ContinuousAlmgrenChriss.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>ContinuousAlmgrenChriss</i> contains the Continuous Version of the Discrete Trading Trajectory
  82.  * generated by the Almgren and Chriss (2000) Scheme under the Criterion of No-Drift. 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.  *          Walia, N. (2006): <i>Optimal Trading: Dynamic Stock Liquidation Strategies</i> Princeton
  104.                 University
  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/nonadaptive/README.md">Almgren-Chriss Static Optimal Trajectory</a></li>
  114.  *  </ul>
  115.  * 
  116.  * @author Lakshmi Krishnamurthy
  117.  */

  119. public class ContinuousAlmgrenChriss extends org.drip.execution.nonadaptive.StaticOptimalSchemeContinuous {

  121.     /**
  122.      * Create the Standard ContinuousAlmgrenChriss Instance
  123.      * 
  124.      * @param dblStartHoldings Trajectory Start Holdings
  125.      * @param dblFinishTime Trajectory Finish Time
  126.      * @param lpep The Linear Impact Expectation Parameters
  127.      * @param dblRiskAversion The Risk Aversion Parameter
  128.      * 
  129.      * @return The ContinuousAlmgrenChriss Instance
  130.      */

  132.     public static final ContinuousAlmgrenChriss Standard (
  133.         final double dblStartHoldings,
  134.         final double dblFinishTime,
  135.         final org.drip.execution.dynamics.LinearPermanentExpectationParameters lpep,
  136.         final double dblRiskAversion)
  137.     {
  138.         try {
  139.             return new ContinuousAlmgrenChriss (new org.drip.execution.strategy.OrderSpecification
  140.                 (dblStartHoldings, dblFinishTime), lpep, new
  141.                     org.drip.execution.risk.MeanVarianceObjectiveUtility (dblRiskAversion));
  142.         } catch (java.lang.Exception e) {
  143.             e.printStackTrace();
  144.         }

  146.         return null;
  147.     }

  149.     /**
  150.      * ContinuousAlmgrenChriss Constructor
  151.      * 
  152.      * @param os The Order Specification
  153.      * @param lpep The Linear Impact Expectation Parameters
  154.      * @param mvou The Mean Variation Objective Utility
  155.      * 
  156.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  157.      */

  159.     public ContinuousAlmgrenChriss (
  160.         final org.drip.execution.strategy.OrderSpecification os,
  161.         final org.drip.execution.dynamics.LinearPermanentExpectationParameters lpep,
  162.         final org.drip.execution.risk.MeanVarianceObjectiveUtility mvou)
  163.         throws java.lang.Exception
  164.     {
  165.         super (os, lpep, mvou);
  166.     }

  168.     @Override public org.drip.execution.optimum.EfficientTradingTrajectory generate()
  169.     {
  170.         org.drip.execution.dynamics.LinearPermanentExpectationParameters lpep =
  171.             (org.drip.execution.dynamics.LinearPermanentExpectationParameters) priceEvolutionParameters();

  173.         org.drip.execution.impact.TransactionFunction tfTemporaryExpectation =
  174.             lpep.temporaryExpectation().epochImpactFunction();

  176.         if (!(tfTemporaryExpectation instanceof org.drip.execution.impact.TransactionFunctionLinear))
  177.             return null;

  179.         double dblEpochVolatility = java.lang.Double.NaN;
  180.         org.drip.execution.impact.TransactionFunctionLinear tflTemporaryExpectation =
  181.             (org.drip.execution.impact.TransactionFunctionLinear) tfTemporaryExpectation;

  183.         try {
  184.             dblEpochVolatility = lpep.arithmeticPriceDynamicsSettings().epochVolatility();
  185.         } catch (java.lang.Exception e) {
  186.             e.printStackTrace();

  188.             return null;
  189.         }

  191.         final double dblSigma = dblEpochVolatility;

  193.         final double dblEta = tflTemporaryExpectation.slope();

  195.         final double dblKappa = java.lang.Math.sqrt (((org.drip.execution.risk.MeanVarianceObjectiveUtility)
  196.             objectiveUtility()).riskAversion() * dblSigma * dblSigma / dblEta);

  198.         org.drip.execution.strategy.OrderSpecification os = orderSpecification();

  200.         final double dblT = os.maxExecutionTime();

  202.         final double dblX = os.size();

