OptimalTrajectoryVolatilityAnalysis.java

  1. package org.drip.sample.athl;

  3. import org.drip.execution.athl.DynamicsParameters;
  4. import org.drip.execution.dynamics.LinearPermanentExpectationParameters;
  5. import org.drip.execution.nonadaptive.ContinuousPowerImpact;
  6. import org.drip.execution.optimum.PowerImpactContinuous;
  7. import org.drip.execution.parameters.AssetFlowSettings;
  8. import org.drip.function.definition.R1ToR1;
  9. import org.drip.numerical.common.FormatUtil;
  10. import org.drip.service.env.EnvManager;

  12. /*
  13.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  14.  */

  16. /*!
  17.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  18.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  19.  * Copyright (C) 2018 Lakshmi Krishnamurthy
  20.  * Copyright (C) 2017 Lakshmi Krishnamurthy
  21.  * Copyright (C) 2016 Lakshmi Krishnamurthy
  22.  * 
  23.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  24.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  25.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  26.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  27.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  28.  *      and computational support.
  29.  *  
  30.  *      https://lakshmidrip.github.io/DROP/
  31.  *  
  32.  *  DROP is composed of three modules:
  33.  *  
  34.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  35.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  36.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  37.  * 
  38.  *  DROP Product Core implements libraries for the following:
  39.  *  - Fixed Income Analytics
  40.  *  - Loan Analytics
  41.  *  - Transaction Cost Analytics
  42.  * 
  43.  *  DROP Portfolio Core implements libraries for the following:
  44.  *  - Asset Allocation Analytics
  45.  *  - Asset Liability Management Analytics
  46.  *  - Capital Estimation Analytics
  47.  *  - Exposure Analytics
  48.  *  - Margin Analytics
  49.  *  - XVA Analytics
  50.  * 
  51.  *  DROP Computational Core implements libraries for the following:
  52.  *  - Algorithm Support
  53.  *  - Computation Support
  54.  *  - Function Analysis
  55.  *  - Model Validation
  56.  *  - Numerical Analysis
  57.  *  - Numerical Optimizer
  58.  *  - Spline Builder
  59.  *  - Statistical Learning
  60.  * 
  61.  *  Documentation for DROP is Spread Over:
  62.  * 
  63.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  64.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  65.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  66.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  67.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  68.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  69.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  70.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  71.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  72.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  73.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  74.  * 
  75.  *  Licensed under the Apache License, Version 2.0 (the "License");
  76.  *      you may not use this file except in compliance with the License.
  77.  *   
  78.  *  You may obtain a copy of the License at
  79.  *      http://www.apache.org/licenses/LICENSE-2.0
  80.  *  
  81.  *  Unless required by applicable law or agreed to in writing, software
  82.  *      distributed under the License is distributed on an "AS IS" BASIS,
  83.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  84.  *  
  85.  *  See the License for the specific language governing permissions and
  86.  *      limitations under the License.
  87.  */

  89. /**
  90.  * <i>OptimalTrajectoryVolatilityAnalysis</i> analyzes the Impact of Input Parameters on the Trade Scheduling
  91.  * using the Equity Market Impact Functions determined empirically by Almgren, Thum, Hauptmann, and Li
  92.  * (2005), using the Parameterization of Almgren (2003) for IBM. The References are:
  93.  *  
  94.  * <br><br>
  95.  *  <ul>
  96.  *      <li>
  97.  *          Almgren, R., and N. Chriss (1999): Value under Liquidation <i>Risk</i> <b>12 (12)</b>
  98.  *      </li>
  99.  *      <li>
  100.  *          Almgren, R., and N. Chriss (2000): Optimal Execution of Portfolio Transactions <i>Journal of
  101.  *              Risk</i> <b>3 (2)</b> 5-39
  102.  *      </li>
  103.  *      <li>
  104.  *          Almgren, R. (2003): Optimal Execution with Nonlinear Impact Functions and Trading-Enhanced Risk
  105.  *              <i>Applied Mathematical Finance</i> <b>10 (1)</b> 1-18
  106.  *      </li>
  107.  *      <li>
  108.  *          Almgren, R., and N. Chriss (2003): Bidding Principles <i>Risk</i> 97-102
  109.  *      </li>
  110.  *      <li>
  111.  *          Almgren, R., C. Thum, E. Hauptmann, and H. Li (2005): Equity Market Impact <i>Risk</i> <b>18
  112.  *              (7)</b> 57-62
  113.  *      </li>
  114.  *  </ul>
  115.  *  
  116.  * <br><br>
  117.  *  <ul>
  118.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ProductCore.md">Product Core Module</a></li>
  119.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/TransactionCostAnalyticsLibrary.md">Transaction Cost Analytics</a></li>
  120.  *      <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>
  121.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/athl/README.md">Almgren, Thum, Hauptmann, and Li (2005) Calibration</a></li>
  122.  *  </ul>
  123.  * <br><br>
  124.  * 
  125.  * @author Lakshmi Krishnamurthy
  126.  */

