ContinuousCoordinatedVariationStochastic.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>ContinuousCoordinatedVariationStochastic</i> uses the Coordinated Variation Version of the Linear
  82.  * Participation Rate Transaction Function as described in the "Trading Time" Model to construct an Optimal
  83.  * Trading Trajectory in the T To Infinite Limit. The References are:
  84.  * 
  85.  * <br><br>
  86.  *  <ul>
  87.  *      <li>
  88.  *          Almgren, R. F., and N. Chriss (2000): Optimal Execution of Portfolio Transactions <i>Journal of
  89.  *              Risk</i> <b>3 (2)</b> 5-39
  90.  *      </li>
  91.  *      <li>
  92.  *          Almgren, R. F. (2009): Optimal Trading in a Dynamic Market
  93.  *              https://www.math.nyu.edu/financial_mathematics/content/02_financial/2009-2.pdf
  94.  *      </li>
  95.  *      <li>
  96.  *          Almgren, R. F. (2012): Optimal Trading with Stochastic Liquidity and Volatility <i>SIAM Journal
  97.  *          of Financial Mathematics</i> <b>3 (1)</b> 163-181
  98.  *      </li>
  99.  *      <li>
  100.  *          Geman, H., D. B. Madan, and M. Yor (2001): Time Changes for Levy Processes <i>Mathematical
  101.  *              Finance</i> <b>11 (1)</b> 79-96
  102.  *      </li>
  103.  *      <li>
  104.  *          Jones, C. M., G. Kaul, and M. L. Lipson (1994): Transactions, Volume, and Volatility <i>Review of
  105.  *              Financial Studies</i> <b>7 (4)</b> 631-651
  106.  *      </li>
  107.  *  </ul>
  108.  *
  109.  *  <br><br>
  110.  *  <ul>
  111.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ProductCore.md">Product Core Module</a></li>
  112.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/TransactionCostAnalyticsLibrary.md">Transaction Cost Analytics</a></li>
  113.  *      <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>
  114.  *      <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>
  115.  *  </ul>
  116.  * 
  117.  * @author Lakshmi Krishnamurthy
  118.  */

  120. public class ContinuousCoordinatedVariationStochastic extends
  121.     org.drip.execution.nonadaptive.StaticOptimalSchemeContinuous {

  123.     /**
  124.      * Create the Standard ContinuousCoordinatedVariationStochastic Instance
  125.      * 
  126.      * @param dblStartHoldings Trajectory Start Holdings
  127.      * @param dblFinishTime Trajectory Finish Time
  128.      * @param apep The Arithmetic Price Evolution Parameters
  129.      * @param dblRiskAversion The Risk Aversion Parameter
  130.      * 
  131.      * @return The ContinuousCoordinatedVariationStochastic Instance
  132.      */

  134.     public static final ContinuousCoordinatedVariationStochastic Standard (
  135.         final double dblStartHoldings,
  136.         final double dblFinishTime,
  137.         final org.drip.execution.dynamics.ArithmeticPriceEvolutionParameters apep,
  138.         final double dblRiskAversion)
  139.     {
  140.         try {
  141.             return new ContinuousCoordinatedVariationStochastic (new
  142.                 org.drip.execution.strategy.OrderSpecification (dblStartHoldings, dblFinishTime), apep, new
  143.                     org.drip.execution.risk.MeanVarianceObjectiveUtility (dblRiskAversion));
  144.         } catch (java.lang.Exception e) {
  145.             e.printStackTrace();
  146.         }

  148.         return null;
  149.     }

  151.     private ContinuousCoordinatedVariationStochastic (
  152.         final org.drip.execution.strategy.OrderSpecification os,
  153.         final org.drip.execution.dynamics.ArithmeticPriceEvolutionParameters apep,
  154.         final org.drip.execution.risk.MeanVarianceObjectiveUtility mvou)
  155.         throws java.lang.Exception
  156.     {
  157.         super (os, apep, mvou);
  158.     }

  160.     @Override public org.drip.execution.optimum.EfficientTradingTrajectory generate()
  161.     {
  162.         org.drip.execution.dynamics.ArithmeticPriceEvolutionParameters apep =
  163.             (org.drip.execution.dynamics.ArithmeticPriceEvolutionParameters) priceEvolutionParameters();

