ContinuousConstantTradingEnhanced.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>ContinuousConstantTradingEnhanced</i> contains the Constant Volatility Trading Trajectory generated by
  82.  * the Almgren and Chriss (2003) Scheme under the Criterion of No-Drift AND Constant Temporary Impact
  83.  * Volatility. 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. F., 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.  *          Almgren, R. (2003): Optimal Execution with Nonlinear Impact Functions and Trading-Enhanced Risk
  96.  *              <i>Applied Mathematical Finance</i> <b>10 (1)</b> 1-18
  97.  *      </li>
  98.  *      <li>
  99.  *          Almgren, R., and N. Chriss (2003): Bidding Principles <i>Risk</i> 97-102
  100.  *      </li>
  101.  *      <li>
  102.  *          Bertsimas, D., and A. W. Lo (1998): Optimal Control of Execution Costs <i>Journal of Financial
  103.  *              Markets</i> <b>1</b> 1-50
  104.  *      </li>
  105.  *  </ul>
  106.  *
  107.  *  <br><br>
  108.  *  <ul>
  109.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ProductCore.md">Product Core Module</a></li>
  110.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/TransactionCostAnalyticsLibrary.md">Transaction Cost Analytics</a></li>
  111.  *      <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>
  112.  *      <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>
  113.  *  </ul>
  114.  * 
  115.  * @author Lakshmi Krishnamurthy
  116.  */

  118. public class ContinuousConstantTradingEnhanced extends
  119.     org.drip.execution.nonadaptive.StaticOptimalSchemeContinuous {

  121.     /**
  122.      * Create the Standard ContinuousConstantTradingEnhanced Instance
  123.      * 
  124.      * @param dblStartHoldings Trajectory Start Holdings
  125.      * @param dblFinishTime Trajectory Finish Time
  126.      * @param apep Almgren 2003 Arithmetic Price Evolution Parameters
  127.      * @param dblRiskAversion The Risk Aversion Parameter
  128.      * 
  129.      * @return The ContinuousConstantTradingEnhanced Instance
  130.      */

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

  146.         return null;
  147.     }

  149.     private ContinuousConstantTradingEnhanced (
  150.         final org.drip.execution.strategy.OrderSpecification os,
  151.         final org.drip.execution.dynamics.ArithmeticPriceEvolutionParameters apep,
  152.         final org.drip.execution.risk.MeanVarianceObjectiveUtility mvou)
  153.         throws java.lang.Exception
  154.     {
  155.         super (os, apep, mvou);
  156.     }

  158.     @Override public org.drip.execution.optimum.EfficientTradingTrajectory generate()
  159.     {
  160.         org.drip.execution.dynamics.ArithmeticPriceEvolutionParameters apep = priceEvolutionParameters();

  162.         double dblLambda = ((org.drip.execution.risk.MeanVarianceObjectiveUtility)
  163.             objectiveUtility()).riskAversion();

  165.         double dblEpochVolatility = java.lang.Double.NaN;

  167.         try {
  168.             dblEpochVolatility = apep.arithmeticPriceDynamicsSettings().epochVolatility();
  169.         } catch (java.lang.Exception e) {
  170.             e.printStackTrace();

  172.             return null;
  173.         }

  175.         final double dblSigma = dblEpochVolatility;

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

  179.         org.drip.execution.impact.TransactionFunction tfTemporaryExpectation =
  180.             apep.temporaryExpectation().epochImpactFunction();

  182.         if (!(tfTemporaryExpectation instanceof org.drip.execution.impact.TransactionFunctionLinear))
  183.             return null;

  185.         final double dblEta = ((org.drip.execution.impact.TransactionFunctionLinear)
  186.             tfTemporaryExpectation).slope();

  188.         org.drip.execution.impact.TransactionFunction tfTemporaryVolatility =
  189.             apep.temporaryVolatility().epochImpactFunction();

  191.         if (!(tfTemporaryVolatility instanceof org.drip.execution.impact.TransactionFunctionLinear))
  192.             return null;

  194.         double dblAlpha = ((org.drip.execution.impact.TransactionFunctionLinear)
  195.             tfTemporaryVolatility).offset();

  197.         final double dblExecutionTime = os.maxExecutionTime();

