PowerLawOptimalTrajectory.java

  1. package org.drip.sample.almgren2003;

  3. import org.drip.execution.dynamics.*;
  4. import org.drip.execution.impact.*;
  5. import org.drip.execution.nonadaptive.ContinuousPowerImpact;
  6. import org.drip.execution.optimum.PowerImpactContinuous;
  7. import org.drip.execution.parameters.ArithmeticPriceDynamicsSettings;
  8. import org.drip.execution.profiletime.*;
  9. import org.drip.function.definition.R1ToR1;
  10. import org.drip.function.r1tor1.FlatUnivariate;
  11. import org.drip.numerical.common.FormatUtil;
  12. import org.drip.service.env.EnvManager;

  14. /*
  15.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  16.  */

  18. /*!
  19.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  20.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  21.  * Copyright (C) 2018 Lakshmi Krishnamurthy
  22.  * Copyright (C) 2017 Lakshmi Krishnamurthy
  23.  * Copyright (C) 2016 Lakshmi Krishnamurthy
  24.  * 
  25.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  26.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  27.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  28.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  29.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  30.  *      and computational support.
  31.  *  
  32.  *      https://lakshmidrip.github.io/DROP/
  33.  *  
  34.  *  DROP is composed of three modules:
  35.  *  
  36.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  37.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  38.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  39.  * 
  40.  *  DROP Product Core implements libraries for the following:
  41.  *  - Fixed Income Analytics
  42.  *  - Loan Analytics
  43.  *  - Transaction Cost Analytics
  44.  * 
  45.  *  DROP Portfolio Core implements libraries for the following:
  46.  *  - Asset Allocation Analytics
  47.  *  - Asset Liability Management Analytics
  48.  *  - Capital Estimation Analytics
  49.  *  - Exposure Analytics
  50.  *  - Margin Analytics
  51.  *  - XVA Analytics
  52.  * 
  53.  *  DROP Computational Core implements libraries for the following:
  54.  *  - Algorithm Support
  55.  *  - Computation Support
  56.  *  - Function Analysis
  57.  *  - Model Validation
  58.  *  - Numerical Analysis
  59.  *  - Numerical Optimizer
  60.  *  - Spline Builder
  61.  *  - Statistical Learning
  62.  * 
  63.  *  Documentation for DROP is Spread Over:
  64.  * 
  65.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  66.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  67.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  68.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  69.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  70.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  71.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  72.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  73.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  74.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  75.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  76.  * 
  77.  *  Licensed under the Apache License, Version 2.0 (the "License");
  78.  *      you may not use this file except in compliance with the License.
  79.  *   
  80.  *  You may obtain a copy of the License at
  81.  *      http://www.apache.org/licenses/LICENSE-2.0
  82.  *  
  83.  *  Unless required by applicable law or agreed to in writing, software
  84.  *      distributed under the License is distributed on an "AS IS" BASIS,
  85.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  86.  *  
  87.  *  See the License for the specific language governing permissions and
  88.  *      limitations under the License.
  89.  */

  91. /**
  92.  * <i>PowerLawOptimalTrajectory</i> sketches out the Optimal Trajectories for 3 different values of k -
  93.  * representing Concave, Linear, and Convex Power's respectively. The References are:
  94.  * 
  95.  * <br><br>
  96.  *  <ul>
  97.  *      <li>
  98.  *          Almgren, R., and N. Chriss (1999): Value under Liquidation <i>Risk</i> <b>12 (12)</b>
  99.  *      </li>
  100.  * 
  101.  *      <li>
  102.  *          Almgren, R., and N. Chriss (2000): Optimal Execution of Portfolio Transactions <i>Journal of
  103.  *              Risk</i> <b>3 (2)</b> 5-39
  104.  *      </li>
  105.  * 
  106.  *      <li>
  107.  *          Almgren, R. (2003): Optimal Execution with Nonlinear Impact Functions and Trading-Enhanced Risk
  108.  *              <i>Applied Mathematical Finance</i> <b>10 (1)</b> 1-18.
  109.  *      </li>
  110.  * 
  111.  *      <li>
  112.  *          Almgren, R., and N. Chriss (2003): Bidding Principles <i>Risk</i> 97-102
  113.  *      </li>
  114.  * 
  115.  *      <li>
  116.  *          Bertsimas, D., and A. W. Lo (1998): Optimal Control of Execution Costs <i>Journal of Financial
  117.  *              Markets</i> <b>1</b> 1-50
  118.  *      </li>
  119.  *  </ul>
  120.  * 
  121.  * <br><br>
  122.  *  <ul>
  123.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ProductCore.md">Product Core Module</a></li>
  124.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/TransactionCostAnalyticsLibrary.md">Transaction Cost Analytics</a></li>
  125.  *      <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>
  126.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/almgren2003/README.md">Almgren (2003) Power Law Liquidity</a></li>
  127.  *  </ul>
  128.  * <br><br>
  129.  * 
  130.  * @author Lakshmi Krishnamurthy
  131.  */

