org.drip.quant.stochastic

Class OrnsteinUhlenbeckProcess1D

java.lang.Object

org.drip.quant.stochastic.OrnsteinUhlenbeckProcess1D

All Implemented Interfaces:

OrnsteinUhlenbeck

public class OrnsteinUhlenbeckProcess1D
extends java.lang.Object
implements OrnsteinUhlenbeck

OrnsteinUhlenbeckProcess1D guides the Random Variable Evolution according to 1D 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
OrnsteinUhlenbeckProcess1D(double dblMeanReversionLevel, double dblBurstiness, double dblRelaxationTime) OrnsteinUhlenbeckProcess1D Constructor

Method Summary

Modifier and Type	Method and Description
double	burstiness() Retrieve the Burstiness Parameter
GenericIncrement	increment(double dblOrnsteinUhlenbeckVariate, double dblRandomRealization, double dblTimeIncrement) Generate the Adjacent Increment from the specified Ornstein Uhlenbeck Random Variate
double	meanReversionLevel() Retrieve the Mean Reversion Level
double	referenceBurstiness() Retrieve the Reference Burstiness Scale
double	referenceMeanReversionLevel() Retrieve the Reference Mean Reversion Level Scale
double	referenceRelaxationTime() Retrieve the Reference Relaxation Time Scale
double	relaxationTime() Retrieve the Relaxation Time
GenericIncrement	weinerIncrement(double dblOrnsteinUhlenbeckVariate, double dblTimeIncrement) Generate the Adjacent Increment from the specified Ornstein Uhlenbeck Variate and a Weiner Driver
static OrnsteinUhlenbeckProcess1D	ZeroMean(double dblBurstiness, double dblRelaxationTime) Construct a Zero-Mean Instance of OrnsteinUhlenbeckProcess1D

Methods inherited from class java.lang.Object

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

Constructor Detail

OrnsteinUhlenbeckProcess1D

public OrnsteinUhlenbeckProcess1D(double dblMeanReversionLevel,
                                  double dblBurstiness,
                                  double dblRelaxationTime)
                           throws java.lang.Exception

OrnsteinUhlenbeckProcess1D Constructor

Parameters:

dblMeanReversionLevel - The Mean Reversion Level

dblBurstiness - The Burstiness Parameter

dblRelaxationTime - The Relaxation Time

Throws:

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

Method Detail

ZeroMean

public static final OrnsteinUhlenbeckProcess1D ZeroMean(double dblBurstiness,
                                                        double dblRelaxationTime)

Construct a Zero-Mean Instance of OrnsteinUhlenbeckProcess1D

Parameters:

dblBurstiness - The Burstiness Parameter

dblRelaxationTime - The Relaxation Time

Returns:

The Zero-Mean Instance of OrnsteinUhlenbeckProcess1D

meanReversionLevel

public double meanReversionLevel()

Retrieve the Mean Reversion Level

Returns:

The Mean Reversion Level

burstiness

public double burstiness()

Retrieve the Burstiness Parameter

Returns:

The Burstiness Parameter

relaxationTime

public double relaxationTime()

Retrieve the Relaxation Time

Returns:

The Relaxation Time

increment

public GenericIncrement increment(double dblOrnsteinUhlenbeckVariate,
                                  double dblRandomRealization,
                                  double dblTimeIncrement)

Generate the Adjacent Increment from the specified Ornstein Uhlenbeck Random Variate

Parameters:

dblOrnsteinUhlenbeckVariate - The Ornstein Uhlenbeck Random Variate

dblRandomRealization - The Random Stochastic Realization Variate

dblTimeIncrement - The Time Increment Evolution Unit

Returns:

The Adjacent Ornstein Uhlenbeck Increment

weinerIncrement

public GenericIncrement weinerIncrement(double dblOrnsteinUhlenbeckVariate,
                                        double dblTimeIncrement)

Generate the Adjacent Increment from the specified Ornstein Uhlenbeck Variate and a Weiner Driver

Parameters:

dblOrnsteinUhlenbeckVariate - The Ornstein Uhlenbeck Random Variate

dblTimeIncrement - The Time Increment Evolution Unit

Returns:

The Adjacent Ornstein Uhlenbeck Increment

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