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

  201.         final double dblTStar = java.lang.Math.sqrt ((dblEta + dblLambda * dblAlpha * dblAlpha) / (dblLambda
  202.             * dblSigma * dblSigma));

  204.         double dblE = 0.5 * dblEta * dblX * dblX / dblTStar;

  206.         double dblV = 0.5 * dblX * dblX * dblSigma * dblSigma * dblTStar * (1. + (dblAlpha * dblAlpha /
  207.             (dblSigma * dblSigma * dblTStar * dblTStar)));

  209.         final org.drip.function.definition.R1ToR1 r1ToR1Holdings = new org.drip.function.definition.R1ToR1
  210.             (null) {
  211.             @Override public double evaluate (
  212.                 final double dblT)
  213.                 throws java.lang.Exception
  214.             {
  215.                 if (!org.drip.numerical.common.NumberUtil.IsValid (dblT))
  216.                     throw new java.lang.Exception
  217.                         ("ContinuousConstantTradingEnhanced::generate::evaluate => Invalid Inputs");

  219.                 return dblX * java.lang.Math.pow (java.lang.Math.E, -1. * dblT/ dblTStar);
  220.             }
  221.         };

  223.         org.drip.function.definition.R1ToR1 r1ToR1TradeRate = new org.drip.function.definition.R1ToR1 (null)
  224.         {
  225.             @Override public double evaluate (
  226.                 final double dblVariate)
  227.                 throws java.lang.Exception
  228.             {
  229.                 return r1ToR1Holdings.derivative (dblVariate, 1);
  230.             }
  231.         };

  233.         final org.drip.function.definition.R1ToR1 r1ToR1TransactionCostExpectationRate = new
  234.             org.drip.function.definition.R1ToR1 (null) {
  235.             @Override public double evaluate (
  236.                 final double dblTime)
  237.                 throws java.lang.Exception
  238.             {
  239.                 double dblTradeRate = r1ToR1Holdings.derivative (dblTime, 1);

  241.                 return dblEta * dblEta * dblTradeRate * dblTradeRate;
  242.             }
  243.         };

  245.         org.drip.function.definition.R1ToR1 r1ToR1TransactionCostExpectation = new
  246.             org.drip.function.definition.R1ToR1 (null) {
  247.             @Override public double evaluate (
  248.                 final double dblTime)
  249.                 throws java.lang.Exception
  250.             {
  251.                 return r1ToR1TransactionCostExpectationRate.integrate (dblTime, dblExecutionTime);
  252.             }
  253.         };

  255.         final org.drip.function.definition.R1ToR1 r1ToR1TransactionCostVarianceRate = new
  256.             org.drip.function.definition.R1ToR1 (null) {
  257.             @Override public double evaluate (
  258.                 final double dblTime)
  259.                 throws java.lang.Exception
  260.             {
  261.                 double dblHoldings = r1ToR1Holdings.evaluate (dblTime);

  263.                 return dblSigma * dblSigma * dblHoldings * dblHoldings;
  264.             }
  265.         };

  267.         org.drip.function.definition.R1ToR1 r1ToR1TransactionCostVariance = new
  268.             org.drip.function.definition.R1ToR1 (null) {
  269.             @Override public double evaluate (
  270.                 final double dblTime)
  271.                 throws java.lang.Exception
  272.             {
  273.                 return r1ToR1TransactionCostVarianceRate.integrate (dblTime, dblExecutionTime);
  274.             }
  275.         };

  277.         try {
  278.             return new org.drip.execution.optimum.EfficientTradingTrajectoryContinuous (dblExecutionTime,
  279.                 dblE, dblV, dblTStar, apep.temporaryExpectation().epochImpactFunction().evaluate (dblX /
  280.                     dblExecutionTime) / (apep.arithmeticPriceDynamicsSettings().epochVolatility() *
  281.                         java.lang.Math.sqrt (dblExecutionTime)), r1ToR1Holdings, r1ToR1TradeRate,
  282.                             r1ToR1TransactionCostExpectation, r1ToR1TransactionCostVariance);
  283.         } catch (java.lang.Exception e) {
  284.             e.printStackTrace();
  285.         }

  287.         return null;
  288.     }
  289. }
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