TransactionFunction.java

  1. package org.drip.execution.impact;

  2. /*
  3.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  4.  */

  5. /*!
  6.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  7.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  8.  * Copyright (C) 2018 Lakshmi Krishnamurthy
  9.  * Copyright (C) 2017 Lakshmi Krishnamurthy
  10.  * Copyright (C) 2016 Lakshmi Krishnamurthy
  11.  *
  12.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  13.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  14.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  15.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  16.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  17.  *      and computational support.
  18.  *  
  19.  *      https://lakshmidrip.github.io/DROP/
  20.  *  
  21.  *  DROP is composed of three modules:
  22.  *  
  23.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  24.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  25.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  26.  *
  27.  *  DROP Product Core implements libraries for the following:
  28.  *  - Fixed Income Analytics
  29.  *  - Loan Analytics
  30.  *  - Transaction Cost Analytics
  31.  *
  32.  *  DROP Portfolio Core implements libraries for the following:
  33.  *  - Asset Allocation Analytics
  34.  *  - Asset Liability Management Analytics
  35.  *  - Capital Estimation Analytics
  36.  *  - Exposure Analytics
  37.  *  - Margin Analytics
  38.  *  - XVA Analytics
  39.  *
  40.  *  DROP Computational Core implements libraries for the following:
  41.  *  - Algorithm Support
  42.  *  - Computation Support
  43.  *  - Function Analysis
  44.  *  - Model Validation
  45.  *  - Numerical Analysis
  46.  *  - Numerical Optimizer
  47.  *  - Spline Builder
  48.  *  - Statistical Learning
  49.  *
  50.  *  Documentation for DROP is Spread Over:
  51.  *
  52.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  53.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  54.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  55.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  56.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  57.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  58.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  59.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  60.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  61.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  62.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  63.  *
  64.  *  Licensed under the Apache License, Version 2.0 (the "License");
  65.  *      you may not use this file except in compliance with the License.
  66.  *  
  67.  *  You may obtain a copy of the License at
  68.  *      http://www.apache.org/licenses/LICENSE-2.0
  69.  *  
  70.  *  Unless required by applicable law or agreed to in writing, software
  71.  *      distributed under the License is distributed on an "AS IS" BASIS,
  72.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  73.  *  
  74.  *  See the License for the specific language governing permissions and
  75.  *      limitations under the License.
  76.  */

  77. /**
  78.  * <i>TransactionFunction</i> exports the Temporary/Permanent Market Impact Displacement/Volatility
  79.  * Functional Dependence on the Trade Rate. The References are:
  80.  *
  81.  * <br>
  82.  *  <ul>
  83.  *      <li>
  84.  *          Almgren, R., and N. Chriss (1999): Value under Liquidation <i>Risk</i> <b>12 (12)</b>
  85.  *      </li>
  86.  *      <li>
  87.  *          Almgren, R., and N. Chriss (2000): Optimal Execution of Portfolio Transactions <i>Journal of
  88.  *              Risk</i> <b>3 (2)</b> 5-39
  89.  *      </li>
  90.  *      <li>
  91.  *          Bertsimas, D., and A. W. Lo (1998): Optimal Control of Execution Costs <i>Journal of Financial
  92.  *              Markets</i> <b>1</b> 1-50
  93.  *      </li>
  94.  *      <li>
  95.  *          Chan, L. K. C., and J. Lakonishak (1995): The Behavior of Stock Prices around Institutional
  96.  *              Trades <i>Journal of Finance</i> <b>50</b> 1147-1174
  97.  *      </li>
  98.  *      <li>
  99.  *          Keim, D. B., and A. Madhavan (1997): Transaction Costs and Investment Style: An Inter-exchange
  100.  *              Analysis of Institutional Equity Trades <i>Journal of Financial Economics</i> <b>46</b>
  101.  *              265-292
  102.  *      </li>
  103.  *  </ul>
  104.  *
  105.  *  <br><br>
  106.  *  <ul>
  107.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ProductCore.md">Product Core Module</a></li>
  108.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/TransactionCostAnalyticsLibrary.md">Transaction Cost Analytics</a></li>
  109.  *      <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>
  110.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/execution/impact/README.md">Market Impact Transaction Function Implementation</a></li>
  111.  *  </ul>
  112.  *
  113.  * @author Lakshmi Krishnamurthy
  114.  */

  115. public abstract class TransactionFunction extends org.drip.function.definition.R1ToR1 {

  116.     protected TransactionFunction()
  117.     {
  118.         super (null);
  119.     }

