Almgren2003Estimator.java

  1. package org.drip.execution.principal;

  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>Almgren2003Estimator</i> generates the Gross Profit Distribution and the Information Ratio for a given
  82.  * Level of Principal Discount for an Optimal Trajectory that is generated using the Almgren (2003) Scheme.
  83.  * The References are:
  84.  * 
  85.  * <br><br>
  86.  *  <ul>
  87.  *  <li>
  88.  *      Almgren, R., and N. Chriss (1999): Value under Liquidation <i>Risk</i> <b>12 (12)</b>
  89.  *  </li>
  90.  *  <li>
  91.  *      Almgren, R., and N. Chriss (2000): Optimal Execution of Portfolio Transactions <i>Journal of Risk</i>
  92.  *          <b>3 (2)</b> 5-39
  93.  *  </li>
  94.  *  <li>
  95.  *      Almgren, R. (2003): Optimal Execution with Nonlinear Impact Functions and Trading-Enhanced Risk
  96.  *          <i>Applied Mathematical Finance</i> <b>10 (1)</b> 1-18
  97.  *  </li>
  98.  *  <li>
  99.  *      Almgren, R., and N. Chriss (2003): Bidding Principles <i>Risk</i> 97-102
  100.  *  </li>
  101.  *  <li>
  102.  *      Almgren, R., C. Thum, E. Hauptmann, and H. Li (2005): Equity Market Impact <i>Risk</i> <b>18 (7)</b>
  103.  *          57-62
  104.  *  </li>
  105.  *  </ul>
  106.  *
  107.  *  <br><br>
  108.  *  <ul>
  109.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ProductCore.md">Product Core Module</a></li>
  110.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/TransactionCostAnalyticsLibrary.md">Transaction Cost Analytics</a></li>
  111.  *      <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>
  112.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/execution/principal/README.md">Information Ratio Based Principal Trades</a></li>
  113.  *  </ul>
  114.  * 
  115.  * @author Lakshmi Krishnamurthy
  116.  */

  118. public class Almgren2003Estimator extends org.drip.execution.principal.GrossProfitEstimator {
  119.     private org.drip.execution.dynamics.LinearPermanentExpectationParameters _lpep =  null;

  121.     /**
  122.      * Almgren2003Estimator Constructor
  123.      * 
  124.      * @param pic The Power Continuous Market Impact Trajectory
  125.      * @param lpep The Linear Permanent Expectation Paremeter
  126.      * 
  127.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  128.      */

  130.     public Almgren2003Estimator (
  131.         final org.drip.execution.optimum.PowerImpactContinuous pic,
  132.         final org.drip.execution.dynamics.LinearPermanentExpectationParameters lpep)
  133.         throws java.lang.Exception
  134.     {
  135.         super (pic);

  137.         if (null == (_lpep = lpep))
  138.             throw new java.lang.Exception ("Almgren2003Estimator Constructor => Invalid Inputs");
  139.     }

  141.     /**
  142.      * Generate the Horizon that results in the Optimal Information Ratio
  143.      * 
  144.      * @param dblD The Principal Discount "D"
  145.      * 
  146.      * @return The Horizon that results in the Optimal Information Ratio
  147.      * 
  148.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  149.      */

  151.     public double optimalInformationRatioHorizon (
  152.         final double dblD)
  153.         throws java.lang.Exception
  154.     {
  155.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblD))
  156.             throw new java.lang.Exception
  157.                 ("Almgren2003Estimator::optimalInformationRatioHorizon => Invalid Inputs");

  159.         org.drip.execution.impact.TransactionFunctionPower tfpTemporaryExpectation =
  160.             (org.drip.execution.impact.TransactionFunctionPower)
  161.                 _lpep.temporaryExpectation().epochImpactFunction();

  163.         double dblGamma = ((org.drip.execution.impact.TransactionFunctionLinear)
  164.             _lpep.linearPermanentExpectation().epochImpactFunction()).slope();

  166.         double dblEta = tfpTemporaryExpectation.constant();

  168.         double dblK = tfpTemporaryExpectation.exponent();

  170.         double dblX = efficientTrajectory().tradeSize();

  172.         return dblX * java.lang.Math.pow (dblEta * (dblK + 1.) * (dblK + 1.) / (3. * dblK + 1.) / (dblD - 0.5
  173.             * dblGamma * dblX), 1. / dblK);
  174.     }

  176.     /**
  177.      * Compute the Optimal Information Ratio
  178.      * 
  179.      * @param dblD The Principal Discount "D"
  180.      * 
  181.      * @return The Optimal Information Ratio
  182.      * 
  183.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  184.      */

  186.     public double optimalInformationRatio (
  187.         final double dblD)
  188.         throws java.lang.Exception
  189.     {
  190.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblD))
  191.             throw new java.lang.Exception
  192.                 ("Almgren2003Estimator::optimalInformationRatio => Invalid Inputs");

