PowerVarianceObjectiveUtility.java

  1. package org.drip.execution.risk;

  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>PowerVarianceObjectiveUtility</i> implements the Mean-Power-Variance Objective Utility Function that
  82.  * needs to be optimized to extract the Optimal Execution Trajectory. The Exact Objective Function is of the
  83.  * Form:
  84.  *  
  85.  *              U[x] = E[x] + lambda * (V[x] ^p)
  86.  *  
  87.  *  where p is greater than 0.
  88.  *  
  89.  *  p = 1
  90.  *  
  91.  *  is the Regular Mean-Variance, and
  92.  *  
  93.  *  p = 0.5
  94.  *  
  95.  *  is VaR Minimization (L-VaR). The References are:
  96.  * 
  97.  * <br><br>
  98.  *  <ul>
  99.  *      <li>
  100.  *          Almgren, R., and N. Chriss (1999): Value under Liquidation <i>Risk</i> <b>12 (12)</b>
  101.  *      </li>
  102.  *      <li>
  103.  *          Almgren, R., and N. Chriss (2000): Optimal Execution of Portfolio Transactions <i>Journal of
  104.  *              Risk</i> <b>3 (2)</b> 5-39
  105.  *      </li>
  106.  *      <li>
  107.  *          Almgren, R. (2003): Optimal Execution with Non-linear Impact Functions and Trading Enhanced Risk
  108.  *              <i>Applied Mathematical Finance</i> <b>10 (1)</b> 1-18
  109.  *      </li>
  110.  *      <li>
  111.  *          Artzner, P., F. Delbaen, J. M. Eber, and D. Heath (1999): Coherent Measures of Risk
  112.  *              <i>Mathematical Finance</i> <b>9</b> 203-228
  113.  *      </li>
  114.  *      <li>
  115.  *          Basak, S., and A. Shapiro (2001): Value-at-Risk Based Risk Management: Optimal Policies and Asset
  116.  *              Prices <i>Review of Financial Studies</i> <b>14</b> 371-405
  117.  *      </li>
  118.  *  </ul>
  119.  *
  120.  *  <br><br>
  121.  *  <ul>
  122.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ProductCore.md">Product Core Module</a></li>
  123.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/TransactionCostAnalyticsLibrary.md">Transaction Cost Analytics</a></li>
  124.  *      <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>
  125.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/execution/risk/README.md">Optimal Execution MVO Efficient Frontier</a></li>
  126.  *  </ul>
  127.  * 
  128.  * @author Lakshmi Krishnamurthy
  129.  */

  131. public class PowerVarianceObjectiveUtility implements org.drip.execution.risk.ObjectiveUtility {
  132.     private double _dblRiskAversion = java.lang.Double.NaN;
  133.     private double _dblVarianceExponent = java.lang.Double.NaN;

  135.     /**
  136.      * Generate the Liquidity VaR Version of the Power Variance Utility Function
  137.      * 
  138.      * @param dblRiskAversion The Risk Aversion Parameter
  139.      * 
  140.      * @return The Liquidity VaR Version of the Power Variance Utility Function
  141.      */

  143.     public static final PowerVarianceObjectiveUtility LiquidityVaR (
  144.         final double dblRiskAversion)
  145.     {
  146.         try {
  147.             return new PowerVarianceObjectiveUtility (0.5, dblRiskAversion);
  148.         } catch (java.lang.Exception e) {
  149.             e.printStackTrace();
  150.         }

  152.         return null;
  153.     }

  155.     /**
  156.      * PowerVarianceObjectiveUtility Constructor
  157.      * 
  158.      * @param dblVarianceExponent The Variance Exponent
  159.      * @param dblRiskAversion The Risk Aversion Parameter
  160.      * 
  161.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  162.      */

  164.     public PowerVarianceObjectiveUtility (
  165.         final double dblVarianceExponent,
  166.         final double dblRiskAversion)
  167.         throws java.lang.Exception
  168.     {
  169.         if (!org.drip.numerical.common.NumberUtil.IsValid (_dblVarianceExponent = dblVarianceExponent) || 0. >
  170.             _dblVarianceExponent || !org.drip.numerical.common.NumberUtil.IsValid (_dblRiskAversion =
  171.                 dblRiskAversion) || 0. > _dblRiskAversion)
  172.             throw new java.lang.Exception ("PowerVarianceObjectiveUtility Constructor => Invalid Inputs!");
  173.     }

  175.     /**
  176.      * Retrieve the Risk Aversion Parameter
  177.      * 
  178.      * @return The Risk Aversion Parameter
  179.      */

  181.     public double riskAversion()
  182.     {
  183.         return _dblRiskAversion;
  184.     }

  186.     /**
  187.      * Retrieve the Variance Exponent
  188.      * 
  189.      * @return The Variance Exponent
  190.      */

  192.     public double varianceExponent()
  193.     {
  194.         return _dblVarianceExponent;
  195.     }

  197.     @Override public org.drip.execution.sensitivity.ControlNodesGreek sensitivity (
  198.         final org.drip.execution.sensitivity.TrajectoryControlNodesGreek tcngExpectation,
  199.         final org.drip.execution.sensitivity.TrajectoryControlNodesGreek tcngVariance)
  200.     {
  201.         if (null == tcngExpectation || null == tcngVariance) return null;

  203.         double[] adblVarianceJacobian = tcngVariance.innerJacobian();

  205.         if (null == adblVarianceJacobian) return null;

  207.         double dblVarianceValue = tcngVariance.value();

  209.         double[][] aadblVarianceHessian = tcngVariance.innerHessian();

  211.         double[] adblExpectationJacobian = tcngExpectation.innerJacobian();

  213.         double[][] aadblExpectationHessian = tcngExpectation.innerHessian();

  215.         int iNumControlNode = adblVarianceJacobian.length;
  216.         double[] adblObjectiveJacobian = new double[iNumControlNode];
  217.         double[][] aadblObjectiveHessian = new double[iNumControlNode][iNumControlNode];

  219.         double dblJacobianMultiplier = _dblVarianceExponent * _dblRiskAversion * java.lang.Math.pow
  220.             (dblVarianceValue, _dblVarianceExponent - 1.);

  222.         double dblJacobianProductMultiplier = _dblVarianceExponent * (_dblVarianceExponent - 1.) *
  223.             _dblRiskAversion * java.lang.Math.pow (dblVarianceValue, _dblVarianceExponent - 2.);

  225.         for (int i = 0; i < iNumControlNode; ++i) {
  226.             adblObjectiveJacobian[i] = adblExpectationJacobian[i] + dblJacobianMultiplier *
  227.                 adblVarianceJacobian[i];

  229.             for (int j = 0; j < iNumControlNode; ++j)
  230.                 aadblObjectiveHessian[i][j] = aadblExpectationHessian[i][j] + dblJacobianProductMultiplier *
  231.                     adblVarianceJacobian[i] * adblVarianceJacobian[j] + dblJacobianMultiplier *
  232.                         aadblVarianceHessian[i][j];
  233.         }

  235.         try {
  236.             return new org.drip.execution.sensitivity.ControlNodesGreek (tcngExpectation.value() +
  237.                 _dblRiskAversion * java.lang.Math.pow (dblVarianceValue, _dblVarianceExponent),
  238.                     adblObjectiveJacobian, aadblObjectiveHessian);
  239.         } catch (java.lang.Exception e) {
  240.             e.printStackTrace();
  241.         }
  242.         return null;
  243.     }
  244. }
Created with JaCoCo 0.7.9.201702052155