Package org.drip.dynamics.process

Class R1ProbabilityDensityFunctionCIR

java.lang.Object

org.drip.dynamics.process.R1ProbabilityDensityFunction

org.drip.dynamics.process.R1ProbabilityDensityFunctionCIR

All Implemented Interfaces:

R2ToR1

public class R1ProbabilityDensityFunctionCIR
extends R1ProbabilityDensityFunction

R1ProbabilityDensityFunctionCIR exposes the R¹ Probability Density Function Evaluation Equation for an Underlying CIR Process. The References are:

• Bogoliubov, N. N., and D. P. Sankevich (1994): N. N. Bogoliubov and Statistical Mechanics Russian Mathematical Surveys 49 (5) 19-49
• Holubec, V., K. Kroy, and S. Steffenoni (2019): Physically Consistent Numerical Solver for Time-dependent Fokker-Planck Equations Physical Review E 99 (4) 032117
• Kadanoff, L. P. (2000): Statistical Physics: Statics, Dynamics, and Re-normalization World Scientific
• Ottinger, H. C. (1996): Stochastic Processes in Polymeric Fluids Springer-Verlag Berlin-Heidelberg
• Wikipedia (2019): Fokker-Planck Equation https://en.wikipedia.org/wiki/Fokker%E2%80%93Planck_equation

• 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
R1ProbabilityDensityFunctionCIR(double r0, CKLSParameters cklsParameters, ModifiedBesselFirstKindEstimator modifiedBesselFirstKindEstimator)	R1ProbabilityDensityFunctionCIR Constructor

Method Summary

Modifier and Type	Method	Description
CKLSParameters	cklsParameters()	Retrieve the CKLS Parameters
double	density(TimeR1Vertex r1TimeVertex)	Calculates the PDF Density Value
ModifiedBesselFirstKindEstimator	modifiedBesselFirstKindEstimator()	Retrieve the Modified Bessel Estimator of the First Kind
double	q()	Retrieve "q"
double	r0()	Retrieve the Starting Value for r

Methods inherited from class org.drip.dynamics.process.R1ProbabilityDensityFunction

evaluate

Methods inherited from class java.lang.Object

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

Constructor Details

R1ProbabilityDensityFunctionCIR

public R1ProbabilityDensityFunctionCIR(double r0,
CKLSParameters cklsParameters,
ModifiedBesselFirstKindEstimator modifiedBesselFirstKindEstimator)
                                throws java.lang.Exception

R1ProbabilityDensityFunctionCIR Constructor

Parameters:

r0 - Starting Value for r

cklsParameters - The CKLS Parameters

modifiedBesselFirstKindEstimator - Modified Bessel Estimator of the First Kind

Throws:

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

Method Details

q

public double q()

Retrieve "q"

Returns:

"q"

r0

public double r0()

Retrieve the Starting Value for r

Returns:

Starting Value for r

cklsParameters

public CKLSParameters cklsParameters()

Retrieve the CKLS Parameters

Returns:

The CKLS Parameters

modifiedBesselFirstKindEstimator

public ModifiedBesselFirstKindEstimator modifiedBesselFirstKindEstimator()

Retrieve the Modified Bessel Estimator of the First Kind

Returns:

The Modified Bessel Estimator of the First Kind

density

public double density(TimeR1Vertex r1TimeVertex)
               throws java.lang.Exception

Description copied from class: R1ProbabilityDensityFunction

Calculates the PDF Density Value

Specified by:

density in class R1ProbabilityDensityFunction

Parameters:

r1TimeVertex - The R¹ Property Variate/Time Coordinate Vertex

Returns:

The PDF Density Value

Throws:

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