StaticOptimalSchemeDiscrete.java

  1. package org.drip.execution.nonadaptive;

  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>StaticOptimalSchemeDiscrete</i> generates the Trade/Holdings List of Static Optimal Execution Schedule
  82.  * based on the Discrete Trade Trajectory Control, the Price Walk Parameters, and the Objective Utility
  83.  * Function. 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
  92.  *              Risk</i> <b>3 (2)</b> 5-39
  93.  *      </li>
  94.  *      <li>
  95.  *          Bertsimas, D., and A. W. Lo (1998): Optimal Control of Execution Costs <i>Journal of Financial
  96.  *              Markets</i> <b>1</b> 1-50
  97.  *      </li>
  98.  *      <li>
  99.  *          Chan, L. K. C., and J. Lakonishak (1995): The Behavior of Stock Prices around Institutional
  100.  *              Trades <i>Journal of Finance</i> <b>50</b> 1147-1174
  101.  *      </li>
  102.  *      <li>
  103.  *          Keim, D. B., and A. Madhavan (1997): Transaction Costs and Investment Style: An Inter-exchange
  104.  *              Analysis of Institutional Equity Trades <i>Journal of Financial Economics</i> <b>46</b>
  105.  *              265-292
  106.  *      </li>
  107.  *  </ul>
  108.  *
  109.  *  <br><br>
  110.  *  <ul>
  111.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ProductCore.md">Product Core Module</a></li>
  112.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/TransactionCostAnalyticsLibrary.md">Transaction Cost Analytics</a></li>
  113.  *      <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>
  114.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/execution/nonadaptive/README.md">Almgren-Chriss Static Optimal Trajectory</a></li>
  115.  *  </ul>
  116.  * 
  117.  * @author Lakshmi Krishnamurthy
  118.  */

  120. public class StaticOptimalSchemeDiscrete extends org.drip.execution.nonadaptive.StaticOptimalScheme {
  121.     private org.drip.execution.strategy.DiscreteTradingTrajectoryControl _dttc = null;

  123.     private double[] completeHoldings (
  124.         final double[] adblInnerHoldings)
  125.     {
  126.         if (null == adblInnerHoldings) return null;

  128.         int iNumCompleteHoldings = adblInnerHoldings.length + 2;
  129.         double[] adblCompleteHoldings = new double[iNumCompleteHoldings];

  131.         for (int i = 0; i < iNumCompleteHoldings; ++i) {
  132.             if (0 == i)
  133.                 adblCompleteHoldings[i] = _dttc.startHoldings();
  134.             else if (iNumCompleteHoldings - 1 == i)
  135.                 adblCompleteHoldings[i] = 0.;
  136.             else
  137.                 adblCompleteHoldings[i] = adblInnerHoldings[i - 1];
  138.         }

  140.         return adblCompleteHoldings;
  141.     }

  143.     private org.drip.execution.sensitivity.ControlNodesGreek objectiveSensitivity (
  144.         final double[] adblInnerHoldings)
  145.     {
  146.         org.drip.execution.capture.TrajectoryShortfallEstimator tse = null;

  148.         try {
  149.             tse = new org.drip.execution.capture.TrajectoryShortfallEstimator
  150.                 (org.drip.execution.strategy.DiscreteTradingTrajectory.Standard (_dttc.executionTimeNodes(),
  151.                     completeHoldings (adblInnerHoldings)));
  152.         } catch (java.lang.Exception e) {
  153.             e.printStackTrace();

  155.             return null;
  156.         }

  158.         org.drip.execution.dynamics.ArithmeticPriceEvolutionParameters apep = priceEvolutionParameters();

  160.         org.drip.execution.sensitivity.ControlNodesGreek cngVariance = tse.varianceContribution (apep);

  162.         org.drip.execution.sensitivity.ControlNodesGreek cngExpectation = tse.expectationContribution (apep);

  164.         if (null == cngExpectation || null == cngVariance) return null;

  166.         return objectiveUtility().sensitivity ((org.drip.execution.sensitivity.TrajectoryControlNodesGreek)
  167.             cngExpectation, (org.drip.execution.sensitivity.TrajectoryControlNodesGreek) cngVariance);
  168.     }

