegrated

        public LIBORVolatilityModelFourParameterExponentialFormIntegrated​(RandomVariableFactory randomVariableFactory,
                                                                          TimeDiscretization timeDiscretization,
                                                                          TimeDiscretization liborPeriodDiscretization,
                                                                          double a,
                                                                          double b,
                                                                          double c,
                                                                          double d,
                                                                          boolean isCalibrateable)
        Creates the volatility model \[ \sigma_{i}(t_{j}) = \sqrt{ \frac{1}{t_{j+1}-t_{j}} \int_{t_{j}}^{t_{j+1}} \left( ( a + b (T_{i}-t) ) \exp(-c (T_{i}-t)) + d \right)^{2} \ \mathrm{d}t } \text{.} \]
        Parameters:
        randomVariableFactory - The random variable factor used to construct random variables from the parameters.
        timeDiscretization - The simulation time discretization tj.
        liborPeriodDiscretization - The period time discretization Ti.
        a - The parameter a: an initial volatility level.
        b - The parameter b: the slope at the short end (shortly before maturity).
        c - The parameter c: exponential decay of the volatility in time-to-maturity.
        d - The parameter d: if c > 0 this is the very long term volatility level.
        isCalibrateable - Set this to true, if the parameters are available for calibration.
      • LIBORVolatilityModelFourParameterExponentialFormIntegrated

        public LIBORVolatilityModelFourParameterExponentialFormIntegrated​(TimeDiscretization timeDiscretization,
                                                                          TimeDiscretization liborPeriodDiscretization,
                                                                          RandomVariable a,
                                                                          RandomVariable b,
                                                                          RandomVariable c,
                                                                          RandomVariable d,
                                                                          boolean isCalibrateable)
        Creates the volatility model \[ \sigma_{i}(t_{j}) = \sqrt{ \frac{1}{t_{j+1}-t_{j}} \int_{t_{j}}^{t_{j+1}} \left( ( a + b (T_{i}-t) ) \exp(-c (T_{i}-t)) + d \right)^{2} \ \mathrm{d}t } \text{.} \]
        Parameters:
        timeDiscretization - The simulation time discretization tj.
        liborPeriodDiscretization - The period time discretization Ti.
        a - The parameter a: an initial volatility level.
        b - The parameter b: the slope at the short end (shortly before maturity).
        c - The parameter c: exponential decay of the volatility in time-to-maturity.
        d - The parameter d: if c > 0 this is the very long term volatility level.
        isCalibrateable - Set this to true, if the parameters are available for calibration.
      • LIBORVolatilityModelFourParameterExponentialFormIntegrated

        public LIBORVolatilityModelFourParameterExponentialFormIntegrated​(TimeDiscretization timeDiscretization,
                                                                          TimeDiscretization liborPeriodDiscretization,
                                                                          double a,
                                                                          double b,
                                                                          double c,
                                                                          double d,
                                                                          boolean isCalibrateable)
        Creates the volatility model \[ \sigma_{i}(t_{j}) = \sqrt{ \frac{1}{t_{j+1}-t_{j}} \int_{t_{j}}^{t_{j+1}} \left( ( a + b (T_{i}-t) ) \exp(-c (T_{i}-t)) + d \right)^{2} \ \mathrm{d}t } \text{.} \]
        Parameters:
        timeDiscretization - The simulation time discretization tj.
        liborPeriodDiscretization - The period time discretization Ti.
        a - The parameter a: an initial volatility level.
        b - The parameter b: the slope at the short end (shortly before maturity).
        c - The parameter c: exponential decay of the volatility in time-to-maturity.
        d - The parameter d: if c > 0 this is the very long term volatility level.
        isCalibrateable - Set this to true, if the parameters are available for calibration.
    • Method Detail

      • getVolatility

        public RandomVariable getVolatility​(int timeIndex,
                                            int liborIndex)
        Description copied from class: LIBORVolatilityModel
        Implement this method to complete the implementation.
        Specified by:
        getVolatility in class LIBORVolatilityModel
        Parameters:
        timeIndex - The time index (for timeDiscretizationFromArray)
        liborIndex - The libor index (for liborPeriodDiscretization)
        Returns:
        A random variable (e.g. as a vector of doubles) representing the volatility for each path.
      • getCloneWithModifiedData

        public LIBORVolatilityModel getCloneWithModifiedData​(Map<String,​Object> dataModified)
        Description copied from class: LIBORVolatilityModel
        Returns a clone of this model where the specified properties have been modified. Note that there is no guarantee that a model reacts on a specification of a properties in the parameter map dataModified. If data is provided which is ignored by the model no exception may be thrown. Furthermore the structure of the correlation model has to match changed data. A change of the time discretizations may requires a change in the parameters but this function will just insert the new time discretization without changing the parameters. An exception may not be thrown.
        Specified by:
        getCloneWithModifiedData in class LIBORVolatilityModel
        Parameters:
        dataModified - Key-value-map of parameters to modify.
        Returns:
        A clone of this model (or a new instance of this model if no parameter was modified).