ConstrainedLinearTemporaryImpact.java

  1. package org.drip.execution.cost;

  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>ConstrainedLinearTemporaryImpact</i> computes and holds the Optimal Trajectory under Trading Rate Sign
  82.  * Constraints using Linear Temporary Impact Function for the given set of Inputs. The References are:
  83.  * 
  84.  * <br><br>
  85.  *  <ul>
  86.  *      <li>
  87.  *          Bertsimas, D., and A. W. Lo (1998): Optimal Control of Execution Costs <i>Journal of Financial
  88.  *              Markets</i> <b>1</b> 1-50
  89.  *      </li>
  90.  *      <li>
  91.  *          Almgren, R., 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.  *          Brunnermeier, L. K., and L. H. Pedersen (2005): Predatory Trading <i>Journal of Finance</i> <b>60
  96.  *              (4)</b> 1825-1863
  97.  *      </li>
  98.  *      <li>
  99.  *          Almgren, R., and J. Lorenz (2006): Bayesian Adaptive Trading with a Daily Cycle <i>Journal of
  100.  *              Trading</i> <b>1 (4)</b> 38-46
  101.  *      </li>
  102.  *      <li>
  103.  *          Kissell, R., and R. Malamut (2007): Algorithmic Decision Making Framework <i>Journal of
  104.  *              Trading</i> <b>1 (1)</b> 12-21
  105.  *      </li>
  106.  *  </ul>
  107.  *
  108.  *  <br><br>
  109.  *  <ul>
  110.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ProductCore.md">Product Core Module</a></li>
  111.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/TransactionCostAnalyticsLibrary.md">Transaction Cost Analytics</a></li>
  112.  *      <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>
  113.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/execution/cost/README.md">Linear Temporary Market Impact Cost</a></li>
  114.  *  </ul>
  115.  * 
  116.  * @author Lakshmi Krishnamurthy
  117.  */

  119. public class ConstrainedLinearTemporaryImpact extends org.drip.execution.cost.LinearTemporaryImpact {
  120.     private double _dblCriticalDrift = java.lang.Double.NaN;
  121.     private double _dblTradeStartTime = java.lang.Double.NaN;
  122.     private double _dblTradeFinishTime = java.lang.Double.NaN;

  124.     /**
  125.      * Generate a ConstrainedLinearTemporaryImpact Instance
  126.      * 
  127.      * @param dblSpotTime Spot Time
  128.      * @param dblFinishTime Finish Time
  129.      * @param dblSpotHoldings Spot Holdings
  130.      * @param pcc The Prior/Conditional Combiner
  131.      * @param dblGrossPriceChange The Gross Price Change
  132.      * @param tflTemporary The Temporary Linear Impact Function
  133.      * 
  134.      * @return The ConstrainedLinearTemporaryImpact Instance
  135.      */

  137.     public static final ConstrainedLinearTemporaryImpact Standard (
  138.         final double dblSpotTime,
  139.         final double dblFinishTime,
  140.         final double dblSpotHoldings,
  141.         final org.drip.execution.bayesian.PriorConditionalCombiner pcc,
  142.         final double dblGrossPriceChange,
  143.         final org.drip.execution.impact.TransactionFunctionLinear tflTemporary)
  144.     {
  145.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblSpotTime) ||
  146.             !org.drip.numerical.common.NumberUtil.IsValid (dblFinishTime) ||
  147.                 !org.drip.numerical.common.NumberUtil.IsValid (dblSpotHoldings) || null == pcc || null ==
  148.                     tflTemporary)
  149.             return null;

  151.         final double dblLiquidityCoefficient = tflTemporary.slope();

  153.         org.drip.measure.gaussian.R1UnivariateNormal r1unPosterior = pcc.posteriorDriftDistribution
  154.             (dblGrossPriceChange);

  156.         if (null == r1unPosterior) return null;

  158.         final double dblDriftEstimate = r1unPosterior.mean();

  160.         double dblTradeStartTime = dblSpotTime;
  161.         double dblTradeFinishTime = dblFinishTime;
  162.         double dblHorizon = dblFinishTime - dblSpotTime;
  163.         double dblInstantaneousTradeRate = java.lang.Double.NaN;
  164.         double dblCriticalDrift = 4. * dblLiquidityCoefficient * dblSpotHoldings / (dblHorizon * dblHorizon);

  166.         if (dblDriftEstimate > dblCriticalDrift) {
  167.             dblTradeStartTime = dblSpotTime;

  169.             dblInstantaneousTradeRate = java.lang.Math.sqrt (dblDriftEstimate * dblSpotHoldings /
  170.                 dblLiquidityCoefficient);

