Package org.drip.measure.dynamics

Class OrnsteinUhlenbeckPair

java.lang.Object

org.drip.measure.dynamics.OrnsteinUhlenbeckPair

All Implemented Interfaces:

OrnsteinUhlenbeck

public class OrnsteinUhlenbeckPair
extends java.lang.Object
implements OrnsteinUhlenbeck

OrnsteinUhlenbeckPair guides the Random Variable Evolution according to 2D Ornstein-Uhlenbeck Mean Reverting Process. The References are:

• Almgren, R. F. (2009): Optimal Trading in a Dynamic Market https://www.math.nyu.edu/financial_mathematics/content/02_financial/2009-2.pdf
• Almgren, R. F. (2012): Optimal Trading with Stochastic Liquidity and Volatility SIAM Journal of Financial Mathematics 3 (1) 163-181
• Geman, H., D. B. Madan, and M. Yor (2001): Time Changes for Levy Processes Mathematical Finance 11 (1) 79-96
• Jones, C. M., G. Kaul, and M. L. Lipson (1994): Transactions, Volume, and Volatility Review of Financial Studies 7 (4) 631-651
• Walia, N. (2006): Optimal Trading - Dynamic Stock Liquidation Strategies Princeton University

It provides the following Functionality:

• OrnsteinUhlenbeckPair Constructor
• Retrieve the Reference R¹ Ornstein-Uhlenbeck Evaluator
• Retrieve the Derived R¹ Ornstein-Uhlenbeck Evaluator
• Retrieve the Correlation between the Ornstein-Uhlenbeck Processes
• Generate the Adjacent Jump Diffusion Edge Increment Array from the specified Ornstein Uhlenbeck Random Variate Pair
• Generate the Weiner Based JumpDiffusionEdge Increment Sequence from the Current Ornstein Uhlenbeck Random Variate
• Retrieve the Reference Relaxation Time Scale
• Retrieve the Reference Burstiness Scale
• Retrieve the Reference Mean Reversion Level Scale

Module	Computational Core Module
Library	Numerical Analysis Library
Project	Rd Continuous/Discrete Probability Measures
Package	Jump Diffusion Evolution Evaluator Variants

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
OrnsteinUhlenbeckPair(DiffusionEvaluatorOrnsteinUhlenbeck referenceDiffusionEvaluator, DiffusionEvaluatorOrnsteinUhlenbeck derivedDiffusionEvaluator, double correlation)	OrnsteinUhlenbeckPair Constructor

Method Summary

Modifier and Type	Method	Description
double	correlation()	Retrieve the Correlation between the Ornstein-Uhlenbeck Processes
DiffusionEvaluatorOrnsteinUhlenbeck	derived()	Retrieve the Derived R1 Ornstein-Uhlenbeck Evaluator
JumpDiffusionEdge[]	increment(double[] variatePair, double[] diffusionPair, double timeIncrement)	Generate the Adjacent Jump Diffusion Edge Increment Array from the specified Ornstein Uhlenbeck Random Variate Pair
DiffusionEvaluatorOrnsteinUhlenbeck	reference()	Retrieve the Reference R1 Ornstein-Uhlenbeck Evaluator
double	referenceBurstiness()	Retrieve the Reference Burstiness Scale
double	referenceMeanReversionLevel()	Retrieve the Reference Mean Reversion Level Scale
double	referenceRelaxationTime()	Retrieve the Reference Relaxation Time Scale
JumpDiffusionEdge[]	weinerIncrement(double[] variatePair, double timeIncrement)	Generate the Weiner Based JumpDiffusionEdge Increment Sequence from the Current Ornstein Uhlenbeck Random Variate

Methods inherited from class java.lang.Object

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

Constructor Details

OrnsteinUhlenbeckPair

public OrnsteinUhlenbeckPair(DiffusionEvaluatorOrnsteinUhlenbeck referenceDiffusionEvaluator,
DiffusionEvaluatorOrnsteinUhlenbeck derivedDiffusionEvaluator,
double correlation)
                      throws java.lang.Exception

OrnsteinUhlenbeckPair Constructor

Parameters:

referenceDiffusionEvaluator - The Reference R¹ Ornstein-Uhlenbeck Evaluator

derivedDiffusionEvaluator - The Derived R¹ Ornstein-Uhlenbeck Evaluator

correlation - The Correlation between the Two Ornstein-Uhlenbeck Processes

Throws:

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

Method Details

reference

public DiffusionEvaluatorOrnsteinUhlenbeck reference()

Retrieve the Reference R¹ Ornstein-Uhlenbeck Evaluator

Returns:

The Reference R¹ Ornstein-Uhlenbeck Evaluator

derived

public DiffusionEvaluatorOrnsteinUhlenbeck derived()

Retrieve the Derived R¹ Ornstein-Uhlenbeck Evaluator

Returns:

The Derived R¹ Ornstein-Uhlenbeck Evaluator

correlation

public double correlation()

Retrieve the Correlation between the Ornstein-Uhlenbeck Processes

Returns:

The Correlation between the Ornstein-Uhlenbeck Processes

increment

public JumpDiffusionEdge[] increment(double[] variatePair,
double[] diffusionPair,
double timeIncrement)

Generate the Adjacent Jump Diffusion Edge Increment Array from the specified Ornstein Uhlenbeck Random Variate Pair

Parameters:

variatePair - The Pair of the Ornstein Uhlenbeck Random Variates

diffusionPair - The Pair of Diffusion Realization

timeIncrement - The Time Increment Evolution Unit

Returns:

The Adjacent Jump Diffusion Edge Increment Array

weinerIncrement

public JumpDiffusionEdge[] weinerIncrement(double[] variatePair,
double timeIncrement)

Generate the Weiner Based JumpDiffusionEdge Increment Sequence from the Current Ornstein Uhlenbeck Random Variate

Parameters:

variatePair - The Ornstein Uhlenbeck Random Variate Pair

timeIncrement - The Time Increment

Returns:

The Weiner Based JumpDiffusionEdge Increment Sequence from the Current Ornstein-Uhlenbeck Random Variate

referenceRelaxationTime

public double referenceRelaxationTime()

Retrieve the Reference Relaxation Time Scale

Specified by:

referenceRelaxationTime in interface OrnsteinUhlenbeck

Returns:

The Reference Relaxation Time Scale

referenceBurstiness

public double referenceBurstiness()

Retrieve the Reference Burstiness Scale

Specified by:

referenceBurstiness in interface OrnsteinUhlenbeck

Returns:

The Reference Burstiness Scale

referenceMeanReversionLevel

public double referenceMeanReversionLevel()

Retrieve the Reference Mean Reversion Level Scale

Specified by:

referenceMeanReversionLevel in interface OrnsteinUhlenbeck

Returns:

The Reference Mean Reversion Level Scale