AdaptiveOptimalCostTrajectory.java

  1. package org.drip.sample.almgren2009;

  3. import org.drip.execution.hjb.*;
  4. import org.drip.execution.latent.MarketStateSystemic;
  5. import org.drip.measure.dynamics.DiffusionEvaluatorOrnsteinUhlenbeck;
  6. import org.drip.measure.process.DiffusionEvolver;
  7. import org.drip.measure.realization.*;
  8. import org.drip.numerical.common.FormatUtil;
  9. import org.drip.service.env.EnvManager;

  11. /*
  12.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  13.  */

  15. /*!
  16.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  17.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  18.  * Copyright (C) 2018 Lakshmi Krishnamurthy
  19.  * Copyright (C) 2017 Lakshmi Krishnamurthy
  20.  * Copyright (C) 2016 Lakshmi Krishnamurthy
  21.  * 
  22.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  23.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  24.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  25.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  26.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  27.  *      and computational support.
  28.  *  
  29.  *      https://lakshmidrip.github.io/DROP/
  30.  *  
  31.  *  DROP is composed of three modules:
  32.  *  
  33.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  34.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  35.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  36.  * 
  37.  *  DROP Product Core implements libraries for the following:
  38.  *  - Fixed Income Analytics
  39.  *  - Loan Analytics
  40.  *  - Transaction Cost Analytics
  41.  * 
  42.  *  DROP Portfolio Core implements libraries for the following:
  43.  *  - Asset Allocation Analytics
  44.  *  - Asset Liability Management Analytics
  45.  *  - Capital Estimation Analytics
  46.  *  - Exposure Analytics
  47.  *  - Margin Analytics
  48.  *  - XVA Analytics
  49.  * 
  50.  *  DROP Computational Core implements libraries for the following:
  51.  *  - Algorithm Support
  52.  *  - Computation Support
  53.  *  - Function Analysis
  54.  *  - Model Validation
  55.  *  - Numerical Analysis
  56.  *  - Numerical Optimizer
  57.  *  - Spline Builder
  58.  *  - Statistical Learning
  59.  * 
  60.  *  Documentation for DROP is Spread Over:
  61.  * 
  62.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  63.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  64.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  65.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  66.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  67.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  68.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  69.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  70.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  71.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  72.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  73.  * 
  74.  *  Licensed under the Apache License, Version 2.0 (the "License");
  75.  *      you may not use this file except in compliance with the License.
  76.  *   
  77.  *  You may obtain a copy of the License at
  78.  *      http://www.apache.org/licenses/LICENSE-2.0
  79.  *  
  80.  *  Unless required by applicable law or agreed to in writing, software
  81.  *      distributed under the License is distributed on an "AS IS" BASIS,
  82.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  83.  *  
  84.  *  See the License for the specific language governing permissions and
  85.  *      limitations under the License.
  86.  */

  88. /**
  89.  * <i>AdaptiveOptimalCostTrajectory</i> traces a Sample Realization of the Adaptive Cost Strategy using the
  90.  * Market State Trajectory the follows the Zero Mean Ornstein-Uhlenbeck Evolution Dynamics. The References
  91.  * are:
  92.  * 
  93.  * <br><br>
  94.  *  <ul>
  95.  *      <li>
  96.  *          Almgren, R. F., and N. Chriss (2000): Optimal Execution of Portfolio Transactions <i>Journal of
  97.  *              Risk</i> <b>3 (2)</b> 5-39
  98.  *      </li>
  99.  *      <li>
  100.  *          Almgren, R. F. (2009): Optimal Trading in a Dynamic Market
  101.  *              https://www.math.nyu.edu/financial_mathematics/content/02_financial/2009-2.pdf
  102.  *      </li>
  103.  *      <li>
  104.  *          Almgren, R. F. (2012): Optimal Trading with Stochastic Liquidity and Volatility <i>SIAM Journal
  105.  *              of Financial Mathematics</i> <b>3 (1)</b> 163-181
  106.  *      </li>
  107.  *      <li>
  108.  *          Geman, H., D. B. Madan, and M. Yor (2001): Time Changes for Levy Processes <i>Mathematical
  109.  *              Finance</i> <b>11 (1)</b> 79-96
  110.  *      </li>
  111.  *      <li>
  112.  *          Walia, N. (2006): Optimal Trading: Dynamic Stock Liquidation Strategies <b>Princeton
  113.  *              University</b>
  114.  *      </li>
  115.  *  </ul>
  116.  * 
  117.  * <br><br>
  118.  *  <ul>
  119.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ProductCore.md">Product Core Module</a></li>
  120.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/TransactionCostAnalyticsLibrary.md">Transaction Cost Analytics</a></li>
  121.  *      <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>
  122.  *      <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>
  123.  *  </ul>
  124.  * <br><br>
  125.  * 
  126.  * @author Lakshmi Krishnamurthy
  127.  */

