ContinuousPowerImpact.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>ContinuousPowerImpact</i> contains the Temporary Impact Power Law Trading Trajectory generated by the
  82.  * Almgren and Chriss (2003) Scheme under the Criterion of No-Drift. The References are:
  83.  * 
  84.  * <br><br>
  85.  *  <ul>
  86.  *      <li>
  87.  *          Almgren, R., and N. Chriss (1999): Value under Liquidation <i>Risk</i> <b>12 (12)</b>
  88.  *      </li>
  89.  *      <li>
  90.  *          Almgren, R. F., and N. Chriss (2000): Optimal Execution of Portfolio Transactions <i>Journal of
  91.  *              Risk</i> <b>3 (2)</b> 5-39
  92.  *      </li>
  93.  *      <li>
  94.  *          Almgren, R. (2003): Optimal Execution with Nonlinear Impact Functions and Trading-Enhanced Risk
  95.  *              <i>Applied Mathematical Finance</i> <b>10 (1)</b> 1-18
  96.  *      </li>
  97.  *      <li>
  98.  *          Almgren, R., and N. Chriss (2003): Bidding Principles <i>Risk</i> 97-102
  99.  *      </li>
  100.  *      <li>
  101.  *          Bertsimas, D., and A. W. Lo (1998): Optimal Control of Execution Costs <i>Journal of Financial
  102.  *              Markets</i> <b>1</b> 1-50
  103.  *      </li>
  104.  *  </ul>
  105.  *
  106.  *  <br><br>
  107.  *  <ul>
  108.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ProductCore.md">Product Core Module</a></li>
  109.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/TransactionCostAnalyticsLibrary.md">Transaction Cost Analytics</a></li>
  110.  *      <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>
  111.  *      <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>
  112.  *  </ul>
  113.  * 
  114.  * @author Lakshmi Krishnamurthy
  115.  */

  117. public class ContinuousPowerImpact extends org.drip.execution.nonadaptive.StaticOptimalSchemeContinuous {

  119.     /**
  120.      * Create the Standard ContinuousPowerImpact Instance
  121.      * 
  122.      * @param dblStartHoldings Trajectory Start Holdings
  123.      * @param dblFinishTime Trajectory Finish Time
  124.      * @param lpep Almgren 2003 Linear Permanent Expectation Market Impact Parameters
  125.      * @param dblRiskAversion The Risk Aversion Parameter
  126.      * 
  127.      * @return The ContinuousPowerImpact Instance
  128.      */

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

  144.         return null;
  145.     }

  147.     private ContinuousPowerImpact (
  148.         final org.drip.execution.strategy.OrderSpecification os,
  149.         final org.drip.execution.dynamics.LinearPermanentExpectationParameters lpep,
  150.         final org.drip.execution.risk.MeanVarianceObjectiveUtility mvou)
  151.         throws java.lang.Exception
  152.     {
  153.         super (os, lpep, mvou);
  154.     }

  156.     @Override public org.drip.execution.optimum.EfficientTradingTrajectory generate()
  157.     {
  158.         org.drip.execution.dynamics.LinearPermanentExpectationParameters lpep =
  159.             (org.drip.execution.dynamics.LinearPermanentExpectationParameters) priceEvolutionParameters();

  161.         final org.drip.execution.impact.TransactionFunction tfTemporaryExpectation =
  162.             lpep.temporaryExpectation().epochImpactFunction();

  164.         if (!(tfTemporaryExpectation instanceof org.drip.execution.impact.TransactionFunctionPower))
  165.             return null;

  167.         double dblEpochVolatility = java.lang.Double.NaN;
  168.         final org.drip.execution.impact.TransactionFunctionPower tfpTemporaryExpectation =
  169.             (org.drip.execution.impact.TransactionFunctionPower) tfTemporaryExpectation;

  171.         double dblLambda = ((org.drip.execution.risk.MeanVarianceObjectiveUtility)
  172.             objectiveUtility()).riskAversion();

  174.         try {
  175.             dblEpochVolatility = lpep.arithmeticPriceDynamicsSettings().epochVolatility();
  176.         } catch (java.lang.Exception e) {
  177.             e.printStackTrace();

  179.             return null;
  180.         }

  182.         final double dblSigma = dblEpochVolatility;

