OrnsteinUhlenbeckSequence.java
package org.drip.execution.latent;
/*
* -*- 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>OrnsteinUhlenbeckSequence</i> holds the Sequence of the Market State that drives the Liquidity and the
* Volatility Market States driven using an Ornstein-Uhlenbeck Process. The References are:
*
* <br><br>
* <ul>
* <li>
* Almgren, R. F., and N. Chriss (2000): Optimal Execution of Portfolio Transactions <i>Journal of
* Risk</i> <b>3 (2)</b> 5-39
* </li>
* <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>
* </ul>
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ProductCore.md">Product Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/TransactionCostAnalyticsLibrary.md">Transaction Cost Analytics</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/execution/README.md">Optimal Impact/Capture Based Trading Trajectories - Deterministic, Stochastic, Static, and Dynamic</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/execution/latent/README.md">Correlated Latent Market State Sequence</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class OrnsteinUhlenbeckSequence {
private int _iCount = 0;
private org.drip.execution.latent.MarketState[] _aMS = null;
private double _dblGenerationInterval = java.lang.Double.NaN;
private org.drip.measure.process.OrnsteinUhlenbeck _ou = null;
/**
* Construct a Standard Systemic Instance of OrnsteinUhlenbeckSequence
*
* @param deou The 1D Ornstein-Uhlenbeck Generator Scheme
* @param dblGenerationInterval The Generation Interval
* @param dblInitialMarketState The Initial Market State
* @param iCount Count of the Number of States to be generated
*
* @return The OrnsteinUhlenbeckSequence Instance
*/
public static final OrnsteinUhlenbeckSequence Systemic (
final org.drip.measure.dynamics.DiffusionEvaluatorOrnsteinUhlenbeck deou,
final double dblGenerationInterval,
final double dblInitialMarketState,
final int iCount)
{
if (null == deou || !org.drip.numerical.common.NumberUtil.IsValid (dblGenerationInterval) || 0 >=
dblGenerationInterval || 1 >= iCount)
return null;
double dblTime = 0.;
org.drip.execution.latent.MarketStateSystemic[] aMSS = new
org.drip.execution.latent.MarketStateSystemic[iCount];
try {
aMSS[0] = new org.drip.execution.latent.MarketStateSystemic (dblInitialMarketState);
org.drip.measure.process.DiffusionEvolver de = new org.drip.measure.process.DiffusionEvolver
(deou);
for (int i = 0; i < iCount - 1; ++i) {
org.drip.measure.realization.JumpDiffusionEdge gi = de.weinerIncrement (new
org.drip.measure.realization.JumpDiffusionVertex (dblTime, aMSS[i].common(), 0., false),
dblGenerationInterval);
aMSS[i + 1] = new org.drip.execution.latent.MarketStateSystemic (aMSS[i].common() +
gi.deterministic() + gi.diffusionStochastic());
dblTime += dblGenerationInterval;
}
} catch (java.lang.Exception e) {
e.printStackTrace();
return null;
}
return new OrnsteinUhlenbeckSequence (deou, aMSS, dblGenerationInterval);
}
/**
* Construct a Standard Correlated Instance of OrnsteinUhlenbeckSequence
*
* @param oup2D The 2D Ornstein-Uhlenbeck Generator Scheme
* @param dblGenerationInterval The Generation Interval
* @param dblInitialLiquidityMarketState The Initial Liquidity Market State
* @param dblInitialVolatilityMarketState The Initial Volatility Market State
* @param iCount Count of the Number of States to be generated
*
* @return The OrnsteinUhlenbeckSequence Instance
*/
public static final OrnsteinUhlenbeckSequence Correlated (
final org.drip.measure.process.OrnsteinUhlenbeckPair oup2D,
final double dblGenerationInterval,
final double dblInitialLiquidityMarketState,
final double dblInitialVolatilityMarketState,
final int iCount)
{
if (null == oup2D || !org.drip.numerical.common.NumberUtil.IsValid (dblGenerationInterval) || 0 >=
dblGenerationInterval || 1 >= iCount)
return null;
org.drip.execution.latent.MarketStateCorrelated[] aMSC = new
org.drip.execution.latent.MarketStateCorrelated[iCount];
try {
aMSC[0] = new org.drip.execution.latent.MarketStateCorrelated (dblInitialLiquidityMarketState,
dblInitialVolatilityMarketState);
for (int i = 0; i < iCount - 1; ++i) {
org.drip.measure.realization.JumpDiffusionEdge[] aGI = oup2D.weinerIncrement
(aMSC[i].realization(), dblGenerationInterval);
if (null == aGI || 2 != aGI.length) return null;
aMSC[i + 1] = new org.drip.execution.latent.MarketStateCorrelated (aMSC[i].liquidity() +
aGI[0].deterministic() + aGI[0].diffusionStochastic(), aMSC[i].volatility() +
aGI[1].deterministic() + aGI[1].diffusionStochastic());
}
} catch (java.lang.Exception e) {
e.printStackTrace();
return null;
}
return new OrnsteinUhlenbeckSequence (oup2D, aMSC, dblGenerationInterval);
}
private OrnsteinUhlenbeckSequence (
final org.drip.measure.process.OrnsteinUhlenbeck ou,
final org.drip.execution.latent.MarketState[] aMS,
final double dblGenerationInterval)
{
_ou = ou;
_aMS = aMS;
_iCount = aMS.length;
_dblGenerationInterval = dblGenerationInterval;
}
/**
* Retrieve the Total Count of States realized
*
* @return The Total Count of States realized
*/
public int count()
{
return _iCount;
}
/**
* Retrieve the Generation Interval
*
* @return The Generation Interval
*/
public double generationInterval()
{
return _dblGenerationInterval;
}
/**
* Retrieve the Sequence of Market State Realization
*
* @return The Sequence of Market State Realization
*/
public org.drip.execution.latent.MarketState[] realizedMarketState()
{
return _aMS;
}
/**
* Retrieve the Ornstein-Uhlenbeck Generator Scheme Parameters
*
* @return The Ornstein-Uhlenbeck Generator Scheme Parameters
*/
public org.drip.measure.process.OrnsteinUhlenbeck scheme()
{
return _ou;
}
/**
* Retrieve the Initial Market State
*
* @return The Initial Market State
*/
public org.drip.execution.latent.MarketState initialMarketState()
{
return _aMS[0];
}
}