  172.             dblTradeFinishTime = dblSpotTime + java.lang.Math.sqrt (4. * dblLiquidityCoefficient *
  173.                 dblSpotHoldings / dblDriftEstimate);
  174.         } else if (dblDriftEstimate < -1. * dblCriticalDrift) {
  175.             dblTradeFinishTime = dblFinishTime - java.lang.Math.sqrt (-4. * dblLiquidityCoefficient *
  176.                 dblSpotHoldings / dblDriftEstimate);

  178.             dblInstantaneousTradeRate = 0.;
  179.             dblTradeFinishTime = dblFinishTime;
  180.         } else
  181.             dblInstantaneousTradeRate = dblSpotHoldings / dblHorizon + dblDriftEstimate * dblHorizon /
  182.                 dblLiquidityCoefficient;

  184.         final double dblt = dblTradeStartTime;
  185.         final double dblT = dblTradeFinishTime;

  187.         org.drip.function.definition.R1ToR1 r1ToR1Holdings = new org.drip.function.definition.R1ToR1 (null) {
  188.             @Override public double evaluate (
  189.                 final double dblTau)
  190.                 throws java.lang.Exception
  191.             {
  192.                 if (!org.drip.numerical.common.NumberUtil.IsValid (dblTau))
  193.                     throw new java.lang.Exception
  194.                         ("ConstrainedLinearTemporaryImpact::Holdings::evaluate => Invalid Inputs");

  196.                 if (dblTau <= dblt) return dblSpotHoldings;

  198.                 if (dblTau >= dblT) return 0.;

  200.                 return (dblT - dblTau) * (dblSpotHoldings / (dblT - dblt) - 0.25 * dblDriftEstimate * (dblTau
  201.                     - dblt) / dblLiquidityCoefficient);
  202.             }
  203.         };

  205.         try {
  206.             return new ConstrainedLinearTemporaryImpact (dblSpotTime, dblFinishTime, dblSpotHoldings, pcc,
  207.                 dblGrossPriceChange, tflTemporary, r1ToR1Holdings, dblInstantaneousTradeRate,
  208.                     dblCriticalDrift, dblTradeStartTime, dblTradeFinishTime);
  209.         } catch (java.lang.Exception e) {
  210.             e.printStackTrace();
  211.         }

  213.         return null;
  214.     }

  216.     protected ConstrainedLinearTemporaryImpact (
  217.         final double dblSpotTime,
  218.         final double dblFinishTime,
  219.         final double dblSpotHoldings,
  220.         final org.drip.execution.bayesian.PriorConditionalCombiner pcc,
  221.         final double dblGrossPriceChange,
  222.         final org.drip.execution.impact.TransactionFunctionLinear tflTemporary,
  223.         final org.drip.function.definition.R1ToR1 r1ToR1Holdings,
  224.         final double dblInstantaneousTradeRate,
  225.         final double dblCriticalDrift,
  226.         final double dblTradeStartTime,
  227.         final double dblTradeFinishTime)
  228.         throws java.lang.Exception
  229.     {
  230.         super (dblSpotTime, dblFinishTime, dblSpotHoldings, pcc, dblGrossPriceChange, tflTemporary,
  231.             dblTradeFinishTime - dblTradeStartTime, r1ToR1Holdings, dblInstantaneousTradeRate);

  233.         if (!org.drip.numerical.common.NumberUtil.IsValid (_dblCriticalDrift = dblCriticalDrift) ||
  234.             !org.drip.numerical.common.NumberUtil.IsValid (_dblTradeStartTime = dblTradeStartTime) ||
  235.             !org.drip.numerical.common.NumberUtil.IsValid (_dblTradeFinishTime = dblTradeFinishTime))
  236.             throw new java.lang.Exception ("ConstrainedLinearTemporaryImpact Constructor => Invalid Inputs");
  237.     }

  239.     /**
  240.      * Retrieve the Critical Drift
  241.      * 
  242.      * @return The Critical Drift
  243.      */

  245.     public double criticalDrift()
  246.     {
  247.         return _dblCriticalDrift;
  248.     }

  250.     /**
  251.      * Retrieve the Trade Start Time
  252.      * 
  253.      * @return The Trade Start Time
  254.      */

  256.     public double tradeStartTime()
  257.     {
  258.         return _dblTradeStartTime;
  259.     }

  261.     /**
  262.      * Retrieve the Trade Finish Time
  263.      * 
  264.      * @return The Trade Finish Time
  265.      */

  267.     public double tradeFinishTime()
  268.     {
  269.         return _dblTradeFinishTime;
  270.     }
  271. }
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