  133. public class PowerLawOptimalTrajectory {

  135.     private static final void RiskAversionRun (
  136.         final double dblLambda)
  137.         throws Exception
  138.     {
  139.         double dblGamma = 0.;
  140.         double dblHRef = 0.50;
  141.         double dblVRef = 100000.;
  142.         double dblDrift = 0.;
  143.         double dblVolatility = 1.;
  144.         double dblSerialCorrelation = 0.;
  145.         double dblX = 100000.;
  146.         double dblFinishTime = 10.;
  147.         int iNumInterval = 10;

  149.         double[] adblK = new double[] {
  150.             0.25,
  151.             0.50,
  152.             0.75,
  153.             1.00,
  154.             1.25,
  155.             1.50,
  156.             1.75,
  157.             2.00,
  158.             2.25,
  159.             2.50,
  160.             2.75,
  161.             3.00
  162.         };

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

  166.         System.out.println ("\t|\tPOWER LAW OPTIMAL TRAJECTORY; RISK TOLERANCE (thousands) => " + FormatUtil.FormatDouble (1. / dblLambda, 1, 0, 1.e-03));

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

  170.         System.out.println ("\t|\t\tL -> R:");

  172.         System.out.println ("\t|\t\t\tTime Node Trajectory Realization (Percent)");

  174.         System.out.println ("\t|\t\t\tCharacteristic Time (Days)");

  176.         System.out.println ("\t|\t\t\tMaximum Execution Time (Days)");

  178.         System.out.println ("\t|\t\t\tTransaction Cost Expectation (Thousands)");

  180.         System.out.println ("\t|\t\t\tTransaction Cost Variance (Thousands)");

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

  184.         ArithmeticPriceDynamicsSettings apds = new ArithmeticPriceDynamicsSettings (
  185.             dblDrift,
  186.             new FlatUnivariate (dblVolatility),
  187.             dblSerialCorrelation
  188.         );

  190.         ParticipationRateLinear prlPermanent = new ParticipationRateLinear (
  191.             0.,
  192.             dblGamma
  193.         );

  195.         double[] adblExecutionTime = new double[iNumInterval];

  197.         for (int i = 1; i <= iNumInterval; ++i)
  198.             adblExecutionTime[i - 1] = ((double) i) / ((double) iNumInterval);

  200.         for (int i = 0; i < adblK.length; ++i) {
  201.             double dblEta = dblHRef / java.lang.Math.pow (dblVRef, adblK[i]);

  203.             LinearPermanentExpectationParameters lpep = ArithmeticPriceEvolutionParametersBuilder.Almgren2003 (
  204.                 apds,
  205.                 new UniformParticipationRateLinear (prlPermanent),
  206.                 new UniformParticipationRate (
  207.                     new ParticipationRatePower (
  208.                         dblEta,
  209.                         adblK[i]
  210.                     )
  211.                 )
  212.             );

  214.             ContinuousPowerImpact cpi = ContinuousPowerImpact.Standard (
  215.                 dblX,
  216.                 dblFinishTime,
  217.                 lpep,
  218.                 dblLambda
  219.             );

  221.             PowerImpactContinuous pic = (PowerImpactContinuous) cpi.generate();

  223.             if (0 == i) {
  224.                 String strExecutionTime = "\t|          |  ";

  226.                 for (int j = 0; j < adblExecutionTime.length; ++j)
  227.                     strExecutionTime = strExecutionTime + "   " + FormatUtil.FormatDouble (adblExecutionTime[j], 1, 2, 1.);

  229.                 System.out.println (strExecutionTime);

  231.                 System.out.println ("\t|------------------------------------------------------------------------------------------------------------------------------------||");
  232.             }

  234.             R1ToR1 r1ToR1Holdings = pic.holdings();

  236.             String strHoldings = "\t| k =" + FormatUtil.FormatDouble (adblK[i], 1, 2, 1.) + " | ";

  238.             for (int j = 0; j < iNumInterval; ++j)
  239.                 strHoldings = strHoldings + "  " + FormatUtil.FormatDouble (r1ToR1Holdings.evaluate (adblExecutionTime[j]) / dblX, 2, 2, 100.);

  241.             double dblExecutionTimeUpperBound = pic.executionTimeUpperBound();

  243.             System.out.println (
  244.                 strHoldings + " | " +
  245.                 FormatUtil.FormatDouble (pic.characteristicTime(), 2, 1, 1.) + " | " +
  246.                 FormatUtil.FormatDouble (Double.isNaN (dblExecutionTimeUpperBound) ? 0. : dblExecutionTimeUpperBound, 2, 1, 1.) + " | " +
  247.                 FormatUtil.FormatDouble (pic.transactionCostExpectation(), 3, 0, 1.e-03) + " | " +
  248.                 FormatUtil.FormatDouble (Math.sqrt (pic.transactionCostVariance()), 3, 0, 1.e-03) + " ||"
  249.             );
  250.         }

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

  255.     public static final void main (
  256.         final String[] astrArgs)
  257.         throws Exception
  258.     {
  259.         EnvManager.InitEnv (
  260.             "",
  261.             true
  262.         );

  264.         double[] adblLambda = new double[] {
  265.             1.e-04,
  266.             5.e-06,
  267.             5.e-07
  268.         };

  270.         for (double dblLambda : adblLambda)
  271.             RiskAversionRun (dblLambda);

  273.         EnvManager.TerminateEnv();
  274.     }
  275. }
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