NonDimensionalCostEvolverSystemic.java

  1. package org.drip.execution.hjb;

  3. /*
  4.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  5.  */

  7. /*!
  8.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  9.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  10.  * Copyright (C) 2018 Lakshmi Krishnamurthy
  11.  * Copyright (C) 2017 Lakshmi Krishnamurthy
  12.  * Copyright (C) 2016 Lakshmi Krishnamurthy
  13.  * 
  14.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  15.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  16.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  17.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  18.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  19.  *      and computational support.
  20.  *  
  21.  *      https://lakshmidrip.github.io/DROP/
  22.  *  
  23.  *  DROP is composed of three modules:
  24.  *  
  25.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  26.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  27.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  28.  * 
  29.  *  DROP Product Core implements libraries for the following:
  30.  *  - Fixed Income Analytics
  31.  *  - Loan Analytics
  32.  *  - Transaction Cost Analytics
  33.  * 
  34.  *  DROP Portfolio Core implements libraries for the following:
  35.  *  - Asset Allocation Analytics
  36.  *  - Asset Liability Management Analytics
  37.  *  - Capital Estimation Analytics
  38.  *  - Exposure Analytics
  39.  *  - Margin Analytics
  40.  *  - XVA Analytics
  41.  * 
  42.  *  DROP Computational Core implements libraries for the following:
  43.  *  - Algorithm Support
  44.  *  - Computation Support
  45.  *  - Function Analysis
  46.  *  - Model Validation
  47.  *  - Numerical Analysis
  48.  *  - Numerical Optimizer
  49.  *  - Spline Builder
  50.  *  - Statistical Learning
  51.  * 
  52.  *  Documentation for DROP is Spread Over:
  53.  * 
  54.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  55.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  56.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  57.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  58.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  59.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  60.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  61.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  62.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  63.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  64.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  65.  * 
  66.  *  Licensed under the Apache License, Version 2.0 (the "License");
  67.  *      you may not use this file except in compliance with the License.
  68.  *   
  69.  *  You may obtain a copy of the License at
  70.  *      http://www.apache.org/licenses/LICENSE-2.0
  71.  *  
  72.  *  Unless required by applicable law or agreed to in writing, software
  73.  *      distributed under the License is distributed on an "AS IS" BASIS,
  74.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  75.  *  
  76.  *  See the License for the specific language governing permissions and
  77.  *      limitations under the License.
  78.  */

  80. /**
  81.  * <i>NonDimensionalCostEvolverSystemic</i> implements the 1D HJB-based Single Step Optimal Trajectory Cost
  82.  * Step Evolver using the Systemic Coordinated Variation Version of the Stochastic Volatility and the
  83.  * Transaction Function arising from the Realization of the Market State Variable as described in the
  84.  * "Trading Time" Model. The References are:
  85.  * 
  86.  * <br><br>
  87.  *  <ul>
  88.  *      <li>
  89.  *          Almgren, R. F., and N. Chriss (2000): Optimal Execution of Portfolio Transactions <i>Journal of
  90.  *              Risk</i> <b>3 (2)</b> 5-39
  91.  *      </li>
  92.  *      <li>
  93.  *          Almgren, R. F. (2009): Optimal Trading in a Dynamic Market
  94.  *              https://www.math.nyu.edu/financial_mathematics/content/02_financial/2009-2.pdf
  95.  *      </li>
  96.  *      <li>
  97.  *          Almgren, R. F. (2012): Optimal Trading with Stochastic Liquidity and Volatility <i>SIAM Journal
  98.  *          of Financial Mathematics</i> <b>3 (1)</b> 163-181
  99.  *      </li>
  100.  *      <li>
  101.  *          Geman, H., D. B. Madan, and M. Yor (2001): Time Changes for Levy Processes <i>Mathematical
  102.  *              Finance</i> <b>11 (1)</b> 79-96
  103.  *      </li>
  104.  *      <li>
  105.  *          Jones, C. M., G. Kaul, and M. L. Lipson (1994): Transactions, Volume, and Volatility <i>Review of
  106.  *              Financial Studies</i> <b>7 (4)</b> 631-651
  107.  *      </li>
  108.  *  </ul>
  109.  *
  110.  *  <br><br>
  111.  *  <ul>
  112.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ProductCore.md">Product Core Module</a></li>
  113.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/TransactionCostAnalyticsLibrary.md">Transaction Cost Analytics</a></li>
  114.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/execution/README.md">Optimal Impact/Capture Based Trading Trajectories - Deterministic, Stochastic, Static, and Dynamic</a></li>
  115.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/execution/hjb/README.md">Hamilton Jacobin Bellman Based Optimal Evolution</a></li>
  116.  *  </ul>
  117.  * 
  118.  * @author Lakshmi Krishnamurthy
  119.  */

  121. public class NonDimensionalCostEvolverSystemic extends org.drip.execution.hjb.NonDimensionalCostEvolver
  122. {

  124.     /**
  125.      * Construct a Standard NonDimensionalCostEvolverSystemic Instance
  126.      * 
  127.      * @param ou The Underlying Ornstein-Unlenbeck Reference Process
  128.      * 
  129.      * @return The Standard NonDimensionalCostEvolverSystemic Instance
  130.      */

  132.     public static final NonDimensionalCostEvolverSystemic Standard (
  133.         final org.drip.measure.process.OrnsteinUhlenbeck ou)
  134.     {
  135.         try {
  136.             return new NonDimensionalCostEvolverSystemic (ou,
  137.                 org.drip.execution.hjb.NonDimensionalCostEvolver.SINGULAR_URGENCY_THRESHOLD, true);
  138.         } catch (java.lang.Exception e) {
  139.             e.printStackTrace();
  140.         }

