RollingHorizonOptimalTradeRate.java
package org.drip.sample.almgren2012;
import org.drip.execution.adaptive.*;
import org.drip.execution.hjb.NonDimensionalCostEvolverSystemic;
import org.drip.execution.latent.*;
import org.drip.execution.risk.MeanVarianceObjectiveUtility;
import org.drip.execution.strategy.OrderSpecification;
import org.drip.execution.tradingtime.CoordinatedVariation;
import org.drip.measure.dynamics.DiffusionEvaluatorOrnsteinUhlenbeck;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
/*
* -*- 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>RollingHorizonOptimalTradeRate</i> simulates the Trade Rate from the Sample Realization of the Adaptive
* Cost Strategy using the Market State Trajectory the follows the Zero Mean Ornstein-Uhlenbeck Evolution
* Dynamics. Instead of a HJB Based Truly Adaptive Strategy, a Rolling Horizon Approximation is used. 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>
* Walia, N. (2006): Optimal Trading: Dynamic Stock Liquidation Strategies <b>Princeton
* University</b>
* </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/sample/README.md">DROP API Construction and Usage</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/almgren2012/README.md">Almgren (2012) Dynamic Optimal Adaptive</a></li>
* </ul>
* <br><br>
*
* @author Lakshmi Krishnamurthy
*/
public class RollingHorizonOptimalTradeRate {
public static final void main (
final String[] astrArgs)
throws Exception
{
EnvManager.InitEnv (
"",
true
);
double dblSize = 1.;
int iNumTimeNode = 51;
double dblBurstiness = 1.;
double dblExecutionTime = 10.;
double dblRelaxationTime = 1.;
double dblReferenceLiquidity = 1.;
double dblReferenceVolatility = 1.;
double dblInitialMarketState = -0.5;
double[] adblRiskAversion = new double[] {
0.01,
0.04,
0.09,
0.16,
0.36,
0.64,
1.00
};
double dblNonDimensionalTimeInterval = dblExecutionTime / (iNumTimeNode - 1) / dblRelaxationTime;
double[][] aadblAdjustedNonDimensionalTradeRate = new double[adblRiskAversion.length][];
OrderSpecification os = new OrderSpecification (
dblSize,
dblExecutionTime
);
CoordinatedVariation cv = new CoordinatedVariation (
dblReferenceVolatility,
dblReferenceLiquidity
);
DiffusionEvaluatorOrnsteinUhlenbeck oup1D = DiffusionEvaluatorOrnsteinUhlenbeck.ZeroMean (
dblBurstiness,
dblRelaxationTime
);
MarketState[] aMS = OrnsteinUhlenbeckSequence.Systemic (
oup1D,
dblNonDimensionalTimeInterval * dblRelaxationTime,
dblInitialMarketState,
iNumTimeNode
).realizedMarketState();
for (int i = 0; i < adblRiskAversion.length; ++i)
aadblAdjustedNonDimensionalTradeRate[i] = new CoordinatedVariationTrajectoryGenerator (
os,
cv,
new MeanVarianceObjectiveUtility (adblRiskAversion[i]),
NonDimensionalCostEvolverSystemic.Standard (oup1D),
CoordinatedVariationTrajectoryGenerator.TRADE_RATE_ZERO_INITIALIZATION
).rollingHorizon (aMS).nonDimensionalTradeRate();
System.out.println();
System.out.println ("\t||-----------------------------------------------------------------------------||");
System.out.println ("\t|| ROLLING HORIZON OPTIMAL TRAJECTORY TRADE RATE ||");
System.out.println ("\t||-----------------------------------------------------------------------------||");
System.out.println ("\t|| L -> R: ||");
System.out.println ("\t|| - Time ||");
for (int j = 0; j < adblRiskAversion.length; ++j)
System.out.println (
"\t|| - Non Dimensional Risk Aversion =>" +
FormatUtil.FormatDouble (dblRelaxationTime * dblReferenceVolatility * Math.sqrt (adblRiskAversion[j] / dblReferenceLiquidity), 1, 2, 1.) +
" ||"
);
System.out.println ("\t||-----------------------------------------------------------------------------||");
for (int i = 0; i < iNumTimeNode - 1; ++i) {
String strDump = "\t|| " + FormatUtil.FormatDouble (i * dblNonDimensionalTimeInterval * dblRelaxationTime, 1, 2, 1.);
for (int j = 0; j < adblRiskAversion.length; ++j)
strDump = strDump + " | " + FormatUtil.FormatDouble (aadblAdjustedNonDimensionalTradeRate[j][i], 1, 4, 1.);
System.out.println (strDump + " ||");
}
System.out.println ("\t||-----------------------------------------------------------------------------||");
EnvManager.TerminateEnv();
}
}