OrnsteinUhlenbeckPair.java
package org.drip.measure.process;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2020 Lakshmi Krishnamurthy
* Copyright (C) 2019 Lakshmi Krishnamurthy
* Copyright (C) 2018 Lakshmi Krishnamurthy
* Copyright (C) 2017 Lakshmi Krishnamurthy
* Copyright (C) 2016 Lakshmi Krishnamurthy
*
* This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
* asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
* analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
* equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
* numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
* and computational support.
*
* https://lakshmidrip.github.io/DROP/
*
* DROP is composed of three modules:
*
* - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
* - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
* - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
*
* DROP Product Core implements libraries for the following:
* - Fixed Income Analytics
* - Loan Analytics
* - Transaction Cost Analytics
*
* DROP Portfolio Core implements libraries for the following:
* - Asset Allocation Analytics
* - Asset Liability Management Analytics
* - Capital Estimation Analytics
* - Exposure Analytics
* - Margin Analytics
* - XVA Analytics
*
* DROP Computational Core implements libraries for the following:
* - Algorithm Support
* - Computation Support
* - Function Analysis
* - Model Validation
* - Numerical Analysis
* - Numerical Optimizer
* - Spline Builder
* - Statistical Learning
*
* Documentation for DROP is Spread Over:
*
* - Main => https://lakshmidrip.github.io/DROP/
* - Wiki => https://github.com/lakshmiDRIP/DROP/wiki
* - GitHub => https://github.com/lakshmiDRIP/DROP
* - Repo Layout Taxonomy => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
* - Javadoc => https://lakshmidrip.github.io/DROP/Javadoc/index.html
* - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
* - Release Versions => https://lakshmidrip.github.io/DROP/version.html
* - Community Credits => https://lakshmidrip.github.io/DROP/credits.html
* - Issues Catalog => https://github.com/lakshmiDRIP/DROP/issues
* - JUnit => https://lakshmidrip.github.io/DROP/junit/index.html
* - Jacoco => https://lakshmidrip.github.io/DROP/jacoco/index.html
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
*
* You may obtain a copy of the License at
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
*
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/**
* <i>OrnsteinUhlenbeckPair</i> guides the Random Variable Evolution according to 2D Ornstein-Uhlenbeck Mean
* Reverting Process. The References are:
*
* <br><br>
* <ul>
* <li>
* Almgren, R. F. (2009): Optimal Trading in a Dynamic Market
* https://www.math.nyu.edu/financial_mathematics/content/02_financial/2009-2.pdf
* </li>
* <li>
* Almgren, R. F. (2012): Optimal Trading with Stochastic Liquidity and Volatility <i>SIAM Journal
* of Financial Mathematics</i> <b>3 (1)</b> 163-181
* </li>
* <li>
* Geman, H., D. B. Madan, and M. Yor (2001): Time Changes for Levy Processes <i>Mathematical
* Finance</i> <b>11 (1)</b> 79-96
* </li>
* <li>
* Jones, C. M., G. Kaul, and M. L. Lipson (1994): Transactions, Volume, and Volatility <i>Review of
* Financial Studies</i> <b>7 (4)</b> 631-651
* </li>
* <li>
* Walia, N. (2006): <i>Optimal Trading - Dynamic Stock Liquidation Strategies</i> <b>Princeton
* University</b>
* </li>
* </ul>
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/measure/README.md">R<sup>d</sup> Continuous/Discrete Probability Measures</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/measure/process/README.md">Jump Diffusion Evolver Process Variants</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class OrnsteinUhlenbeckPair implements org.drip.measure.process.OrnsteinUhlenbeck {
private double _dblCorrelation = java.lang.Double.NaN;
private org.drip.measure.dynamics.DiffusionEvaluatorOrnsteinUhlenbeck _deouDerived = null;
private org.drip.measure.dynamics.DiffusionEvaluatorOrnsteinUhlenbeck _deouReference = null;
/**
* OrnsteinUhlenbeckPair Constructor
*
* @param deouReference The Reference R^1 Ornstein-Uhlenbeck Evaluator
* @param deouDerived The Derived R^1 Ornstein-Uhlenbeck Evaluator
* @param dblCorrelation The Correlation between the Two Ornstein-Uhlenbeck Processes
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public OrnsteinUhlenbeckPair (
final org.drip.measure.dynamics.DiffusionEvaluatorOrnsteinUhlenbeck deouReference,
final org.drip.measure.dynamics.DiffusionEvaluatorOrnsteinUhlenbeck deouDerived,
final double dblCorrelation)
throws java.lang.Exception
{
if (null == (_deouReference = deouReference) || null == (_deouDerived = deouDerived) ||
!org.drip.numerical.common.NumberUtil.IsValid (_dblCorrelation = dblCorrelation) || _dblCorrelation <
-1. || _dblCorrelation > 1.)
