LinearImpactWithDrift.java

  1. package org.drip.sample.execution;

  3. import org.drip.execution.capture.LinearImpactTrajectoryEstimator;
  4. import org.drip.execution.dynamics.*;
  5. import org.drip.execution.impact.*;
  6. import org.drip.execution.nonadaptive.StaticOptimalSchemeDiscrete;
  7. import org.drip.execution.optimum.EfficientTradingTrajectoryDiscrete;
  8. import org.drip.execution.parameters.*;
  9. import org.drip.execution.profiletime.UniformParticipationRateLinear;
  10. import org.drip.execution.risk.MeanVarianceObjectiveUtility;
  11. import org.drip.execution.strategy.*;
  12. import org.drip.function.r1tor1.FlatUnivariate;
  13. import org.drip.measure.gaussian.R1UnivariateNormal;
  14. import org.drip.numerical.common.FormatUtil;
  15. import org.drip.service.env.EnvManager;

  17. /*
  18.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  19.  */

  21. /*!
  22.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  23.  * Copyright (C) 2018 Lakshmi Krishnamurthy
  24.  * Copyright (C) 2017 Lakshmi Krishnamurthy
  25.  * Copyright (C) 2016 Lakshmi Krishnamurthy
  26.  * 
  27.  *  This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
  28.  *      calculations, valuation adjustment, and portfolio construction within and across fixed income,
  29.  *      credit, commodity, equity, FX, and structured products.
  30.  *  
  31.  *      https://lakshmidrip.github.io/DROP/
  32.  *  
  33.  *  DROP is composed of three modules:
  34.  *  
  35.  *  - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
  36.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  37.  *  - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
  38.  * 
  39.  *  DROP Analytics Core implements libraries for the following:
  40.  *  - Fixed Income Analytics
  41.  *  - Asset Backed Analytics
  42.  *  - XVA Analytics
  43.  *  - Exposure and Margin Analytics
  44.  * 
  45.  *  DROP Portfolio Core implements libraries for the following:
  46.  *  - Asset Allocation Analytics
  47.  *  - Transaction Cost Analytics
  48.  * 
  49.  *  DROP Numerical Core implements libraries for the following:
  50.  *  - Statistical Learning
  51.  *  - Numerical Optimizer
  52.  *  - Spline Builder
  53.  *  - Algorithm Support
  54.  * 
  55.  *  Documentation for DROP is Spread Over:
  56.  * 
  57.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  58.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  59.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  60.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  61.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  62.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  63.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  64.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  65.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  66.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  67.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  68.  * 
  69.  *  Licensed under the Apache License, Version 2.0 (the "License");
  70.  *      you may not use this file except in compliance with the License.
  71.  *   
  72.  *  You may obtain a copy of the License at
  73.  *      http://www.apache.org/licenses/LICENSE-2.0
  74.  *  
  75.  *  Unless required by applicable law or agreed to in writing, software
  76.  *      distributed under the License is distributed on an "AS IS" BASIS,
  77.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  78.  *  
  79.  *  See the License for the specific language governing permissions and
  80.  *      limitations under the License.
  81.  */

  83. /**
  84.  * <i>LinearImpactWithDrift</i> generates the Trade/Holdings List of Optimal Execution Schedule based on the
  85.  * Evolution Walk Parameters specified. The Generation follows a Numerical Optimizer Scheme, as opposed to
  86.  * the Almgren-Chriss Closed Form; it includes the Impact of Drift. The References are:
  87.  * 
  88.  * <br><br>
  89.  *  <ul>
  90.  *      <li>
  91.  *          Almgren, R., and N. Chriss (1999): Value under Liquidation <i>Risk</i> <b>12 (12)</b>
  92.  *      </li>
  93.  *      <li>
  94.  *          Almgren, R., and N. Chriss (2000): Optimal Execution of Portfolio Transactions <i>Journal of
  95.  *              Risk</i> <b>3 (2)</b> 5-39
  96.  *      </li>
  97.  *      <li>
  98.  *          Bertsimas, D., and A. W. Lo (1998): Optimal Control of Execution Costs <i>Journal of Financial
  99.  *              Markets</i> <b>1</b> 1-50
  100.  *      </li>
  101.  *      <li>
  102.  *          Chan, L. K. C., and J. Lakonishak (1995): The Behavior of Stock Prices around Institutional
  103.  *              Trades <i>Journal of Finance</i> <b>50</b> 1147-1174
  104.  *      </li>
  105.  *      <li>
  106.  *          Keim, D. B., and A. Madhavan (1997): Transaction Costs and Investment Style: An Inter-exchange
  107.  *              Analysis of Institutional Equity Trades <i>Journal of Financial Economics</i> <b>46</b>
  108.  *              265-292
  109.  *      </li>
  110.  *  </ul>
  111.  * 
  112.  * <br><br>
  113.  *  <ul>
  114.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/PortfolioCore.md">Portfolio Core Module</a></li>
  115.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/TransactionCostAnalyticsLibrary.md">Transaction Cost Analytics Library</a></li>
  116.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">Sample</a></li>
  117.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/execution/README.md">Execution</a></li>
  118.  *  </ul>
  119.  * <br><br>
  120.  * 
  121.  * @author Lakshmi Krishnamurthy
  122.  */

