Package org.drip.dynamics.process

Class R1StochasticEvolver

java.lang.Object

org.drip.dynamics.process.R1StochasticEvolver

Direct Known Subclasses:

R1BrownianStochasticEvolver, R1CKLSStochasticEvolver

public class R1StochasticEvolver
extends java.lang.Object

R1StochasticEvolver implements the R¹ 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 = Ito-Dynamics Based Stochastic Process

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
R1StochasticEvolver(R1ToR1Drift driftFunction, R1ToR1Volatility volatilityFunction, R1StochasticDriver stochasticDriver)	R1StochasticEvolver Constructor

Method Summary

Modifier and Type	Method	Description
R1ToR1Drift	driftFunction()	Retrieve the Drift Function
TimeR1Vertex	evolve(TimeR1Vertex currentVertex, double timeIncrement)	Generate the Next Vertex in the Iteration
R1FokkerPlanck	fokkerPlanckGenerator()	Construct the Fokker Planck PDF Generator corresponding to R1 Stochastic Evolver
R1Univariate	futureValueDistribution(double x0, double t)	Generate the Future Value Distribution at Time t
PopulationCentralMeasures	steadyStatePopulationCentralMeasures(double x0)	Generate the Steady State Population Central Measures
R1StochasticDriver	stochasticDriver()	Retrieve the Stochastic Driver
PopulationCentralMeasures	temporalPopulationCentralMeasures(double x0, double t)	Estimate the Temporal Central Measures for the Underlier given the Delta 0 Starting PDF
R1ToR1Volatility	volatilityFunction()	Retrieve the Volatility Function

Methods inherited from class java.lang.Object

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

Constructor Details

R1StochasticEvolver

public R1StochasticEvolver(R1ToR1Drift driftFunction,
R1ToR1Volatility volatilityFunction,
R1StochasticDriver stochasticDriver)
                    throws java.lang.Exception

R1StochasticEvolver Constructor

Parameters:

driftFunction - Drift Function

volatilityFunction - Volatility Function

stochasticDriver - Stochastic Driver

Throws:

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

Method Details

driftFunction

public R1ToR1Drift driftFunction()

Retrieve the Drift Function

Returns:

The Drift Function

volatilityFunction

public R1ToR1Volatility volatilityFunction()

Retrieve the Volatility Function

Returns:

The Volatility Function

stochasticDriver

public R1StochasticDriver stochasticDriver()

Retrieve the Stochastic Driver

Returns:

The Stochastic Driver

evolve

public TimeR1Vertex evolve(TimeR1Vertex currentVertex,
double timeIncrement)

Generate the Next Vertex in the Iteration

Parameters:

currentVertex - The Current Vertex

timeIncrement - The Time Increment

Returns:

The Next Vertex

temporalPopulationCentralMeasures

public PopulationCentralMeasures temporalPopulationCentralMeasures(double x0,
double t)

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

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)

Generate the Steady State Population Central Measures

Parameters:

x0 - Starting Variate

Returns:

The Steady State Population Central Measures

fokkerPlanckGenerator

public R1FokkerPlanck fokkerPlanckGenerator()

Construct the Fokker Planck PDF Generator corresponding to R¹ Stochastic Evolver

Returns:

The Fokker Planck PDF Generator corresponding to R¹ Stochastic Evolver

futureValueDistribution

public R1Univariate futureValueDistribution(double x0,
double t)

Generate the Future Value Distribution at Time t

Parameters:

x0 - Starting Variate

t - Time

Returns:

The Future Value Distribution