  194.         org.drip.execution.impact.TransactionFunctionPower tfpTemporaryExpectation =
  195.             (org.drip.execution.impact.TransactionFunctionPower)
  196.                 _lpep.temporaryExpectation().epochImpactFunction();

  198.         double dblSigma = _lpep.arithmeticPriceDynamicsSettings().epochVolatility();

  200.         double dblGamma = ((org.drip.execution.impact.TransactionFunctionLinear)
  201.             _lpep.linearPermanentExpectation().epochImpactFunction()).slope();

  203.         double dblEta = tfpTemporaryExpectation.constant();

  205.         double dblK = tfpTemporaryExpectation.exponent();

  207.         double dblX = efficientTrajectory().tradeSize();

  209.         return java.lang.Math.pow (3. * dblK + 1.              , (1. * dblK + 2.) / (2. * dblK)) /
  210.                java.lang.Math.pow (1. * dblK + 1.              , (3. * dblK + 4.) / (2. * dblK)) *
  211.                java.lang.Math.pow (dblD - 0.5 * dblGamma * dblX, (1. * dblK + 1.) / (1. * dblK)) /
  212.                java.lang.Math.pow (dblEta                      , (0. * dblK + 1.) / (1. * dblK)) /
  213.                (dblX * dblSigma);
  214.     }

  216.     /**
  217.      * Compute the Principal Discount Hurdle given the Information Ratio
  218.      * 
  219.      * @param dblI The Optimal Information Ratio "I"
  220.      * 
  221.      * @return The Principal Discount Hurdle
  222.      * 
  223.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  224.      */

  226.     public double principalDiscountHurdle (
  227.         final double dblI)
  228.         throws java.lang.Exception
  229.     {
  230.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblI))
  231.             throw new java.lang.Exception
  232.                 ("Almgren2003Estimator::principalDiscountHurdle => Invalid Inputs");

  234.         org.drip.execution.impact.TransactionFunctionPower tfpTemporaryExpectation =
  235.             (org.drip.execution.impact.TransactionFunctionPower)
  236.                 _lpep.temporaryExpectation().epochImpactFunction();

  238.         double dblEta = tfpTemporaryExpectation.constant();

  240.         double dblGamma = ((org.drip.execution.impact.TransactionFunctionLinear)
  241.             _lpep.linearPermanentExpectation().epochImpactFunction()).slope();

  243.         double dblSigma = _lpep.arithmeticPriceDynamicsSettings().epochVolatility();

  245.         double dblK = tfpTemporaryExpectation.exponent();

  247.         double dblX = efficientTrajectory().tradeSize();

  249.         return java.lang.Math.pow (
  250.                0.5 * dblGamma * dblX +
  251.                java.lang.Math.pow (1. * dblK + 1.              , (3. * dblK + 4.) / (2. * dblK)) /
  252.                java.lang.Math.pow (3. * dblK + 1.              , (1. * dblK + 2.) / (2. * dblK)) *
  253.                java.lang.Math.pow (dblEta                      , (0. * dblK + 1.) / (1. * dblK)) *
  254.                (dblX * dblSigma * dblI),
  255.                dblK / (dblK + 1.)
  256.         );
  257.     }

  259.     /**
  260.      * Generate the Constant/Exponent Dependencies on the Market Parameters for the Optimal Execution Horizon
  261.      *  / Information Ratio
  262.      *  
  263.      * @return The Optimal Execution Horizon/Information Ratio Dependency
  264.      */

  266.     public org.drip.execution.principal.HorizonInformationRatioDependence optimalMeasures()
  267.     {
  268.         org.drip.execution.impact.TransactionFunctionPower tfpTemporaryExpectation =
  269.             (org.drip.execution.impact.TransactionFunctionPower)
  270.                 _lpep.temporaryExpectation().epochImpactFunction();

  272.         double dblK = tfpTemporaryExpectation.exponent();

  274.         try {
  275.             return new org.drip.execution.principal.HorizonInformationRatioDependence (
  276.                 new org.drip.execution.principal.OptimalMeasureDependence (
  277.                     java.lang.Math.pow ((dblK + 1.) * (dblK + 1.) / (3. * dblK + 1.), 1. / dblK),
  278.                     1. / dblK,
  279.                     1.,
  280.                     0.,
  281.                     -1. / dblK
  282.                 ),
  283.                 new org.drip.execution.principal.OptimalMeasureDependence (
  284.                     java.lang.Math.pow (3. * dblK + 1., (1. * dblK + 2.) / (2. * dblK)) /
  285.                         java.lang.Math.pow (1. * dblK + 1., (3. * dblK + 4.) / (2. * dblK)),
  286.                     -1. / dblK,
  287.                     -1.,
  288.                     -1.,
  289.                     (dblK + 1.) / dblK
  290.                 )
  291.             );
  292.         } catch (java.lang.Exception e) {
  293.             e.printStackTrace();
  294.         }

  296.         return null;
  297.     }
  298. }
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