EnhancedEulerScheme.java

  1. package org.drip.sample.almgren2009;

  3. import org.drip.function.r1tor1.AlmgrenEnhancedEulerUpdate;
  4. import org.drip.numerical.common.FormatUtil;
  5. import org.drip.service.env.EnvManager;

  7. /*
  8.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  9.  */

  11. /*!
  12.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  13.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  14.  * Copyright (C) 2018 Lakshmi Krishnamurthy
  15.  * Copyright (C) 2017 Lakshmi Krishnamurthy
  16.  * Copyright (C) 2016 Lakshmi Krishnamurthy
  17.  * 
  18.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  19.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  20.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  21.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  22.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  23.  *      and computational support.
  24.  *  
  25.  *      https://lakshmidrip.github.io/DROP/
  26.  *  
  27.  *  DROP is composed of three modules:
  28.  *  
  29.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  30.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  31.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  32.  * 
  33.  *  DROP Product Core implements libraries for the following:
  34.  *  - Fixed Income Analytics
  35.  *  - Loan Analytics
  36.  *  - Transaction Cost Analytics
  37.  * 
  38.  *  DROP Portfolio Core implements libraries for the following:
  39.  *  - Asset Allocation Analytics
  40.  *  - Asset Liability Management Analytics
  41.  *  - Capital Estimation Analytics
  42.  *  - Exposure Analytics
  43.  *  - Margin Analytics
  44.  *  - XVA Analytics
  45.  * 
  46.  *  DROP Computational Core implements libraries for the following:
  47.  *  - Algorithm Support
  48.  *  - Computation Support
  49.  *  - Function Analysis
  50.  *  - Model Validation
  51.  *  - Numerical Analysis
  52.  *  - Numerical Optimizer
  53.  *  - Spline Builder
  54.  *  - Statistical Learning
  55.  * 
  56.  *  Documentation for DROP is Spread Over:
  57.  * 
  58.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  59.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  60.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  61.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  62.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  63.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  64.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  65.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  66.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  67.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  68.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  69.  * 
  70.  *  Licensed under the Apache License, Version 2.0 (the "License");
  71.  *      you may not use this file except in compliance with the License.
  72.  *   
  73.  *  You may obtain a copy of the License at
  74.  *      http://www.apache.org/licenses/LICENSE-2.0
  75.  *  
  76.  *  Unless required by applicable law or agreed to in writing, software
  77.  *      distributed under the License is distributed on an "AS IS" BASIS,
  78.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  79.  *  
  80.  *  See the License for the specific language governing permissions and
  81.  *      limitations under the License.
  82.  */

  84. /**
  85.  * <i>EnhancedEulerScheme</i> demonstrates the Enhancement used by Almgren (2009, 2012) to deal with Time
  86.  * Evolution under Singular Initial Conditions. The References are:
  87.  * 
  88.  * <br><br>
  89.  *  <ul>
  90.  *      <li>
  91.  *          Almgren, R. F., and N. Chriss (2000): Optimal Execution of Portfolio Transactions <i>Journal of
  92.  *              Risk</i> <b>3 (2)</b> 5-39
  93.  *      </li>
  94.  *      <li>
  95.  *          Almgren, R. F. (2009): Optimal Trading in a Dynamic Market
  96.  *              https://www.math.nyu.edu/financial_mathematics/content/02_financial/2009-2.pdf
  97.  *      </li>
  98.  *      <li>
  99.  *          Almgren, R. F. (2012): Optimal Trading with Stochastic Liquidity and Volatility <i>SIAM Journal
  100.  *              of Financial Mathematics</i> <b>3 (1)</b> 163-181
  101.  *      </li>
  102.  *      <li>
  103.  *          Geman, H., D. B. Madan, and M. Yor (2001): Time Changes for Levy Processes <i>Mathematical
  104.  *              Finance</i> <b>11 (1)</b> 79-96
  105.  *      </li>
  106.  *      <li>
  107.  *          Walia, N. (2006): Optimal Trading: Dynamic Stock Liquidation Strategies <b>Princeton
  108.  *              University</b>
  109.  *      </li>
  110.  *  </ul>
  111.  * 
  112.  * <br><br>
  113.  *  <ul>
  114.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ProductCore.md">Product Core Module</a></li>
  115.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/TransactionCostAnalyticsLibrary.md">Transaction Cost Analytics</a></li>
  116.  *      <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>
  117.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/almgren2009/README.md">Almgren (2009) Optimal Adaptive HJB</a></li>
  118.  *  </ul>
  119.  * <br><br>
  120.  * 
  121.  * @author Lakshmi Krishnamurthy
  122.  */