  120.     /**
  121.      * Regularize the Input Function using the specified Trade Inputs
  122.      *
  123.      * @param dblTradeInterval The Trade Interval
  124.      *
  125.      * @return The Regularize Input
  126.      *
  127.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  128.      */

  129.     public abstract double regularize (
  130.         final double dblTradeInterval)
  131.         throws java.lang.Exception;

  132.     /**
  133.      * Modulate/Scale the Impact Output
  134.      *
  135.      * @param dblTradeInterval The Trade Interval
  136.      *
  137.      * @return The Modulated Output
  138.      *
  139.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  140.      */

  141.     public abstract double modulate (
  142.         final double dblTradeInterval)
  143.         throws java.lang.Exception;

  144.     /**
  145.      * Evaluate the Impact Function at the specified Trade Parameters
  146.      *
  147.      * @param dblTradeAmount The Trade Amount
  148.      * @param dblTradeInterval The Trade Interval
  149.      *
  150.      * @return The Value of the Impact Function
  151.      *
  152.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  153.      */

  154.     public double evaluate (
  155.         final double dblTradeAmount,
  156.         final double dblTradeInterval)
  157.         throws java.lang.Exception
  158.     {
  159.         return modulate (dblTradeInterval) * evaluate (dblTradeAmount * regularize (dblTradeInterval));
  160.     }

  161.     /**
  162.      * Compute the Sensitivity to the Left Holdings
  163.      *
  164.      * @param dblTradeAmount The Trade Amount
  165.      * @param dblTradeInterval The Trade Interval
  166.      * @param iOrder Order of the Derivative
  167.      *
  168.      * @return The Sensitivity to the Left Holdings of the Impact Function
  169.      *
  170.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  171.      */

  172.     public double leftHoldingsDerivative (
  173.         final double dblTradeAmount,
  174.         final double dblTradeInterval,
  175.         final int iOrder)
  176.         throws java.lang.Exception
  177.     {
  178.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblTradeAmount) || 0 >= iOrder)
  179.             throw new java.lang.Exception ("TransactionFunction::leftHoldingsDerivative => Invalid Inputs");

  180.         double dblRegularizedInput = regularize (dblTradeInterval);

  181.         return modulate (dblTradeInterval) * java.lang.Math.pow (-1. * dblRegularizedInput, iOrder) *
  182.             derivative (dblTradeAmount * dblRegularizedInput, iOrder);
  183.     }

  184.     /**
  185.      * Compute the Sensitivity to the Right Holdings
  186.      *
  187.      * @param dblTradeAmount The Trade Amount
  188.      * @param dblTradeInterval The Trade Interval
  189.      * @param iOrder Order of the Derivative
  190.      *
  191.      * @return The Sensitivity to the Right Holdings of the Impact Function
  192.      *
  193.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  194.      */

  195.     public double rightHoldingsDerivative (
  196.         final double dblTradeAmount,
  197.         final double dblTradeInterval,
  198.         final int iOrder)
  199.         throws java.lang.Exception
  200.     {
  201.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblTradeAmount) || 0 >= iOrder)
  202.             throw new java.lang.Exception ("TransactionFunction::rightHoldingsDerivative => Invalid Inputs");

  203.         double dblRegularizedInput = regularize (dblTradeInterval);

  204.         return modulate (dblTradeInterval) * java.lang.Math.pow (dblRegularizedInput, iOrder) * derivative
  205.             (dblTradeAmount * dblRegularizedInput, iOrder);
  206.     }

  207.     /**
  208.      * Compute the Second Order Sensitivity to the Left/Right Holdings
  209.      *
  210.      * @param dblTradeAmount The Trade Amount
  211.      * @param dblTradeInterval The Trade Interval
  212.      *
  213.      * @return The Second Order Sensitivity to the Left/Right Holdings of the Impact Function
  214.      *
  215.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  216.      */

  217.     public double crossHoldingsDerivative (
  218.         final double dblTradeAmount,
  219.         final double dblTradeInterval)
  220.         throws java.lang.Exception
  221.     {
  222.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblTradeAmount))
  223.             throw new java.lang.Exception ("TransactionFunction::crossHoldingsDerivative => Invalid Inputs");

  224.         double dblRegularizedInput = regularize (dblTradeInterval);

  225.         return -1. * modulate (dblTradeInterval) * dblRegularizedInput * dblRegularizedInput * derivative
  226.             (dblTradeAmount * dblRegularizedInput, 2);
  227.     }
  228. }