CoordinatedVariation.java

  1. package org.drip.execution.tradingtime;

  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>CoordinatedVariation</i> implements the Coordinated Variation of the Volatility and Liquidity as
  82.  * described in the "Trading Time" Model. The References are:
  83.  * 
  84.  * <br><br>
  85.  *  <ul>
  86.  *      <li>
  87.  *          Almgren, R. F., 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.  *          Almgren, R. F. (2009): Optimal Trading in a Dynamic Market
  92.  *              https://www.math.nyu.edu/financial_mathematics/content/02_financial/2009-2.pdf
  93.  *      </li>
  94.  *      <li>
  95.  *          Almgren, R. F. (2012): Optimal Trading with Stochastic Liquidity and Volatility <i>SIAM Journal
  96.  *          of Financial Mathematics</i> <b>3 (1)</b> 163-181
  97.  *      </li>
  98.  *      <li>
  99.  *          Geman, H., D. B. Madan, and M. Yor (2001): Time Changes for Levy Processes <i>Mathematical
  100.  *              Finance</i> <b>11 (1)</b> 79-96
  101.  *      </li>
  102.  *      <li>
  103.  *          Jones, C. M., G. Kaul, and M. L. Lipson (1994): Transactions, Volume, and Volatility <i>Review of
  104.  *              Financial Studies</i> <b>7 (4)</b> 631-651
  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/tradingtime/README.md">Coordinated Variation Trading Time Models</a></li>
  114.  *  </ul>
  115.  * 
  116.  * @author Lakshmi Krishnamurthy
  117.  */

  119. public class CoordinatedVariation {
  120.     private double _dblInvariant = java.lang.Double.NaN;
  121.     private double _dblReferenceLiquidity = java.lang.Double.NaN;
  122.     private double _dblReferenceVolatility = java.lang.Double.NaN;

  124.     /**
  125.      * CoordinatedVariation Constructor
  126.      * 
  127.      * @param dblReferenceVolatility The Reference Volatility
  128.      * @param dblReferenceLiquidity The Reference Liquidity
  129.      * 
  130.      * @throws java.lang.Exception Thrwon if the Inputs are Invalid
  131.      */

  133.     public CoordinatedVariation (
  134.         final double dblReferenceVolatility,
  135.         final double dblReferenceLiquidity)
  136.         throws java.lang.Exception
  137.     {
  138.         if (!org.drip.numerical.common.NumberUtil.IsValid (_dblReferenceVolatility = dblReferenceVolatility) ||
  139.             0. >= _dblReferenceVolatility || !org.drip.numerical.common.NumberUtil.IsValid
  140.                 (_dblReferenceLiquidity = dblReferenceLiquidity) || 0. >= _dblReferenceLiquidity)
  141.             throw new java.lang.Exception ("CoordinatedVariation Constructor => Invalid Inputs");

  143.         _dblInvariant = _dblReferenceVolatility * _dblReferenceVolatility * _dblReferenceLiquidity;
  144.     }

  146.     /**
  147.      * Retrieve the Reference Liquidity
  148.      * 
  149.      * @return The Reference Liquidity
  150.      */

  152.     public double referenceLiquidity()
  153.     {
  154.         return _dblReferenceLiquidity;
  155.     }

  157.     /**
  158.      * Retrieve the Reference Volatility
  159.      * 
  160.      * @return The Reference Volatility
  161.      */

  163.     public double referenceVolatility()
  164.     {
  165.         return _dblReferenceVolatility;
  166.     }

  168.     /**
  169.      * Retrieve the Volatility/Liquidity Invariant
  170.      * 
  171.      * @return The Volatility/Liquidity Invariant
  172.      */

  174.     public double invariant()
  175.     {
  176.         return _dblInvariant;
  177.     }

  179.     /**
  180.      * Estimate the Liquidity given the Volatility
  181.      * 
  182.      * @param dblVolatility The Volatility
  183.      * 
  184.      * @return Liquidity Estimate using the Volatility
  185.      * 
  186.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  187.      */

  189.     public double liquidity (
  190.         final double dblVolatility)
  191.         throws java.lang.Exception
  192.     {
  193.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblVolatility))
  194.             throw new java.lang.Exception ("CoordinatedVariation::liquidity => Invalid Inputs");

  196.         return _dblInvariant / (dblVolatility * dblVolatility);
  197.     }

  199.     /**
  200.      * Estimate the Volatility given the Liquidity
  201.      * 
  202.      * @param dblLiquidity The Liquidity
  203.      * 
  204.      * @return Volatility Estimate using the Liquidity
  205.      * 
  206.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  207.      */

  209.     public double volatility (
  210.         final double dblLiquidity)
  211.         throws java.lang.Exception
  212.     {
  213.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblLiquidity))
  214.             throw new java.lang.Exception ("CoordinatedVariation::volatility => Invalid Inputs");

  216.         return java.lang.Math.sqrt (_dblInvariant / dblLiquidity);
  217.     }

  219.     /**
  220.      * Compute the Volatility Function from the Liquidity Function
  221.      * 
  222.      * @param r1ToR1Liquidity The R^1 To R^1 Liquidity Function
  223.      * 
  224.      * @return The R^1 To R^1 Volatility Function
  225.      */

  227.     public org.drip.function.definition.R1ToR1 volatilityFunction (
  228.         final org.drip.function.definition.R1ToR1 r1ToR1Liquidity)
  229.     {
  230.         if (null == r1ToR1Liquidity) return null;

  232.         return new org.drip.function.definition.R1ToR1 (null) {
  233.             @Override public double evaluate (
  234.                 final double dblTime)
  235.                 throws java.lang.Exception
  236.             {
  237.                 return java.lang.Math.sqrt (_dblInvariant / r1ToR1Liquidity.evaluate (dblTime));
  238.             }
  239.         };
  240.     }
  241. }
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