org.drip.quant.stochastic

Class OrnsteinUhlenbeckProcess2D

java.lang.Object

org.drip.quant.stochastic.OrnsteinUhlenbeckProcess2D

All Implemented Interfaces:

OrnsteinUhlenbeck

public class OrnsteinUhlenbeckProcess2D
extends java.lang.Object
implements OrnsteinUhlenbeck

OrnsteinUhlenbeckProcess2D 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, Senior Thesis, Princeton University.

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor and Description
OrnsteinUhlenbeckProcess2D(OrnsteinUhlenbeckProcess1D oupReference, OrnsteinUhlenbeckProcess1D oupDerived, double dblCorrelation) OrnsteinUhlenbeckProcess2D Constructor

Method Summary

Modifier and Type	Method and Description
double	correlation() Retrieve the Correlation between the Ornstein-Uhlenbeck Processes
OrnsteinUhlenbeckProcess1D	derived() Retrieve the Derived 1D Ornstein-Uhlenbeck Process
GenericIncrement[]	increment(double[] adblOrnsteinUhlenbeckVariate, double[] adblRandomRealization, double dblTimeIncrement) Generate the Adjacent Increment Set from the specified Ornstein Uhlenbeck Random Variate Pair
OrnsteinUhlenbeckProcess1D	reference() Retrieve the Reference 1D Ornstein-Uhlenbeck Process
double	referenceBurstiness() Retrieve the Reference Burstiness Scale
double	referenceMeanReversionLevel() Retrieve the Reference Mean Reversion Level Scale
double	referenceRelaxationTime() Retrieve the Reference Relaxation Time Scale
GenericIncrement[]	weinerIncrement(double[] adblOrnsteinUhlenbeckVariate, double dblTimeIncrement) Generate the Weiner Based 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 Detail

OrnsteinUhlenbeckProcess2D

public OrnsteinUhlenbeckProcess2D(OrnsteinUhlenbeckProcess1D oupReference,
                                  OrnsteinUhlenbeckProcess1D oupDerived,
                                  double dblCorrelation)
                           throws java.lang.Exception

OrnsteinUhlenbeckProcess2D Constructor

Parameters:

oupReference - The Reference 1D Ornstein-Uhlenbeck Process

oupDerived - The Derived 1D Ornstein-Uhlenbeck Process

dblCorrelation - The Correlation between the Two Ornstein-Uhlenbeck Processes

Throws:

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

Method Detail

reference

public OrnsteinUhlenbeckProcess1D reference()

Retrieve the Reference 1D Ornstein-Uhlenbeck Process

Returns:

The Reference 1D Ornstein-Uhlenbeck Process

derived

public OrnsteinUhlenbeckProcess1D derived()

Retrieve the Derived 1D Ornstein-Uhlenbeck Process

Returns:

The Derived 1D Ornstein-Uhlenbeck Process

correlation

public double correlation()

Retrieve the Correlation between the Ornstein-Uhlenbeck Processes

Returns:

The Correlation between the Ornstein-Uhlenbeck Processes

increment

public GenericIncrement[] increment(double[] adblOrnsteinUhlenbeckVariate,
                                    double[] adblRandomRealization,
                                    double dblTimeIncrement)

Generate the Adjacent Increment Set from the specified Ornstein Uhlenbeck Random Variate Pair

Parameters:

adblOrnsteinUhlenbeckVariate - The Array of the Ornstein Uhlenbeck Random Variates

adblRandomRealization - The Array of the Random Stochastic Realization Variates

dblTimeIncrement - The Time Increment Evolution Unit

Returns:

The Adjacent Ornstein Uhlenbeck Increment Set

weinerIncrement

public GenericIncrement[] weinerIncrement(double[] adblOrnsteinUhlenbeckVariate,
                                          double dblTimeIncrement)

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

Parameters:

adblOrnsteinUhlenbeckVariate - The Current Ornstein Uhlenbeck Random Variate

dblTimeIncrement - The Time Increment

Returns:

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

referenceRelaxationTime

public double referenceRelaxationTime()

Description copied from interface: OrnsteinUhlenbeck

Retrieve the Reference Relaxation Time Scale

Specified by:

referenceRelaxationTime in interface OrnsteinUhlenbeck

Returns:

The Reference Relaxation Time Scale

referenceBurstiness

public double referenceBurstiness()

Description copied from interface: OrnsteinUhlenbeck

Retrieve the Reference Burstiness Scale

Specified by:

referenceBurstiness in interface OrnsteinUhlenbeck

Returns:

The Reference Burstiness Scale

referenceMeanReversionLevel

public double referenceMeanReversionLevel()

Description copied from interface: OrnsteinUhlenbeck

Retrieve the Reference Mean Reversion Level Scale

Specified by:

referenceMeanReversionLevel in interface OrnsteinUhlenbeck

Returns:

The Reference Mean Reversion Level Scale