  124. public class LinearImpactWithDrift {

  126.     public static void main (
  127.         final String[] astrArgs)
  128.         throws Exception
  129.     {
  130.         EnvManager.InitEnv ("");

  132.         double dblS0 = 50.;
  133.         double dblX = 1000000.;
  134.         double dblT = 5.;
  135.         int iN = 5;
  136.         double dblAnnualVolatility = 0.30;
  137.         double dblAnnualReturns = 0.10;
  138.         double dblBidAsk = 0.125;
  139.         double dblDailyVolume = 5.e06;
  140.         double dblDailyVolumePermanentImpact = 0.1;
  141.         double dblDailyVolumeTemporaryImpact = 0.01;
  142.         double dblLambdaU = 1.e-06;

  144.         ArithmeticPriceDynamicsSettings apds = ArithmeticPriceDynamicsSettings.FromAnnualReturnsSettings (
  145.             dblAnnualReturns,
  146.             dblAnnualVolatility,
  147.             0.,
  148.             dblS0
  149.         );

  151.         double dblAlpha = apds.drift();

  153.         double dblSigma = apds.epochVolatility();

  155.         PriceMarketImpactLinear pmil = new PriceMarketImpactLinear (
  156.             new AssetTransactionSettings (
  157.                 dblS0,
  158.                 dblDailyVolume,
  159.                 dblBidAsk
  160.             ),
  161.             dblDailyVolumePermanentImpact,
  162.             dblDailyVolumeTemporaryImpact
  163.         );

  165.         ParticipationRateLinear prlPermanent = (ParticipationRateLinear) pmil.permanentTransactionFunction();

  167.         ParticipationRateLinear prlTemporary = (ParticipationRateLinear) pmil.temporaryTransactionFunction();

  169.         DiscreteTradingTrajectoryControl dttc = DiscreteTradingTrajectoryControl.FixedInterval (
  170.             new OrderSpecification (
  171.                 dblX,
  172.                 dblT
  173.             ),
  174.             iN
  175.         );

  177.         LinearPermanentExpectationParameters lpep = ArithmeticPriceEvolutionParametersBuilder.LinearExpectation (
  178.             new ArithmeticPriceDynamicsSettings (
  179.                 dblAlpha,
  180.                 new FlatUnivariate (dblSigma),
  181.                 0.
  182.             ),
  183.             new UniformParticipationRateLinear (prlPermanent),
  184.             new UniformParticipationRateLinear (prlTemporary)
  185.         );

  187.         EfficientTradingTrajectoryDiscrete ettd = (EfficientTradingTrajectoryDiscrete) new StaticOptimalSchemeDiscrete (
  188.             dttc,
  189.             lpep,
  190.             new MeanVarianceObjectiveUtility (dblLambdaU)
  191.         ).generate();

  193.         double[] adblExecutionTimeNode = ettd.executionTimeNode();

  195.         double[] adblTradeList = ettd.tradeList();

  197.         double[] adblHoldings = ettd.holdings();

  199.         LinearImpactTrajectoryEstimator lite = new LinearImpactTrajectoryEstimator (ettd);

  201.         R1UnivariateNormal r1un = lite.totalCostDistributionSynopsis (lpep);

  203.         System.out.println ("\n\t|---------------------------------------------||");

  205.         System.out.println ("\t| ALMGREN-CHRISS TRAJECTORY GENERATOR INPUTS  ||");

  207.         System.out.println ("\t|---------------------------------------------||");

  209.         System.out.println ("\t| Initial Stock Price           : " + dblS0);

  211.         System.out.println ("\t| Initial Holdings              : " + dblX);

  213.         System.out.println ("\t| Liquidation Time              : " + dblT);

  215.         System.out.println ("\t| Number of Time Periods        : " + iN);

  217.         System.out.println ("\t| Annual Volatility             :" + FormatUtil.FormatDouble (dblAnnualVolatility, 1, 0, 100.) + "%");

