Package org.drip.dynamics.meanreverting

Class R1CIRStochasticEvolver

java.lang.Object

org.drip.dynamics.process.R1StochasticEvolver

org.drip.dynamics.meanreverting.R1CKLSStochasticEvolver

org.drip.dynamics.meanreverting.R1CIRStochasticEvolver

public class R1CIRStochasticEvolver
extends R1CKLSStochasticEvolver

R1CIRStochasticEvolver implements the R¹ Cos-Ingersoll-Ross Stochastic Evolver. The References are:

• Doob, J. L. (1942): The Brownian Movement and Stochastic Equations Annals of Mathematics 43 (2) 351-369
• Gardiner, C. W. (2009): Stochastic Methods: A Handbook for the Natural and Social Sciences 4^th Edition Springer-Verlag
• Kadanoff, L. P. (2000): Statistical Physics: Statics, Dynamics, and Re-normalization World Scientific
• Karatzas, I., and S. E. Shreve (1991): Brownian Motion and Stochastic Calculus 2^nd Edition Springer-Verlag
• Risken, H., and F. Till (1996): The Fokker-Planck Equation – Methods of Solution and Applications Springer

• Module = Product Core Module
• Library = Fixed Income Analytics
• Project = HJM, Hull White, LMM, and SABR Dynamic Evolution Models
• Package = Mean Reverting Stochastic Process Dynamics

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
R1CIRStochasticEvolver(double meanReversionSpeed, double meanReversionLevel, double volatilityCoefficient, R1StochasticDriver r1StochasticDriver)	R1CIRStochasticEvolver Constructor

Method Summary

Modifier and Type	Method	Description
boolean	evolutionStrictlyPositive()	Indicate it the Evolution includes Zero, or is strictly Positive
R1FokkerPlanckCIR	fokkerPlanckGenerator()	Construct the Fokker Planck PDF Generator corresponding to R1 Stochastic Evolver
R1NonCentral	futureValueDistribution(double r0, double t)	Generate the Future Value Distribution at Time t
double	mean(double x0, double t)	Compute the Expected Value of x at a time t from a Starting Value x0
PopulationCentralMeasures	steadyStatePopulationCentralMeasures(double x0)	Generate the Steady State Population Central Measures
PopulationCentralMeasures	temporalPopulationCentralMeasures(double x0, double t)	Estimate the Temporal Central Measures for the Underlier given the Delta 0 Starting PDF
double	timeVariance(double x0, double t)	Compute the Time Variance of x across at a Time Value t
static R1CIRStochasticEvolver	Wiener(double meanReversionSpeed, double meanReversionLevel, double volatility, double timeWidth)	Construct a Weiner Instance of R1CIRStochasticEvolver Process

Methods inherited from class org.drip.dynamics.meanreverting.R1CKLSStochasticEvolver

cklsParameters, Wiener

Methods inherited from class org.drip.dynamics.process.R1StochasticEvolver

driftFunction, evolve, stochasticDriver, volatilityFunction

Methods inherited from class java.lang.Object

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

Constructor Details

R1CIRStochasticEvolver

public R1CIRStochasticEvolver(double meanReversionSpeed,
double meanReversionLevel,
double volatilityCoefficient,
R1StochasticDriver r1StochasticDriver)
                       throws java.lang.Exception

R1CIRStochasticEvolver Constructor

Parameters:

meanReversionSpeed - The Mean Reversion Speed

meanReversionLevel - The Mean Reversion Level

volatilityCoefficient - The Volatility Coefficient

r1StochasticDriver - The Stochastic Driver

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Method Details

Wiener

public static R1CIRStochasticEvolver Wiener(double meanReversionSpeed,
double meanReversionLevel,
double volatility,
double timeWidth)

Construct a Weiner Instance of R1CIRStochasticEvolver Process

Parameters:

meanReversionSpeed - The Mean Reversion Speed

meanReversionLevel - The Mean Reversion Level

volatility - The Volatility

timeWidth - Wiener Time Width

Returns:

Weiner Instance of R1CIRStochasticEvolver Process

evolutionStrictlyPositive

public boolean evolutionStrictlyPositive()

Indicate it the Evolution includes Zero, or is strictly Positive

Returns:

TRUE - Evoltuion is Strictly Positive

mean

public double mean(double x0,
double t)
            throws java.lang.Exception

Compute the Expected Value of x at a time t from a Starting Value x0

Parameters:

x0 - Starting Variate

t - Time

Returns:

Expected Value of x

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

timeVariance

public double timeVariance(double x0,
double t)
                    throws java.lang.Exception

Compute the Time Variance of x across at a Time Value t

Parameters:

x0 - Starting Variate

t - Time t

Returns:

Time Variance of x

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

temporalPopulationCentralMeasures

public PopulationCentralMeasures temporalPopulationCentralMeasures(double x0,
double t)

Description copied from class: R1StochasticEvolver

Estimate the Temporal Central Measures for the Underlier given the Delta 0 Starting PDF

Overrides:

temporalPopulationCentralMeasures in class R1StochasticEvolver

Parameters:

x0 - The X Anchor for the Delta Function

t - The Forward Time

Returns:

The Temporal Central Measures for the Underlier

steadyStatePopulationCentralMeasures

public PopulationCentralMeasures steadyStatePopulationCentralMeasures(double x0)

Description copied from class: R1StochasticEvolver

Generate the Steady State Population Central Measures

Overrides:

steadyStatePopulationCentralMeasures in class R1StochasticEvolver

Parameters:

x0 - Starting Variate

Returns:

The Steady State Population Central Measures

futureValueDistribution

public R1NonCentral futureValueDistribution(double r0,
double t)

Description copied from class: R1StochasticEvolver

Generate the Future Value Distribution at Time t

Overrides:

futureValueDistribution in class R1StochasticEvolver

Parameters:

r0 - Starting Variate

t - Time

Returns:

The Future Value Distribution

fokkerPlanckGenerator

public R1FokkerPlanckCIR fokkerPlanckGenerator()

Description copied from class: R1StochasticEvolver

Construct the Fokker Planck PDF Generator corresponding to R¹ Stochastic Evolver

Overrides:

fokkerPlanckGenerator in class R1CKLSStochasticEvolver

Returns:

The Fokker Planck PDF Generator corresponding to R¹ Stochastic Evolver