Package org.drip.dynamics.meanreverting

Class R1VasicekStochasticEvolver

java.lang.Object

org.drip.dynamics.process.R1StochasticEvolver

org.drip.dynamics.meanreverting.R1CKLSStochasticEvolver

org.drip.dynamics.meanreverting.R1VasicekStochasticEvolver

Direct Known Subclasses:

LangevinEvolver, R1OrnsteinUhlenbeckStochasticEvolver

public class R1VasicekStochasticEvolver
extends R1CKLSStochasticEvolver

R1VasicekStochasticEvolver implements the R¹ Vasicek 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
R1VasicekStochasticEvolver(double meanReversionSpeed, double meanReversionLevel, double volatility, R1StochasticDriver r1StochasticDriver)	R1VasicekStochasticEvolver Constructor

Method Summary

Modifier and Type	Method	Description
double[][]	aitSahaliaMLEAsymptote(double intervalWidth)	Construct the Ait-Sahalia Maximum Likelihood Estimation Sampling Interval Discreteness Error
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	timeCovariance(double x0, double s, double t)	Compute the Time Co-variance of x across Time Values t and s
static R1VasicekStochasticEvolver	Wiener(double meanReversionSpeed, double meanReversionLevel, double volatility, double timeWidth)	Construct a Weiner Instance of R1VasicekStochasticEvolver Process

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

cklsParameters, fokkerPlanckGenerator, Wiener

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

driftFunction, evolve, futureValueDistribution, stochasticDriver, volatilityFunction

Methods inherited from class java.lang.Object

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

Constructor Details

R1VasicekStochasticEvolver

public R1VasicekStochasticEvolver(double meanReversionSpeed,
double meanReversionLevel,
double volatility,
R1StochasticDriver r1StochasticDriver)
                           throws java.lang.Exception

R1VasicekStochasticEvolver Constructor

Parameters:

meanReversionSpeed - The Mean Reversion Speed

meanReversionLevel - The Mean Reversion Level

volatility - The Volatility

r1StochasticDriver - The Stochastic Driver

Throws:

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

Method Details

Wiener

public static R1VasicekStochasticEvolver Wiener(double meanReversionSpeed,
double meanReversionLevel,
double volatility,
double timeWidth)

Construct a Weiner Instance of R1VasicekStochasticEvolver Process

Parameters:

meanReversionSpeed - The Mean Reversion Speed

meanReversionLevel - The Mean Reversion Level

volatility - The Volatility

timeWidth - Wiener Time Width

Returns:

Weiner Instance of R1VasicekStochasticEvolver Process

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

timeCovariance

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

Compute the Time Co-variance of x across Time Values t and s

Parameters:

x0 - Starting Variate

s - Time s

t - Time t

Returns:

Time Co-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

aitSahaliaMLEAsymptote

public double[][] aitSahaliaMLEAsymptote(double intervalWidth)

Construct the Ait-Sahalia Maximum Likelihood Estimation Sampling Interval Discreteness Error

Parameters:

intervalWidth - Sampling Interval Width

Returns:

The Ait-Sahalia Maximum Likelihood Estimation Sampling Interval Discreteness Error