throw new java.lang.Exception ("OrnsteinUhlenbeckPair Constructor => Invalid Inputs");
}
/**
* Retrieve the Reference R^1 Ornstein-Uhlenbeck Evaluator
*
* @return The Reference R^1 Ornstein-Uhlenbeck Evaluator
*/
public org.drip.measure.dynamics.DiffusionEvaluatorOrnsteinUhlenbeck reference()
{
return _deouReference;
}
/**
* Retrieve the Derived R^1 Ornstein-Uhlenbeck Evaluator
*
* @return The Derived R^1 Ornstein-Uhlenbeck Evaluator
*/
public org.drip.measure.dynamics.DiffusionEvaluatorOrnsteinUhlenbeck derived()
{
return _deouDerived;
}
/**
* Retrieve the Correlation between the Ornstein-Uhlenbeck Processes
*
* @return The Correlation between the Ornstein-Uhlenbeck Processes
*/
public double correlation()
{
return _dblCorrelation;
}
/**
* Generate the Adjacent JumpDiffusionEdge Increment Array from the specified Ornstein Uhlenbeck Random
* Variate Pair
*
* @param adblVariatePair The Pair of the Ornstein Uhlenbeck Random Variates
* @param adblDiffusionPair The Pair of Diffusion Realizations
* @param dblTimeIncrement The Time Increment Evolution Unit
*
* @return The Adjacent JumpDiffusionEdge Increment Array
*/
public org.drip.measure.realization.JumpDiffusionEdge[] increment (
final double[] adblVariatePair,
final double[] adblDiffusionPair,
final double dblTimeIncrement)
{
if (null == adblVariatePair || 2 != adblVariatePair.length ||
!org.drip.numerical.common.NumberUtil.IsValid (adblVariatePair) || null == adblDiffusionPair || 2 !=
adblDiffusionPair.length || !org.drip.numerical.common.NumberUtil.IsValid (adblDiffusionPair) ||
!org.drip.numerical.common.NumberUtil.IsValid (dblTimeIncrement) || 0. >= dblTimeIncrement)
return null;
double dblRelaxationTime0 = _deouReference.relaxationTime();
double dblRelaxationTime1 = _deouDerived.relaxationTime();
try {
return new org.drip.measure.realization.JumpDiffusionEdge[] {
org.drip.measure.realization.JumpDiffusionEdge.Standard (
adblVariatePair[0],
-1. * adblVariatePair[0] / dblRelaxationTime0 * dblTimeIncrement,
_deouReference.burstiness() * adblDiffusionPair[0] * java.lang.Math.sqrt (dblTimeIncrement / dblRelaxationTime0),
null,
new org.drip.measure.realization.JumpDiffusionEdgeUnit (
dblTimeIncrement,
adblDiffusionPair[0],
0.
)
),
org.drip.measure.realization.JumpDiffusionEdge.Standard (
adblVariatePair[1],
-1. * adblVariatePair[1] / dblRelaxationTime1 * dblTimeIncrement,
_deouDerived.burstiness() * adblDiffusionPair[1] * java.lang.Math.sqrt (dblTimeIncrement / dblRelaxationTime1),
null,
new org.drip.measure.realization.JumpDiffusionEdgeUnit (
dblTimeIncrement,
adblDiffusionPair[1],
0.
)
)
};
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
/**
* Generate the Weiner Based JumpDiffusionEdge Increment Sequence from the Current Ornstein Uhlenbeck
* Random Variate
*
* @param adblVariatePair The Ornstein Uhlenbeck Random Variate Pair
* @param dblTimeIncrement The Time Increment
*
* @return The Weiner Based JumpDiffusionEdge Increment Sequence from the Current Ornstein Uhlenbeck
* Random Variate
*/
public org.drip.measure.realization.JumpDiffusionEdge[] weinerIncrement (
final double[] adblVariatePair,
final double dblTimeIncrement)
{
try {
double dblFirstWeiner = org.drip.measure.gaussian.NormalQuadrature.Random();
return increment (adblVariatePair, new double[] {dblFirstWeiner, dblFirstWeiner * _dblCorrelation
+ org.drip.measure.gaussian.NormalQuadrature.Random() * java.lang.Math.sqrt (1. -
_dblCorrelation * _dblCorrelation)}, dblTimeIncrement);
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
@Override public double referenceRelaxationTime()
{
return _deouReference.relaxationTime();
}
@Override public double referenceBurstiness()
{
return _deouReference.burstiness();
}
@Override public double referenceMeanReversionLevel()
{
return _deouReference.meanReversionLevel();
}
}