  219.         System.out.println ("\t| Annual Growth                 :" + FormatUtil.FormatDouble (dblAnnualReturns, 1, 0, 100.) + "%");

  221.         System.out.println ("\t| Bid-Ask Spread                : " + dblBidAsk);

  223.         System.out.println ("\t| Daily Volume                  : " + dblDailyVolume);

  225.         System.out.println ("\t| Daily Volume Temporary Impact : " + dblDailyVolumeTemporaryImpact);

  227.         System.out.println ("\t| Daily Volume Permanent Impact : " + dblDailyVolumePermanentImpact);

  229.         System.out.println ("\t| Daily Volume 5 million Shares : " + prlPermanent.slope());

  231.         System.out.println ("\t| Static Holdings 11,000 Shares : " + dblLambdaU);

  233.         System.out.println ("\t|");

  235.         System.out.println (
  236.             "\t| Daily Volatility              : " +
  237.             FormatUtil.FormatDouble (dblSigma, 1, 4, 1.)
  238.         );

  240.         System.out.println (
  241.             "\t| Daily Returns                 : " +
  242.             FormatUtil.FormatDouble (dblAlpha, 1, 4, 1.)
  243.         );

  245.         System.out.println ("\t| Temporary Impact Fixed Offset :  " + prlTemporary.offset());

  247.         System.out.println ("\t| Eta                           :  " + prlTemporary.slope());

  249.         System.out.println ("\t| Gamma                         :  " + prlPermanent.slope());

  251.         System.out.println ("\t|---------------------------------------------||");

  253.         System.out.println ("\n\t|-----------------------------||");

  255.         System.out.println ("\t| Optimal Trading Trajectory  ||");

  257.         System.out.println ("\t| ------- ------- ----------  ||");

  259.         System.out.println ("\t|     L -> R:                 ||");

  261.         System.out.println ("\t|        Time Node            ||");

  263.         System.out.println ("\t|        Holdings             ||");

  265.         System.out.println ("\t|        Trade Amount         ||");

  267.         System.out.println ("\t|-----------------------------||");

  269.         for (int i = 0; i <= iN; ++i) {
  270.             if (i == 0)
  271.                 System.out.println (
  272.                     "\t|" + FormatUtil.FormatDouble (adblExecutionTimeNode[i], 1, 0, 1.) + " => " +
  273.                     FormatUtil.FormatDouble (adblHoldings[i], 7, 1, 1.) + " | " +
  274.                     FormatUtil.FormatDouble (0., 6, 1, 1.) + " ||"
  275.                 );
  276.             else
  277.                 System.out.println (
  278.                     "\t|" + FormatUtil.FormatDouble (adblExecutionTimeNode[i], 1, 0, 1.) + " => " +
  279.                     FormatUtil.FormatDouble (adblHoldings[i], 7, 1, 1.) + " | " +
  280.                     FormatUtil.FormatDouble (adblTradeList[i - 1], 6, 1, 1.) + " ||"
  281.                 );
  282.         }

  284.         System.out.println ("\t|-----------------------------||");

  286.         System.out.println ("\n\t|--------------------------------------------------------------||");

  288.         System.out.println ("\t| TRANSACTION COST RECONCILIATION: OPTIMAL vs. EXPLICIT LINEAR ||");

  290.         System.out.println ("\t|--------------------------------------------------------------||");

  292.         System.out.println (
  293.             "\t| Transaction Cost Expectation         : " +
  294.             FormatUtil.FormatDouble (r1un.mean(), 6, 1, 1.) + " | " +
  295.             FormatUtil.FormatDouble (ettd.transactionCostExpectation(), 6, 1, 1.) + " ||"
  296.         );

  298.         System.out.println (
  299.             "\t| Transaction Cost Variance (X 10^-06) : " +
  300.             FormatUtil.FormatDouble (r1un.variance(), 6, 1, 1.e-06) + " | " +
  301.             FormatUtil.FormatDouble (ettd.transactionCostVariance(), 6, 1, 1.e-06) + " ||"
  302.         );

  304.         System.out.println ("\t|--------------------------------------------------------------||");

  306.         EnvManager.TerminateEnv();
  307.     }
  308. }
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