  124. public class EnhancedEulerScheme {

  126.     public static final void main (
  127.         final String[] astrArgs)
  128.         throws Exception
  129.     {
  130.         EnvManager.InitEnv (
  131.             "",
  132.             true
  133.         );

  135.         double dblA = 2.;
  136.         double dblB = 1.;
  137.         double dblTimeIncrement = 0.1;
  138.         double dblSimulationTime = 1.0;
  139.         int iK = 2;

  141.         int iNumSimulationSteps = (int) (dblSimulationTime / dblTimeIncrement);
  142.         double dblInitialOrder0 = 1. / (iK * dblTimeIncrement);
  143.         double dblInitialOrder1 = dblInitialOrder0 + 0.5 * (dblA + dblB);
  144.         double dblOrder0Euler = dblInitialOrder0;
  145.         double dblOrder1Euler = dblInitialOrder1;
  146.         double dblOrder0EnhancedEuler = dblInitialOrder0;
  147.         double dblOrder1EnhancedEuler = dblInitialOrder1;

  149.         AlmgrenEnhancedEulerUpdate aeeu = new AlmgrenEnhancedEulerUpdate (
  150.             dblA,
  151.             dblB
  152.         );

  154.         System.out.println();

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

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

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

  162.         System.out.println ("\t||            - Exact Solution                        ||");

  164.         System.out.println ("\t||            - Order 1 Initial + Enhanced Euler      ||");

  166.         System.out.println ("\t||            - Order 0 Initial + Enhanced Euler      ||");

  168.         System.out.println ("\t||            - Order 1 Initial + Regular Euler       ||");

  170.         System.out.println ("\t||            - Order 0 Initial + Regular Euler       ||");

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

  174.         for (int i = iK; i <= iNumSimulationSteps; ++i) {
  175.             double dblTime = i * dblTimeIncrement;

  177.             System.out.println (
  178.                 "\t|| " +
  179.                 FormatUtil.FormatDouble (dblTime, 1, 1, 1.) + " => " +
  180.                 FormatUtil.FormatDouble (aeeu.evaluate (dblTime), 1, 3, 1.) + " | " +
  181.                 FormatUtil.FormatDouble (dblOrder1EnhancedEuler, 1, 3, 1.) + " | " +
  182.                 FormatUtil.FormatDouble (dblOrder0EnhancedEuler, 1, 3, 1.) + " | " +
  183.                 FormatUtil.FormatDouble (dblOrder1Euler, 1, 3, 1.) + " | " +
  184.                 FormatUtil.FormatDouble (dblOrder0Euler, 1, 3, 1.) + " ||"
  185.             );

  187.             double dblOrder0EulerIncrement = -1. * (dblOrder0Euler - dblA) * (dblOrder0Euler - dblB) * dblTimeIncrement;
  188.             double dblOrder1EulerIncrement = -1. * (dblOrder1Euler - dblA) * (dblOrder1Euler - dblB) * dblTimeIncrement;
  189.             dblOrder0Euler = dblOrder0Euler + dblOrder0EulerIncrement;
  190.             dblOrder1Euler = dblOrder1Euler + dblOrder1EulerIncrement;
  191.             double dblOrder0EnhancedEulerIncrement = -1. * (dblOrder0EnhancedEuler - dblA) * (dblOrder0EnhancedEuler - dblB)
  192.                 * dblTimeIncrement * iK / (iK + 1);
  193.             dblOrder0EnhancedEuler = dblOrder0EnhancedEuler + dblOrder0EnhancedEulerIncrement;
  194.             double dblOrder1EnhancedEulerIncrement = -1. * (dblOrder1EnhancedEuler - dblA) * (dblOrder1EnhancedEuler - dblB)
  195.                 * dblTimeIncrement * iK / (iK + 1);
  196.             dblOrder1EnhancedEuler = dblOrder1EnhancedEuler + dblOrder1EnhancedEulerIncrement;
  197.         }

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

  201.         EnvManager.TerminateEnv();
  202.     }
  203. }
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