net.finmath.montecarlo.interestrate.modelplugins

Class LIBORVolatilityModelFourParameterExponentialForm

java.lang.Object

net.finmath.montecarlo.interestrate.modelplugins.LIBORVolatilityModel

net.finmath.montecarlo.interestrate.modelplugins.LIBORVolatilityModelFourParameterExponentialForm

public class LIBORVolatilityModelFourParameterExponentialForm
extends LIBORVolatilityModel

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 \( \{ t_{j} \} \). For the exact integration of this formula see LIBORVolatilityModelFourParameterExponentialFormIntegrated.

Author:

Christian Fries

Constructor Summary

Constructors

Constructor and Description
LIBORVolatilityModelFourParameterExponentialForm(TimeDiscretizationInterface timeDiscretization, TimeDiscretizationInterface liborPeriodDiscretization, double a, double b, double c, double d, boolean isCalibrateable) Creates the volatility model σi(tj) = ( a + b * (Ti-tj) ) * exp(-c (Ti-tj)) + d

Method Summary

Modifier and Type	Method and Description
Object	clone()
double[]	getParameter()
RandomVariableInterface	getVolatility(int timeIndex, int liborIndex) Implement this method to complete the implementation.
void	setParameter(double[] parameter)

Methods inherited from class net.finmath.montecarlo.interestrate.modelplugins.LIBORVolatilityModel

getLiborPeriodDiscretization, getTimeDiscretization

Methods inherited from class java.lang.Object

equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

LIBORVolatilityModelFourParameterExponentialForm

public LIBORVolatilityModelFourParameterExponentialForm(TimeDiscretizationInterface timeDiscretization,
                                                        TimeDiscretizationInterface liborPeriodDiscretization,
                                                        double a,
                                                        double b,
                                                        double c,
                                                        double d,
                                                        boolean isCalibrateable)

Creates the volatility model σ_i(t_j) = ( a + b * (T_i-t_j) ) * exp(-c (T_i-t_j)) + d

Parameters:

timeDiscretization - The simulation time discretization t_j.

liborPeriodDiscretization - The period time discretization T_i.

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

getParameter

public double[] getParameter()

Specified by:

getParameter in class LIBORVolatilityModel

setParameter

public void setParameter(double[] parameter)

Specified by:

setParameter in class LIBORVolatilityModel

getVolatility

public RandomVariableInterface 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 timeDiscretization)

liborIndex - The libor index (for liborPeriodDiscretization)

Returns:

A random variable (e.g. as a vector of doubles) representing the volatility for each path.

clone

public Object clone()

Specified by:

clone in class LIBORVolatilityModel