Module net.finmath.lib

Package net.finmath.montecarlo.interestrate.models.covariance

Class LIBORVolatilityModelFourParameterExponentialFormIntegrated

java.lang.Object

net.finmath.montecarlo.interestrate.models.covariance.LIBORVolatilityModel

net.finmath.montecarlo.interestrate.models.covariance.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 Summary

Constructors

Constructor	Description
LIBORVolatilityModelFourParameterExponentialFormIntegrated(RandomVariableFactory randomVariableFactory, TimeDiscretization timeDiscretization, TimeDiscretization liborPeriodDiscretization, double a, double b, double c, double d, boolean isCalibrateable)	Creates the volatility model \[ \sigma_{i}(t_{j}) = \sqrt{ \frac{1}{t_{j+1}-t_{j}} \int_{t_{j}}^{t_{j+1}} \left( ( a + b (T_{i}-t) ) \exp(-c (T_{i}-t)) + d \right)^{2} \ \mathrm{d}t } \text{.} \]
LIBORVolatilityModelFourParameterExponentialFormIntegrated(TimeDiscretization timeDiscretization, TimeDiscretization liborPeriodDiscretization, double a, double b, double c, double d, boolean isCalibrateable)	Creates the volatility model \[ \sigma_{i}(t_{j}) = \sqrt{ \frac{1}{t_{j+1}-t_{j}} \int_{t_{j}}^{t_{j+1}} \left( ( a + b (T_{i}-t) ) \exp(-c (T_{i}-t)) + d \right)^{2} \ \mathrm{d}t } \text{.} \]
LIBORVolatilityModelFourParameterExponentialFormIntegrated(TimeDiscretization timeDiscretization, TimeDiscretization liborPeriodDiscretization, RandomVariable a, RandomVariable b, RandomVariable c, RandomVariable d, boolean isCalibrateable)	Creates the volatility model \[ \sigma_{i}(t_{j}) = \sqrt{ \frac{1}{t_{j+1}-t_{j}} \int_{t_{j}}^{t_{j+1}} \left( ( a + b (T_{i}-t) ) \exp(-c (T_{i}-t)) + d \right)^{2} \ \mathrm{d}t } \text{.} \]

Method Summary

Modifier and Type	Method	Description
Object	clone()
LIBORVolatilityModel	getCloneWithModifiedData(Map<String,Object> dataModified)	Returns a clone of this model where the specified properties have been modified.
LIBORVolatilityModelFourParameterExponentialFormIntegrated	getCloneWithModifiedParameter(RandomVariable[] parameter)
RandomVariable[]	getParameter()
RandomVariable	getVolatility(int timeIndex, int liborIndex)	Implement this method to complete the implementation.

Methods inherited from class net.finmath.montecarlo.interestrate.models.covariance.LIBORVolatilityModel

getLiborPeriodDiscretization, getParameterAsDouble, getTimeDiscretization

Methods inherited from class java.lang.Object

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

Constructor Details

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 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.

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 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.

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 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 Details

getParameter

public RandomVariable[] getParameter()

Specified by:

getParameter in class LIBORVolatilityModel

getCloneWithModifiedParameter

public LIBORVolatilityModelFourParameterExponentialFormIntegrated getCloneWithModifiedParameter(RandomVariable[] parameter)

Specified by:

getCloneWithModifiedParameter in class LIBORVolatilityModel

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.

clone

public Object clone()

Specified by:

clone in class LIBORVolatilityModel

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).