  165.         org.drip.execution.profiletime.BackgroundParticipationRate bprTemporary =
  166.             apep.temporaryExpectation();

  168.         if (!(bprTemporary instanceof org.drip.execution.profiletime.BackgroundParticipationRateLinear))
  169.             return null;

  171.         double dblInitialVolatility = java.lang.Double.NaN;
  172.         final org.drip.execution.profiletime.BackgroundParticipationRateLinear bprlTemporary =
  173.             (org.drip.execution.profiletime.BackgroundParticipationRateLinear) bprTemporary;

  175.         org.drip.execution.impact.TransactionFunctionLinear tflTemporaryExpectation =
  176.             bprlTemporary.epochLiquidityFunction();

  178.         try {
  179.             dblInitialVolatility = apep.arithmeticPriceDynamicsSettings().epochVolatility();
  180.         } catch (java.lang.Exception e) {
  181.             e.printStackTrace();

  183.             return null;
  184.         }

  186.         final double dblEpochVolatility = dblInitialVolatility;

  188.         final double dblEpochLiquidity = tflTemporaryExpectation.slope();

  190.         final double dblLambda = ((org.drip.execution.risk.MeanVarianceObjectiveUtility)
  191.             objectiveUtility()).riskAversion();

  193.         double dblEpochUrgency = java.lang.Math.sqrt (dblLambda * dblEpochVolatility * dblEpochVolatility /
  194.             dblEpochLiquidity);

  196.         final org.drip.function.definition.R1ToR1 r1ToR1VolatilityFunction =
  197.             apep.arithmeticPriceDynamicsSettings().volatilityFunction();

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

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

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

  205.         final org.drip.function.definition.R1ToR1 r1ToR1Holdings = new org.drip.function.definition.R1ToR1
  206.             (null) {
  207.             @Override public double evaluate (
  208.                 final double dblTime)
  209.                 throws java.lang.Exception
  210.             {
  211.                 double dblVolatility = r1ToR1VolatilityFunction.evaluate (dblTime);

  213.                 double dblKappa = java.lang.Math.sqrt (dblLambda * dblVolatility * dblVolatility /
  214.                     bprlTemporary.liquidityFunction (dblTime).slope());

  216.                 return java.lang.Math.sinh (dblKappa * (dblT - dblTime)) / java.lang.Math.sinh (dblKappa *
  217.                     dblT) * dblX;
  218.             }
  219.         };

  221.         org.drip.function.definition.R1ToR1 r1ToR1TradeRate = new org.drip.function.definition.R1ToR1 (null)
  222.         {
  223.             @Override public double evaluate (
  224.                 final double dblTime)
  225.                 throws java.lang.Exception
  226.             {
  227.                 double dblVolatility = r1ToR1VolatilityFunction.evaluate (dblTime);

  229.                 return java.lang.Math.sqrt (dblLambda * dblVolatility * dblVolatility /
  230.                     bprlTemporary.liquidityFunction (dblTime).slope()) * r1ToR1Holdings.evaluate (dblTime);
  231.             }
  232.         };

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

  242.                 double dblVolatility = r1ToR1VolatilityFunction.evaluate (dblTime);

  244.                 return java.lang.Math.sqrt (dblLambda * dblVolatility * dblVolatility *
  245.                     bprlTemporary.liquidityFunction (dblTime).slope()) * dblHoldings * dblHoldings;
  246.             }
  247.         };

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

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

  267.                 double dblVolatility = r1ToR1VolatilityFunction.evaluate (dblTime);

  269.                 return dblVolatility * dblVolatility * 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,
  285.                 dblEpochLiquidity * dblEpochUrgency * dblX * dblX / java.lang.Math.tanh (dblEpochUrgency *
  286.                     dblT), r1ToR1TransactionCostExpectation.evaluate (0.), 1. / dblEpochUrgency,
  287.                         dblEpochLiquidity * dblX / (dblT * dblEpochVolatility * java.lang.Math.sqrt (dblT)),
  288.                             r1ToR1Holdings, r1ToR1TradeRate, r1ToR1TransactionCostExpectation,
  289.                                 r1ToR1TransactionCostVariance);
  290.         } catch (java.lang.Exception e) {
  291.             e.printStackTrace();
  292.         }

  294.         return null;
  295.     }
  296. }
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