ConstantLiquidityVolatility.java

  1. package org.drip.sample.almgren2003;

  3. import org.drip.execution.dynamics.*;
  4. import org.drip.execution.impact.ParticipationRateLinear;
  5. import org.drip.execution.nonadaptive.ContinuousConstantTradingEnhanced;
  6. import org.drip.execution.optimum.EfficientTradingTrajectoryContinuous;
  7. import org.drip.execution.profiletime.UniformParticipationRateLinear;
  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>ConstantLiquidityVolatility</i> demonstrates the Dependence of the Optimal Trading Trajectory as a
  91.  * Function of Constant Trading Enhanced Volatilities. The References are:
  92.  * 
  93.  * <br><br>
  94.  *  <ul>
  95.  *      <li>
  96.  *          Almgren, R., and N. Chriss (1999): Value under Liquidation <i>Risk</i> <b>12 (12)</b>
  97.  *      </li>
  98.  * 
  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.  * 
  104.  *      <li>
  105.  *          Almgren, R. (2003): Optimal Execution with Nonlinear Impact Functions and Trading-Enhanced Risk
  106.  *              <i>Applied Mathematical Finance</i> <b>10 (1)</b> 1-18.
  107.  *      </li>
  108.  * 
  109.  *      <li>
  110.  *          Almgren, R., and N. Chriss (2003): Bidding Principles <i>Risk</i> 97-102
  111.  *      </li>
  112.  * 
  113.  *      <li>
  114.  *          Bertsimas, D., and A. W. Lo (1998): Optimal Control of Execution Costs <i>Journal of Financial
  115.  *              Markets</i> <b>1</b> 1-50
  116.  *      </li>
  117.  *  </ul>
  118.  * 
  119.  * <br><br>
  120.  *  <ul>
  121.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ProductCore.md">Product Core Module</a></li>
  122.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/TransactionCostAnalyticsLibrary.md">Transaction Cost Analytics</a></li>
  123.  *      <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>
  124.  *      <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>
  125.  *  </ul>
  126.  * <br><br>
  127.  * 
  128.  * @author Lakshmi Krishnamurthy
  129.  */

  131. public class ConstantLiquidityVolatility {

  133.     private static final void AlphaRun (
  134.         final double dblAlpha,
  135.         final double dblT,
  136.         final int iNumInterval)
  137.         throws Exception
  138.     {
  139.         double dblEta = 5.e-06;
  140.         double dblSigma = 1.;
  141.         double dblLambda = 1.e-05;
  142.         double dblX = 100000.;

  144.         ArithmeticPriceEvolutionParameters apep = ArithmeticPriceEvolutionParametersBuilder.TradingEnhancedVolatility (
  145.             dblSigma,
  146.             new UniformParticipationRateLinear (ParticipationRateLinear.SlopeOnly (dblEta)),
  147.             new UniformParticipationRateLinear (
  148.                 new ParticipationRateLinear (
  149.                     dblAlpha,
  150.                     0.
  151.                 )
  152.             )
  153.         );

  155.         ContinuousConstantTradingEnhanced ccte = ContinuousConstantTradingEnhanced.Standard (
  156.             dblX,
  157.             dblT,
  158.             apep,
  159.             dblLambda
  160.         );

  162.         EfficientTradingTrajectoryContinuous ettc = (EfficientTradingTrajectoryContinuous) ccte.generate();

  164.         R1ToR1 r1ToR1Holdings = ettc.holdings();

  166.         double[] adblHoldings = new double[iNumInterval];
  167.         double[] adblExecutionTime = new double[iNumInterval];

  169.         for (int i = 1; i <= iNumInterval; ++i) {
  170.             adblExecutionTime[i - 1] = dblT * i / iNumInterval;

  172.             adblHoldings[i - 1] = r1ToR1Holdings.evaluate (adblExecutionTime[i - 1]);
  173.         }

  175.         String strDump = "\t|" + FormatUtil.FormatDouble (dblAlpha, 1, 1, 1.) + " =>";

  177.         for (int i = 0; i < adblExecutionTime.length; ++i)
  178.             strDump = strDump + FormatUtil.FormatDouble (adblHoldings[i] / dblX, 2, 1, 100.) + "% ";

  180.         strDump = strDump + FormatUtil.FormatDouble (ettc.transactionCostExpectation(), 5, 0, 1.) + " | ";

  182.         strDump = strDump + FormatUtil.FormatDouble (ettc.transactionCostVariance(), 5, 0, 1.e-06) + " | ";

  184.         strDump = strDump + FormatUtil.FormatDouble (ettc.characteristicTime(), 1, 3, 1.) + " ||";

  186.         System.out.println (strDump);
  187.     }

  189.     public static final void main (
  190.         final String[] astrArgs)
  191.         throws Exception
  192.     {
  193.         EnvManager.InitEnv (
  194.             "",
  195.             true
  196.         );

  198.         double dblT = 5.;
  199.         int iNumInterval = 10;

  201.         double[] adblAlpha = new double[] {
  202.             0.0,
  203.             0.1,
  204.             0.2,
  205.             0.3,
  206.             0.4,
  207.             0.5,
  208.             0.6,
  209.             0.7,
  210.             0.8,
  211.             0.9,
  212.             1.0,
  213.             1.1,
  214.             1.2,
  215.             1.3,
  216.             1.4,
  217.             1.5,
  218.             1.6,
  219.             1.7,
  220.             1.8,
  221.             1.9,
  222.             2.0
  223.         };

  225.         System.out.println();

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

  229.         System.out.println ("\t|                   ALMGREN (2003) CONSTANT TEMPORARY IMPACT VOLATILITY - OFFSET DEPENDENCE                    ||");

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

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

  235.         System.out.println ("\t|              Alpha Level                                                                                     ||");

  237.         System.out.println ("\t|              Outstanding Trajectory (%)                                                                      ||");

  239.         System.out.println ("\t|              Transaction Cost Expectation                                                                    ||");

  241.         System.out.println ("\t|              Transaction Cost Variance (X 10^-06)                                                            ||");

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

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

  247.         String strTimeNode = "\t|        ";

  249.         for (int i = 0; i <= iNumInterval; ++i)
  250.             strTimeNode = strTimeNode + FormatUtil.FormatDouble (dblT * i / iNumInterval, 1, 2, 1.) + "  ";

  252.         System.out.println (strTimeNode);

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

  256.         for (double dblAlpha : adblAlpha)
  257.             AlphaRun (
  258.                 dblAlpha,
  259.                 dblT,
  260.                 iNumInterval
  261.             );

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

  265.         EnvManager.TerminateEnv();
  266.     }
  267. }
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