  170.     private org.drip.function.definition.RdToR1 optimizerRdToR1()
  171.     {
  172.         return new org.drip.function.definition.RdToR1 (null) {
  173.             @Override public int dimension()
  174.             {
  175.                 return _dttc.executionTimeNodes().length - 2;
  176.             }

  178.             @Override public double evaluate (
  179.                 final double[] adblInnerHoldings)
  180.                 throws java.lang.Exception
  181.             {
  182.                 org.drip.execution.sensitivity.ControlNodesGreek cngObjectiveUtility = objectiveSensitivity
  183.                     (adblInnerHoldings);

  185.                 if (null == cngObjectiveUtility)
  186.                     throw new java.lang.Exception
  187.                         ("StaticOptimalSchemeDiscrete::optimizerRdToR1::evaluate => Invalid Inputs");

  189.                 return cngObjectiveUtility.value();
  190.             }

  192.             @Override public double[] jacobian (
  193.                 final double[] adblInnerHoldings)
  194.             {
  195.                 org.drip.execution.sensitivity.ControlNodesGreek cngObjectiveUtility = objectiveSensitivity
  196.                     (adblInnerHoldings);

  198.                 return null == cngObjectiveUtility ? null : cngObjectiveUtility.jacobian();
  199.             }

  201.             @Override public double[][] hessian (
  202.                 final double[] adblInnerHoldings)
  203.             {
  204.                 org.drip.execution.sensitivity.ControlNodesGreek cngObjectiveUtility = objectiveSensitivity
  205.                     (adblInnerHoldings);

  207.                 return null == cngObjectiveUtility ? null : cngObjectiveUtility.hessian();
  208.             }
  209.         };
  210.     }

  212.     /**
  213.      * StaticOptimalSchemeDiscrete Constructor
  214.      * 
  215.      * @param dttc The Discrete Trading Trajectory Control Parameters
  216.      * @param apep The Arithmetic Price Walk Parameters
  217.      * @param ou The Optimizer Objective Utility Function
  218.      * 
  219.      * @throws java.lang.Exception Thrown if the Inputs are not valid
  220.      */

  222.     public StaticOptimalSchemeDiscrete (
  223.         final org.drip.execution.strategy.DiscreteTradingTrajectoryControl dttc,
  224.         final org.drip.execution.dynamics.ArithmeticPriceEvolutionParameters apep,
  225.         final org.drip.execution.risk.ObjectiveUtility ou)
  226.         throws java.lang.Exception
  227.     {
  228.         super (apep, ou);

  230.         if (null == (_dttc = dttc))
  231.             throw new java.lang.Exception ("StaticOptimalSchemeDiscrete Constructor => Invalid Inputs");
  232.     }

  234.     /**
  235.      * Retrieve the Discrete Trajectory Control Settings
  236.      * 
  237.      * @return The Discrete Trajectory Control Settings
  238.      */

  240.     public org.drip.execution.strategy.DiscreteTradingTrajectoryControl control()
  241.     {
  242.         return _dttc;
  243.     }

  245.     @Override public org.drip.execution.optimum.EfficientTradingTrajectory generate()
  246.     {
  247.         double[] adblExecutionTimeNode = _dttc.executionTimeNodes();

  249.         org.drip.execution.strategy.DiscreteTradingTrajectory dtt =
  250.             org.drip.execution.strategy.DiscreteTradingTrajectory.Linear (adblExecutionTimeNode,
  251.                 _dttc.startHoldings(), 0.);

  253.         if (null == dtt) return null;

  255.         org.drip.function.rdtor1solver.VariateInequalityConstraintMultiplier vicm = null;

  257.         try {
  258.             if (null == (vicm = new org.drip.function.rdtor1solver.NewtonFixedPointFinder (optimizerRdToR1(),
  259.                 null, org.drip.function.rdtor1solver.ConvergenceControl.Standard()).convergeVariate (new
  260.                     org.drip.function.rdtor1solver.VariateInequalityConstraintMultiplier (false,
  261.                         dtt.innerHoldings(), null))))
  262.                 return null;
  263.         } catch (java.lang.Exception e) {
  264.             e.printStackTrace();

  266.             return null;
  267.         }

  269.         return org.drip.execution.optimum.EfficientTradingTrajectoryDiscrete.Standard (adblExecutionTimeNode,
  270.             completeHoldings (vicm.variateArray()), priceEvolutionParameters());
  271.     }
  272. }
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