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

  186.         double dblGamma = ((org.drip.execution.impact.TransactionFunctionLinear)
  187.             lpep.linearPermanentExpectation().epochImpactFunction()).slope();

  189.         final double dblK = tfpTemporaryExpectation.exponent();

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

  193.         double dblEta = tfpTemporaryExpectation.constant();

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

  197.         final double dblTStar = java.lang.Math.pow (dblK * dblEta * java.lang.Math.pow (dblX, dblK - 1.) /
  198.             (dblLambda * dblSigma * dblSigma), 1. / (dblK + 1.));

  200.         double dblTMax = dblK > 1. ? (dblK + 1.) / (dblK - 1.) * dblTStar : java.lang.Double.NaN;

  202.         double dblE = 0.5 * dblGamma * dblX * dblX + (dblK + 1.) / (3. * dblK + 1.) * dblEta *
  203.             java.lang.Math.pow (dblX / dblTStar, dblK + 1.) * dblTStar;

  205.         double dblV = (dblK + 1.) / (3. * dblK + 1.) * dblSigma * dblSigma * dblTStar * dblX * dblX;

  207.         double dblHyperboloidBoundaryValue = java.lang.Math.pow ((dblK + 1.) / (3. * dblK + 1.), dblK + 1.) *
  208.             dblEta * java.lang.Math.pow (dblSigma, 2. * dblK) * java.lang.Math.pow (dblX, 3. * dblK + 1.);

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

  220.                 if (1. > dblK)
  221.                     return dblX * java.lang.Math.pow (1. + ((1. - dblK) * dblT) / ((1. + dblK) * dblTStar),
  222.                         -1. * (1. + dblK) / (1. - dblK));

  224.                 if (1. == dblK) return dblX * java.lang.Math.pow (java.lang.Math.E, -1. * dblT/ dblTStar);

  226.                 double dblHoldings = dblX *  java.lang.Math.pow (1. - ((dblK - 1.) * dblT) / ((dblK + 1.) *
  227.                     dblTStar), (dblK + 1.) / (dblK + 1.));

  229.                 return 0. > dblX * dblHoldings ? 0. : dblHoldings;
  230.             }
  231.         };

  233.         final org.drip.function.definition.R1ToR1 r1ToR1TradeRateSquared = 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.                 double dblTemporaryImpactCoefficient = tfpTemporaryExpectation.evaluate (dblTradeRate);

  243.                 return dblTemporaryImpactCoefficient * dblTemporaryImpactCoefficient * dblTradeRate *
  244.                     dblTradeRate;
  245.             }
  246.         };

  248.         org.drip.function.definition.R1ToR1 r1ToR1TransactionCostExpectation = new
  249.             org.drip.function.definition.R1ToR1 (null) {
  250.             @Override public double evaluate (
  251.                 final double dblTime)
  252.                 throws java.lang.Exception
  253.             {
  254.                 return r1ToR1TradeRateSquared.integrate (dblTime, dblExecutionTime);
  255.             }
  256.         };

  258.         final org.drip.function.definition.R1ToR1 r1ToR1HoldingsSquared = new
  259.             org.drip.function.definition.R1ToR1 (null) {
  260.             @Override public double evaluate (
  261.                 final double dblTime)
  262.                 throws java.lang.Exception
  263.             {
  264.                 double dblHoldings = r1ToR1Holdings.evaluate (dblTime);

  266.                 return dblHoldings * dblHoldings;
  267.             }
  268.         };

  270.         org.drip.function.definition.R1ToR1 r1ToR1TransactionCostVariance = new
  271.             org.drip.function.definition.R1ToR1 (null) {
  272.             @Override public double evaluate (
  273.                 final double dblTime)
  274.                 throws java.lang.Exception
  275.             {
  276.                 return dblSigma * dblSigma * r1ToR1HoldingsSquared.integrate (dblTime, dblExecutionTime);
  277.             }
  278.         };

  280.         return org.drip.execution.optimum.PowerImpactContinuous.Standard (dblExecutionTime, dblE,
  281.             dblV, dblTStar, dblTMax, dblHyperboloidBoundaryValue, dblEta * (dblX / dblExecutionTime) /
  282.                 (dblEpochVolatility * java.lang.Math.sqrt (dblExecutionTime)), r1ToR1Holdings,
  283.                     r1ToR1TransactionCostExpectation, r1ToR1TransactionCostVariance);
  284.     }
  285. }
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