  142.         return null;
  143.     }

  145.     @Override protected double advance (
  146.         final org.drip.execution.hjb.NonDimensionalCost ndc,
  147.         final org.drip.execution.latent.MarketState ms,
  148.         final double[] adblMarketStateTweak,
  149.         final double dblNonDimensionalRiskAversion)
  150.         throws java.lang.Exception
  151.     {
  152.         double dblNonDimensionalCost = ndc.realization();

  154.         double dblMarketState = ms.liquidity() + adblMarketStateTweak[0];

  156.         double dblBurstiness = ornsteinUnlenbeckProcess().referenceBurstiness();

  158.         org.drip.execution.hjb.NonDimensionalCostSystemic ndcs =
  159.             (org.drip.execution.hjb.NonDimensionalCostSystemic) ndc;

  161.         return java.lang.Math.exp (-dblMarketState) * (dblNonDimensionalRiskAversion *
  162.             dblNonDimensionalRiskAversion - dblNonDimensionalCost * dblNonDimensionalCost) + 0.5 *
  163.                 dblBurstiness * dblBurstiness * ndcs.jacobian() - dblMarketState * ndcs.gradient();
  164.     }

  166.     /**
  167.      * NonDimensionalCostEvolverSystemic Constructor
  168.      * 
  169.      * @param ou The Underlying Ornstein-Unlenbeck Reference Process
  170.      * @param bAsymptoticEnhancedEulerCorrection Asymptotic Enhanced Euler Correction Application Flag
  171.      * @param dblAsymptoticEulerUrgencyThreshold The Asymptotic Euler Urgency Threshold
  172.      * 
  173.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  174.      */

  176.     public NonDimensionalCostEvolverSystemic (
  177.         final org.drip.measure.process.OrnsteinUhlenbeck ou,
  178.         final double dblAsymptoticEulerUrgencyThreshold,
  179.         final boolean bAsymptoticEnhancedEulerCorrection)
  180.         throws java.lang.Exception
  181.     {
  182.         super (ou, dblAsymptoticEulerUrgencyThreshold, bAsymptoticEnhancedEulerCorrection);
  183.     }

  185.     @Override public org.drip.execution.hjb.NonDimensionalCost evolve (
  186.         final org.drip.execution.hjb.NonDimensionalCost ndc,
  187.         final org.drip.execution.latent.MarketState ms,
  188.         final double dblNonDimensionalRiskAversion,
  189.         final double dblNonDimensionalTime,
  190.         final double dblNonDimensionalTimeIncrement)
  191.     {
  192.         if (null == ndc || !(ndc instanceof org.drip.execution.hjb.NonDimensionalCostSystemic) || null
  193.             == ms || !org.drip.numerical.common.NumberUtil.IsValid (dblNonDimensionalRiskAversion) ||
  194.                 !org.drip.numerical.common.NumberUtil.IsValid (dblNonDimensionalTime) ||
  195.                     !org.drip.numerical.common.NumberUtil.IsValid (dblNonDimensionalTimeIncrement))
  196.             return null;

  198.         double dblMarketState = ms.liquidity();

  200.         double dblMarketStateIncrement = 0.01 * dblMarketState;

  202.         double dblMarketStateExponentiation = java.lang.Math.exp (dblMarketState);

  204.         if (asymptoticEulerUrgencyThreshold() * dblNonDimensionalTime < 1.) {
  205.             if (!asymptoticEnhancedEulerCorrection())
  206.                 return org.drip.execution.hjb.NonDimensionalCostSystemic.LinearThreshold
  207.                     (dblMarketStateExponentiation, dblNonDimensionalTime);

  209.             double dblBurstiness = ornsteinUnlenbeckProcess().referenceBurstiness();

  211.             double dblNonDimensionalCostCross = -0.5 * dblMarketState * dblMarketStateExponentiation;

  213.             return org.drip.execution.hjb.NonDimensionalCostSystemic.EulerEnhancedLinearThreshold
  214.                 (dblMarketState, ((1. / dblNonDimensionalTimeIncrement) + 0.25 * dblBurstiness *
  215.                     dblBurstiness) * java.lang.Math.exp (dblMarketState) + dblNonDimensionalCostCross,
  216.                         dblNonDimensionalCostCross);
  217.         }

  219.         try {
  220.             double dblCostIncrementMid = advance (ndc, ms, new double[] {0.}, dblNonDimensionalRiskAversion)
  221.                 * dblNonDimensionalTimeIncrement;

  223.             double dblCostIncrementUp = advance (ndc, ms, new double[] {dblMarketStateIncrement},
  224.                 dblNonDimensionalRiskAversion) * dblNonDimensionalTimeIncrement;

  226.             double dblCostIncrementDown = advance (ndc, ms, new double[] {-1. * dblMarketStateIncrement},
  227.                 dblNonDimensionalRiskAversion) * dblNonDimensionalTimeIncrement;

  229.             double dblCost = ndc.realization() + dblCostIncrementMid;

  231.             return new org.drip.execution.hjb.NonDimensionalCostSystemic (dblCost, 0.5 *
  232.                 (dblCostIncrementUp - dblCostIncrementDown) / dblMarketStateIncrement, (dblCostIncrementUp +
  233.                     dblCostIncrementDown - 2. * dblCostIncrementMid) / (dblMarketStateIncrement *
  234.                         dblMarketStateIncrement), dblCost / dblMarketStateExponentiation);
  235.         } catch (java.lang.Exception e) {
  236.             e.printStackTrace();
  237.         }

  239.         return null;
  240.     }
  241. }
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