  129. public class AdaptiveOptimalCostTrajectory {

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

  140.         double dblTime = 0.;
  141.         double dblBurstiness = 1.;
  142.         double dblDimensionlessRiskAversion = 0.1;
  143.         double dblRelaxationTime = 1.;
  144.         double dblSimulationTime = 10.;
  145.         double dblTimeInterval = 0.25;
  146.         double dblInitialMarketState = -0.5;

  148.         double dblNonDimensionalHoldings = 1.;
  149.         int iNumTimeNode = (int) (dblSimulationTime / dblTimeInterval);
  150.         MarketStateSystemic[] aMSS = new MarketStateSystemic[iNumTimeNode + 1];

  152.         aMSS[0] = new MarketStateSystemic (dblInitialMarketState);

  154.         DiffusionEvaluatorOrnsteinUhlenbeck deou = DiffusionEvaluatorOrnsteinUhlenbeck.ZeroMean (
  155.             dblBurstiness,
  156.             dblRelaxationTime
  157.         );

  159.         DiffusionEvolver oup1D = new DiffusionEvolver (deou);

  161.         for (int i = 0; i < iNumTimeNode; ++i) {
  162.             JumpDiffusionEdge gi = oup1D.weinerIncrement (
  163.                 new JumpDiffusionVertex (
  164.                     dblTime,
  165.                     aMSS[i].common(),
  166.                     0.,
  167.                     false
  168.                 ),
  169.                 dblTimeInterval
  170.             );

  172.             dblTime += dblTimeInterval;

  174.             aMSS[i + 1] = new MarketStateSystemic (aMSS[i].common() + gi.deterministic() + gi.diffusionStochastic());
  175.         }

  177.         NonDimensionalCostEvolverSystemic ndces = NonDimensionalCostEvolverSystemic.Standard (deou);

  179.         NonDimensionalCostSystemic ndcs = NonDimensionalCostSystemic.Zero();

  181.         System.out.println();

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

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

  187.         System.out.println ("\t||              - Non Dimensional Time                               ||");

  189.         System.out.println ("\t||              - Realized Market State                              ||");

  191.         System.out.println ("\t||              - Non Dimensional Cost                               ||");

  193.         System.out.println ("\t||              - Non Dimensional Cost Gradient                      ||");

  195.         System.out.println ("\t||              - Non Dimensional Cost Jacobian                      ||");

  197.         System.out.println ("\t||              - Non Dimensional Cost Trade Velocity                ||");

  199.         System.out.println ("\t||              - Non Dimensional Outstanding Holdings               ||");

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

  203.         System.out.println ("\t||" + 
  204.             FormatUtil.FormatDouble (0., 1, 2, 1.) + " => " +
  205.             FormatUtil.FormatDouble (aMSS[0].common(), 1, 4, 1.) + " | " +
  206.             FormatUtil.FormatDouble (ndcs.realization(), 1, 4, 1.) + " | " +
  207.             FormatUtil.FormatDouble (ndcs.gradient(), 1, 4, 1.) + " | " +
  208.             FormatUtil.FormatDouble (ndcs.jacobian(), 1, 4, 1.) + " | " +
  209.             FormatUtil.FormatDouble (ndcs.nonDimensionalTradeRate(), 1, 4, 1.) + " | " +
  210.             FormatUtil.FormatDouble (dblNonDimensionalHoldings, 1, 4, 1.) + " ||"
  211.         );

  213.         for (int i = 1; i < iNumTimeNode; ++i) {
  214.             ndcs = (NonDimensionalCostSystemic) ndces.evolve (
  215.                 ndcs,
  216.                 aMSS[i],
  217.                 dblDimensionlessRiskAversion,
  218.                 (iNumTimeNode - i) * dblTimeInterval,
  219.                 dblTimeInterval
  220.             );

  222.             double dblNonDimensionalTradeRate = dblNonDimensionalHoldings * ndcs.nonDimensionalTradeRate();

  224.             dblNonDimensionalHoldings = dblNonDimensionalHoldings - dblNonDimensionalTradeRate * dblTimeInterval;

  226.             System.out.println ("\t||" + 
  227.                 FormatUtil.FormatDouble (dblTimeInterval * i, 1, 2, 1.) + " => " +
  228.                 FormatUtil.FormatDouble (aMSS[i].common(), 1, 4, 1.) + " | " +
  229.                 FormatUtil.FormatDouble (ndcs.realization(), 1, 4, 1.) + " | " +
  230.                 FormatUtil.FormatDouble (ndcs.gradient(), 1, 4, 1.) + " | " +
  231.                 FormatUtil.FormatDouble (ndcs.jacobian(), 1, 4, 1.) + " | " +
  232.                 FormatUtil.FormatDouble (dblNonDimensionalTradeRate, 1, 4, 1.) + " | " +
  233.                 FormatUtil.FormatDouble (dblNonDimensionalHoldings, 1, 4, 1.) + " ||"
  234.             );
  235.         }

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

  239.         EnvManager.TerminateEnv();
  240.     }
  241. }
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