StaticContinuousOptimalTrajectory.java

  1. package org.drip.sample.almgren2009;

  3. import org.drip.execution.dynamics.*;
  4. import org.drip.execution.impact.ParticipationRateLinear;
  5. import org.drip.execution.nonadaptive.ContinuousAlmgrenChriss;
  6. import org.drip.execution.optimum.EfficientTradingTrajectoryContinuous;
  7. import org.drip.execution.parameters.*;
  8. import org.drip.execution.profiletime.UniformParticipationRateLinear;
  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>StaticContinuousOptimalTrajectory</i> demonstrates the Generation and Usage of Continuous Version of
  93.  * the Discrete Trading Trajectory generated by the Almgren and Chriss (2000) Scheme under the Criterion of
  94.  * No-Drift. The References are:
  95.  * 
  96.  * <br><br>
  97.  *  <ul>
  98.  *      <li>
  99.  *          Almgren, R. F., and N. Chriss (2000): Optimal Execution of Portfolio Transactions <i>Journal of
  100.  *              Risk</i> <b>3 (2)</b> 5-39
  101.  *      </li>
  102.  *      <li>
  103.  *          Almgren, R. F. (2009): Optimal Trading in a Dynamic Market
  104.  *              https://www.math.nyu.edu/financial_mathematics/content/02_financial/2009-2.pdf
  105.  *      </li>
  106.  *      <li>
  107.  *          Almgren, R. F. (2012): Optimal Trading with Stochastic Liquidity and Volatility <i>SIAM Journal
  108.  *              of Financial Mathematics</i> <b>3 (1)</b> 163-181
  109.  *      </li>
  110.  *      <li>
  111.  *          Geman, H., D. B. Madan, and M. Yor (2001): Time Changes for Levy Processes <i>Mathematical
  112.  *              Finance</i> <b>11 (1)</b> 79-96
  113.  *      </li>
  114.  *      <li>
  115.  *          Walia, N. (2006): Optimal Trading: Dynamic Stock Liquidation Strategies <b>Princeton
  116.  *              University</b>
  117.  *      </li>
  118.  *  </ul>
  119.  * 
  120.  * <br><br>
  121.  *  <ul>
  122.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ProductCore.md">Product Core Module</a></li>
  123.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/TransactionCostAnalyticsLibrary.md">Transaction Cost Analytics</a></li>
  124.  *      <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>
  125.  *      <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>
  126.  *  </ul>
  127.  * <br><br>
  128.  * 
  129.  * @author Lakshmi Krishnamurthy
  130.  */

  132. public class StaticContinuousOptimalTrajectory {

  134.     public static void main (
  135.         final String[] astrArgs)
  136.         throws Exception
  137.     {
  138.         EnvManager.InitEnv (
  139.             "",
  140.             true
  141.         );

  143.         double dblS0 = 50.;
  144.         double dblX = 1000000.;
  145.         double dblT = 5.;
  146.         double dblAnnualVolatility = 0.30;
  147.         double dblAnnualReturns = 0.10;
  148.         double dblBidAsk = 0.125;
  149.         double dblDailyVolume = 5.e06;
  150.         double dblDailyVolumePermanentImpact = 0.1;
  151.         double dblDailyVolumeTemporaryImpact = 0.01;
  152.         double dblLambdaU = 1.e-06;

  154.         int iN = 20;

  156.         double dblTime = 0.;
  157.         double dblTimeWidth = dblT / iN;

  159.         ArithmeticPriceDynamicsSettings apds = ArithmeticPriceDynamicsSettings.FromAnnualReturnsSettings (
  160.             dblAnnualReturns,
  161.             dblAnnualVolatility,
  162.             0.,
  163.             dblS0
  164.         );

  166.         double dblSigma = apds.epochVolatility();

  168.         PriceMarketImpactLinear pmil = new PriceMarketImpactLinear (
  169.             new AssetTransactionSettings (
  170.                 dblS0,
  171.                 dblDailyVolume,
  172.                 dblBidAsk
  173.             ),
  174.             dblDailyVolumePermanentImpact,
  175.             dblDailyVolumeTemporaryImpact
  176.         );

  178.         ParticipationRateLinear prlPermanent = (ParticipationRateLinear) pmil.permanentTransactionFunction();

  180.         ParticipationRateLinear prlTemporary = (ParticipationRateLinear) pmil.temporaryTransactionFunction();

  182.         LinearPermanentExpectationParameters lpep = ArithmeticPriceEvolutionParametersBuilder.LinearExpectation (
  183.             new ArithmeticPriceDynamicsSettings (
  184.                 0.,
  185.                 new FlatUnivariate (dblSigma),
  186.                 0.
  187.             ),
  188.             new UniformParticipationRateLinear (prlPermanent),
  189.             new UniformParticipationRateLinear (prlTemporary)
  190.         );

  192.         ContinuousAlmgrenChriss cac = ContinuousAlmgrenChriss.Standard (
  193.             dblX,
  194.             dblT,
  195.             lpep,
  196.             dblLambdaU
  197.         );

  199.         EfficientTradingTrajectoryContinuous ettc = (EfficientTradingTrajectoryContinuous) cac.generate();

  201.         R1ToR1 r1ToR1Holdings = ettc.holdings();

  203.         R1ToR1 r1ToR1TradeRate = ettc.tradeRate();

  205.         R1ToR1 r1ToR1TransactionCostVariance = ettc.transactionCostVarianceFunction();

  207.         R1ToR1 r1ToR1TransactionCostExpectation = ettc.transactionCostExpectationFunction();

  209.         System.out.println ();

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

  213.         System.out.println ("\t|    STATIC CONTINUOUS OPTIMAL TRAJECTORY   ||");

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

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

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

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

  223.         System.out.println ("\t|            - Trade Rate                   ||");

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

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

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

  231.         for (int i = 1; i <= iN; ++i) {
  232.             dblTime = dblTime + dblTimeWidth;

  234.             System.out.println (
  235.                 "\t|" +
  236.                 FormatUtil.FormatDouble (dblTime, 1, 2, 1.) + " => " +
  237.                 FormatUtil.FormatDouble (r1ToR1Holdings.evaluate (dblTime) / dblX, 1, 3, 1.) + " | " +
  238.                 FormatUtil.FormatDouble (r1ToR1TradeRate.evaluate (dblTime) * dblTimeWidth / dblX, 1, 3, 1.) + " | " +
  239.                 FormatUtil.FormatDouble (r1ToR1TransactionCostExpectation.evaluate (dblTime) / dblX, 1, 3, 1.) + " | " +
  240.                 FormatUtil.FormatDouble (Math.sqrt (r1ToR1TransactionCostVariance.evaluate (dblTime)) / dblX, 1, 3, 1.) + " ||"
  241.             );
  242.         }

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

  246.         EnvManager.TerminateEnv();
  247.     }
  248. }
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