  128. public class OptimalTrajectoryVolatilityAnalysis {

  130.     private static final void VolatilitySensitivity (
  131.         final String strAssetName,
  132.         final double dblAverageDailyVolume,
  133.         final double dblDailyVolatility,
  134.         final double dblSharesOutstanding,
  135.         final double dblTradeSize)
  136.         throws Exception
  137.     {
  138.         double dblTradeTime = 0.5;
  139.         int iNumInterval = 10;

  141.         double dblRiskAversion = 1.e-02;

  143.         LinearPermanentExpectationParameters lpep = new DynamicsParameters (
  144.             new AssetFlowSettings (
  145.                 strAssetName,
  146.                 dblAverageDailyVolume,
  147.                 dblSharesOutstanding,
  148.                 dblDailyVolatility
  149.             )
  150.         ).almgren2003();

  152.         ContinuousPowerImpact cpi = ContinuousPowerImpact.Standard (
  153.             dblTradeSize,
  154.             dblTradeTime,
  155.             lpep,
  156.             dblRiskAversion
  157.         );

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

  161.         R1ToR1 r1ToR1Holdings = pic.holdings();

  163.         double[] adblHoldings = new double[iNumInterval];
  164.         double[] adblExecutionTime = new double[iNumInterval];

  166.         for (int i = 1; i <= iNumInterval; ++i) {
  167.             adblExecutionTime[i - 1] = dblTradeTime * i / iNumInterval;

  169.             adblHoldings[i - 1] = r1ToR1Holdings.evaluate (adblExecutionTime[i - 1]);
  170.         }

  172.         String strDump = "";

  174.         for (int i = 0; i < adblHoldings.length; ++i)
  175.             strDump = strDump + FormatUtil.FormatDouble (adblHoldings[i] / dblTradeSize, 2, 2, 100.) + "% | ";

  177.         System.out.println (
  178.             "\t| " +
  179.             FormatUtil.FormatDouble (dblDailyVolatility, 1, 2, 1.) + "% | " + strDump +
  180.             FormatUtil.FormatDouble (pic.characteristicTime(), 1, 3, 1.) + " ||"
  181.         );
  182.     }

  184.     public static final void main (
  185.         final String[] astrArgs)
  186.         throws Exception
  187.     {
  188.         EnvManager.InitEnv (
  189.             "",
  190.             true
  191.         );

  193.         String strAssetName = "IBM";
  194.         double dblAverageDailyVolume = 6561000.;
  195.         double dblSharesOutstanding = 1728000000.;
  196.         double dblTradeSize = 656100.;

  198.         double[] adblDailyVolatility = new double[] {
  199.             0.75,
  200.             1.00,
  201.             1.25,
  202.             1.50,
  203.             1.75,
  204.             2.00,
  205.             2.25,
  206.             2.50,
  207.             2.75,
  208.             3.00
  209.         };

  211.         System.out.println();

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

  215.         System.out.println ("\t|                                         Trade Size Dependence on the Execution Schedule                                        ||");

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

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

  221.         System.out.println ("\t|                                                        Daily Volatility                                                        ||");

  223.         System.out.println ("\t|                                                        Execution Time Nodes                                                    ||");

  225.         System.out.println ("\t|                                                        Characteristic Time                                                     ||");

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

  229.         for (double dblDailyVolatility : adblDailyVolatility)
  230.             VolatilitySensitivity (
  231.                 strAssetName,
  232.                 dblAverageDailyVolume,
  233.                 dblDailyVolatility,
  234.                 dblSharesOutstanding,
  235.                 dblTradeSize
  236.             );

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

  240.         EnvManager.TerminateEnv();
  241.     }
  242. }
Created with JaCoCo 0.7.9.201702052155