NonDimensionalCostEvolverCorrelated.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>NonDimensionalCostEvolverCorrelated</i> implements the Correlated HJB-based Single Step Optimal
  82.  * Trajectory Cost Step Evolver using the Correlated Coordinated Variation Version of the Stochastic
  83.  * Volatility and the Transaction Function arising from the Realization of the Market State Variable as
  84.  * described in the "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 NonDimensionalCostEvolverCorrelated extends
  122.     org.drip.execution.hjb.NonDimensionalCostEvolver {

  124.     @Override protected double advance (
  125.         final org.drip.execution.hjb.NonDimensionalCost ndc,
  126.         final org.drip.execution.latent.MarketState ms,
  127.         final double[] adblMarketStateTweak,
  128.         final double dblNonDimensionalRiskAversion)
  129.         throws java.lang.Exception
  130.     {
  131.         org.drip.execution.hjb.NonDimensionalCostCorrelated ndcc =
  132.             (org.drip.execution.hjb.NonDimensionalCostCorrelated) ndc;

  134.         org.drip.measure.process.OrnsteinUhlenbeckPair oup2D =
  135.             (org.drip.measure.process.OrnsteinUhlenbeckPair) ornsteinUnlenbeckProcess();

  137.         org.drip.measure.dynamics.DiffusionEvaluatorOrnsteinUhlenbeck oup1DLiquidity = oup2D.reference();

  139.         org.drip.measure.dynamics.DiffusionEvaluatorOrnsteinUhlenbeck oup1DVolatility = oup2D.derived();

  141.         double dblVolatilityMarketState = ms.volatility() + adblMarketStateTweak[1];

  143.         double dblLiquidityMarketState = ms.liquidity() + adblMarketStateTweak[0];

  145.         double dblMu = oup1DLiquidity.relaxationTime() / oup1DVolatility.relaxationTime();

  147.         double dblVolatilityBurstiness = oup1DVolatility.burstiness();

  149.         double dblLiquidityBurstiness = oup1DLiquidity.burstiness();

  151.         double dblNonDimensionalCost = ndc.realization();

  153.         return
  154.             dblNonDimensionalRiskAversion * dblNonDimensionalRiskAversion * java.lang.Math.exp (2. *
  155.                 dblVolatilityMarketState) -
  156.             dblNonDimensionalCost * dblNonDimensionalCost * java.lang.Math.exp (-dblLiquidityMarketState) +
  157.             oup2D.correlation() + java.lang.Math.sqrt (dblMu) * dblLiquidityBurstiness *
  158.                 dblVolatilityBurstiness * ndcc.liquidityVolatilityGradient() +
  159.             0.5 * dblLiquidityBurstiness * dblLiquidityBurstiness * ndcc.liquidityJacobian() +
  160.             0.5 * dblMu * dblVolatilityBurstiness * dblVolatilityBurstiness * ndcc.volatilityJacobian() -
  161.             dblLiquidityMarketState * ndcc.liquidityGradient() -
  162.             dblMu * dblVolatilityMarketState * ndcc.volatilityGradient();
  163.     }

  165.     /**
  166.      * NonDimensionalCostEvolverCorrelated Constructor
  167.      * 
  168.      * @param oup2D The 2D Ornstein-Unlenbeck Generator Process
  169.      * @param bAsymptoticEnhancedEulerCorrection Asymptotic Enhanced Euler Correction Application Flag
  170.      * @param dblAsymptoticEulerUrgencyThreshold The Asymptotic Euler Urgency Threshold
  171.      * 
  172.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  173.      */

  175.     public NonDimensionalCostEvolverCorrelated (
  176.         final org.drip.measure.process.OrnsteinUhlenbeckPair oup2D,
  177.         final double dblAsymptoticEulerUrgencyThreshold,
  178.         final boolean bAsymptoticEnhancedEulerCorrection)
  179.         throws java.lang.Exception
  180.     {
  181.         super (oup2D, dblAsymptoticEulerUrgencyThreshold, bAsymptoticEnhancedEulerCorrection);
  182.     }

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

  197.         double dblLiquidityMarketState = ms.liquidity();

  199.         double dblLiquidityMarketStateIncrement = 0.01 * dblLiquidityMarketState;

  201.         double dblVolatilityMarketStateIncrement = 0.01 * ms.volatility();

  203.         try {
  204.             double dblCostIncrementMid = advance (ndc, ms, new double[] {0., 0.},
  205.                 dblNonDimensionalRiskAversion) * dblNonDimensionalTimeIncrement;

  207.             double dblCostIncrementLiquidityUp = advance (ndc, ms, new double[]
  208.                 {dblLiquidityMarketStateIncrement, 0.}, dblNonDimensionalRiskAversion) *
  209.                     dblNonDimensionalTimeIncrement;

  211.             double dblCostIncrementLiquidityDown = advance (ndc, ms, new double[]
  212.                 {-dblLiquidityMarketStateIncrement, 0.}, dblNonDimensionalRiskAversion) *
  213.                     dblNonDimensionalTimeIncrement;

  215.             double dblCostIncrementVolatilityUp = advance (ndc, ms, new double[] {0.,
  216.                 dblVolatilityMarketStateIncrement}, dblNonDimensionalRiskAversion) *
  217.                     dblNonDimensionalTimeIncrement;

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

  223.             double dblCostIncrementCrossUp = advance (ndc, ms, new double[]
  224.                 {dblLiquidityMarketStateIncrement, dblVolatilityMarketStateIncrement},
  225.                     dblNonDimensionalRiskAversion) * dblNonDimensionalTimeIncrement;

  227.             double dblCostIncrementCrossDown = advance (ndc, ms, new double[]
  228.                 {-dblLiquidityMarketStateIncrement, -dblVolatilityMarketStateIncrement},
  229.                     dblNonDimensionalRiskAversion) * dblNonDimensionalTimeIncrement;

  231.             double dblNonDimensionalCost = ndc.realization() + dblCostIncrementMid;

  233.             return new org.drip.execution.hjb.NonDimensionalCostCorrelated (
  234.                 dblNonDimensionalCost,
  235.                 0.5 * (dblCostIncrementLiquidityUp - dblCostIncrementLiquidityDown) /
  236.                     dblLiquidityMarketStateIncrement,
  237.                 (dblCostIncrementLiquidityUp + dblCostIncrementLiquidityDown - 2. * dblCostIncrementMid) /
  238.                     (dblLiquidityMarketStateIncrement * dblLiquidityMarketStateIncrement),
  239.                 0.5 * (dblCostIncrementVolatilityUp - dblCostIncrementVolatilityDown) /
  240.                     dblVolatilityMarketStateIncrement,
  241.                 (dblCostIncrementVolatilityUp + dblCostIncrementVolatilityDown - 2. * dblCostIncrementMid) /
  242.                     (dblVolatilityMarketStateIncrement * dblVolatilityMarketStateIncrement),
  243.                 0.25 * (dblCostIncrementCrossUp - dblCostIncrementCrossDown) /
  244.                     (dblLiquidityMarketStateIncrement * dblVolatilityMarketStateIncrement),
  245.                 dblNonDimensionalCost * java.lang.Math.exp (-dblLiquidityMarketState));
  246.         } catch (java.lang.Exception e) {
  247.             e.printStackTrace();
  248.         }

  250.         return null;
  251.     }
  252. }
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