OptimalTrajectoryNoDrift.java

  1. package org.drip.sample.lvar;

  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.ArithmeticPriceDynamicsSettings;
  9. import org.drip.execution.profiletime.UniformParticipationRateLinear;
  10. import org.drip.execution.risk.PowerVarianceObjectiveUtility;
  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>OptimalTrajectoryNoDrift</i> generates the Trade/Holdings List of Optimal Execution Schedule based on
  85.  * the Evolution Walk Parameters specified according to the Liquidity VaR Optimal Objective Function,
  86.  * exclusive of Drift. The Generation follows a Numerical Optimizer Scheme. 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.  *          Almgren, R. (2003): Optimal Execution with Non-linear Impact Functions and Trading Enhanced Risk
  99.  *              <i>Applied Mathematical Finance</i> <b>10</b> 1-18
  100.  *      </li>
  101.  *      <li>
  102.  *          Artzner, P., F. Delbaen, J. M. Eber, and D. Heath (1999): Coherent Measures of Risk
  103.  *              <i>Mathematical Finance</i> <b>9</b> 203-228
  104.  *      </li>
  105.  *      <li>
  106.  *          Basak, S., and A. Shapiro (2001): Value-at-Risk Based Risk Management: Optimal Policies and Asset
  107.  *              Prices <i>Review of Financial Studies</i> <b>14</b> 371-405
  108.  *      </li>
  109.  *  </ul>
  110.  * 
  111.  * <br><br>
  112.  *  <ul>
  113.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/PortfolioCore.md">Portfolio Core Module</a></li>
  114.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/TransactionCostAnalyticsLibrary.md">Transaction Cost Analytics Library</a></li>
  115.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">Sample</a></li>
  116.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/lvar/README.md">Liquidity VaR</a></li>
  117.  *  </ul>
  118.  * <br><br>
  119.  * 
  120.  * @author Lakshmi Krishnamurthy
  121.  */

  123. public class OptimalTrajectoryNoDrift {

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

  131.         double dblS0 = 50.;
  132.         double dblSigma = 0.9487;
  133.         double dblAlpha = 0.02;
  134.         double dblEpsilon = 0.0625;
  135.         double dblGamma = 2.5e-07;
  136.         double dblEta = 2.5e-06;
  137.         double dblConfidenceLevel = 0.90;

  139.         double dblX = 1000000.;
  140.         double dblT = 5.;
  141.         int iN = 5;

  143.         double dblLambdaV = R1UnivariateNormal.Standard().confidenceInterval (dblConfidenceLevel);

  145.         DiscreteTradingTrajectoryControl dttc = DiscreteTradingTrajectoryControl.FixedInterval (
  146.             new OrderSpecification (
  147.                 dblX,
  148.                 dblT
  149.             ),
  150.             iN
  151.         );

  153.         LinearPermanentExpectationParameters lpep = ArithmeticPriceEvolutionParametersBuilder.LinearExpectation (
  154.             new ArithmeticPriceDynamicsSettings (
  155.                 0.,
  156.                 new FlatUnivariate (dblSigma),
  157.                 0.
  158.             ),
  159.             new UniformParticipationRateLinear (
  160.                 new ParticipationRateLinear (
  161.                     0.,
  162.                     dblGamma
  163.                 )
  164.             ),
  165.             new UniformParticipationRateLinear (
  166.                 new ParticipationRateLinear (
  167.                     dblEpsilon,
  168.                     dblEta
  169.                 )
  170.             )
  171.         );

  173.         EfficientTradingTrajectoryDiscrete ettd = (EfficientTradingTrajectoryDiscrete) new StaticOptimalSchemeDiscrete (
  174.             dttc,
  175.             lpep,
  176.             PowerVarianceObjectiveUtility.LiquidityVaR (dblLambdaV)
  177.         ).generate();

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

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

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

  185.         LinearImpactTrajectoryEstimator lite = new LinearImpactTrajectoryEstimator (ettd);

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

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

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

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

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

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

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

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

  203.         System.out.println ("\t| Daily Volume 5 million Shares : " + dblGamma);

  205.         System.out.println ("\t| VaR Confidence Level          :" + FormatUtil.FormatDouble (dblConfidenceLevel, 2, 2, 100.) + "%");

  207.         System.out.println ("\t| VaR Based Risk Aversion       : " + dblLambdaV);

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

  211.         System.out.println (
  212.             "\t| Daily Volatility              : " +
  213.             FormatUtil.FormatDouble (dblSigma, 1, 4, 1.)
  214.         );

  216.         System.out.println (
  217.             "\t| Daily Returns                 : " +
  218.             FormatUtil.FormatDouble (dblAlpha, 1, 4, 1.)
  219.         );

  221.         System.out.println ("\t| Temporary Impact Fixed Offset :  " + dblEpsilon);

  223.         System.out.println ("\t| Eta                           :  " + dblEta);

  225.         System.out.println ("\t| Gamma                         :  " + dblGamma);

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

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

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

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

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

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

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

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

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

  245.         for (int i = 0; i <= iN; ++i) {
  246.             if (i == 0)
  247.                 System.out.println (
  248.                     "\t|" + FormatUtil.FormatDouble (adblExecutionTimeNode[i], 1, 0, 1.) + " => " +
  249.                     FormatUtil.FormatDouble (adblHoldings[i], 7, 1, 1.) + " | " +
  250.                     FormatUtil.FormatDouble (0., 6, 1, 1.) + " ||"
  251.                 );
  252.             else
  253.                 System.out.println (
  254.                     "\t|" + FormatUtil.FormatDouble (adblExecutionTimeNode[i], 1, 0, 1.) + " => " +
  255.                     FormatUtil.FormatDouble (adblHoldings[i], 7, 1, 1.) + " | " +
  256.                     FormatUtil.FormatDouble (adblTradeList[i - 1], 6, 1, 1.) + " ||"
  257.                 );
  258.         }

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

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

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

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

  268.         System.out.println (
  269.             "\t| Transaction Cost Expectation         : " +
  270.             FormatUtil.FormatDouble (r1un.mean(), 7, 1, 1.) + " | " +
  271.             FormatUtil.FormatDouble (ettd.transactionCostExpectation(), 7, 1, 1.) + " ||"
  272.         );

  274.         System.out.println (
  275.             "\t| Transaction Cost Variance (X 10^-06) : " +
  276.             FormatUtil.FormatDouble (r1un.variance(), 7, 1, 1.e-06) + " | " +
  277.             FormatUtil.FormatDouble (ettd.transactionCostVariance(), 7, 1, 1.e-06) + " ||"
  278.         );

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

  282.         EnvManager.TerminateEnv();
  283.     }
  284. }
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