  204.         final org.drip.function.definition.R1ToR1 r1ToR1Holdings = new org.drip.function.definition.R1ToR1
  205.             (null) {
  206.             @Override public double evaluate (
  207.                 final double dblTime)
  208.                 throws java.lang.Exception
  209.             {
  210.                 if (!org.drip.numerical.common.NumberUtil.IsValid (dblTime))
  211.                     throw new java.lang.Exception
  212.                         ("ContinuousAlmgrenChriss::Holdings::evaluate => Invalid Inputs");

  214.                 return java.lang.Math.sinh (dblKappa * (dblT - dblTime)) / java.lang.Math.sinh (dblKappa *
  215.                     dblT) * dblX;
  216.             }
  217.         };

  219.         final org.drip.function.definition.R1ToR1 r1ToR1TradeRate = new org.drip.function.definition.R1ToR1
  220.             (null)
  221.         {
  222.             @Override public double evaluate (
  223.                 final double dblTime)
  224.                 throws java.lang.Exception
  225.             {
  226.                 if (!org.drip.numerical.common.NumberUtil.IsValid (dblTime))
  227.                     throw new java.lang.Exception
  228.                         ("ContinuousAlmgrenChriss::TradeRate::evaluate => Invalid Inputs");

  230.                 return dblKappa * dblX * java.lang.Math.cosh (dblKappa * (dblT - dblTime)) /
  231.                     java.lang.Math.sinh (dblKappa * dblT);
  232.             }
  233.         };

  235.         final org.drip.function.definition.R1ToR1 r1ToR1TransactionCostExpectationRate = new
  236.             org.drip.function.definition.R1ToR1 (null) {
  237.             @Override public double evaluate (
  238.                 final double dblTime)
  239.                 throws java.lang.Exception
  240.             {
  241.                 double dblTradeRate = r1ToR1TradeRate.evaluate (dblTime);

  243.                 if (!org.drip.numerical.common.NumberUtil.IsValid (dblTradeRate))
  244.                     throw new java.lang.Exception
  245.                         ("ContinuousAlmgrenChriss::ExpectationRate::evaluate => Invalid Inputs");

  247.                 return dblEta * dblTradeRate * dblTradeRate;
  248.             }
  249.         };

  251.         org.drip.function.definition.R1ToR1 r1ToR1TransactionCostExpectation = new
  252.             org.drip.function.definition.R1ToR1 (null) {
  253.             @Override public double evaluate (
  254.                 final double dblTime)
  255.                 throws java.lang.Exception
  256.             {
  257.                 return r1ToR1TransactionCostExpectationRate.integrate (dblTime, dblT);
  258.             }
  259.         };

  261.         final org.drip.function.definition.R1ToR1 r1ToR1TransactionCostVarianceRate = new
  262.             org.drip.function.definition.R1ToR1 (null) {
  263.             @Override public double evaluate (
  264.                 final double dblTime)
  265.                 throws java.lang.Exception
  266.             {
  267.                 double dblHoldings = r1ToR1Holdings.evaluate (dblTime);

  269.                 return dblSigma * dblSigma * dblHoldings * dblHoldings;
  270.             }
  271.         };

  273.         org.drip.function.definition.R1ToR1 r1ToR1TransactionCostVariance = new
  274.             org.drip.function.definition.R1ToR1 (null) {
  275.             @Override public double evaluate (
  276.                 final double dblTime)
  277.                 throws java.lang.Exception
  278.             {
  279.                 return r1ToR1TransactionCostVarianceRate.integrate (dblTime, dblT);
  280.             }
  281.         };

  283.         try {
  284.             return new org.drip.execution.optimum.EfficientTradingTrajectoryContinuous (dblT, dblEta *
  285.                 dblKappa * dblX * dblX / java.lang.Math.tanh (dblKappa * dblT),
  286.                     r1ToR1TransactionCostExpectation.evaluate (0.), 1. / dblKappa, dblEta * dblX / (dblT *
  287.                         dblEpochVolatility * java.lang.Math.sqrt (dblT)), r1ToR1Holdings, r1ToR1TradeRate,
  288.                             r1ToR1TransactionCostExpectation, r1ToR1TransactionCostVariance);
  289.         } catch (java.lang.Exception e) {
  290.             e.printStackTrace();
  291.         }

  293.         return null;
  294.     }
  295. }
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