LinearTemporaryImpact.java

  1. package org.drip.execution.cost;

  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>LinearTemporaryImpact</i> computes and holds the Optimal Trajectory using the Linear Temporary Impact
  82.  * Function for the given set of Inputs. It provides a Default Unconstrained Trajectory Implementation. The
  83.  * References are:
  84.  * 
  85.  * <br><br>
  86.  *  <ul>
  87.  *      <li>
  88.  *          Bertsimas, D., and A. W. Lo (1998): Optimal Control of Execution Costs <i>Journal of Financial
  89.  *              Markets</i> <b>1</b> 1-50
  90.  *      </li>
  91.  *      <li>
  92.  *          Almgren, R., and N. Chriss (2000): Optimal Execution of Portfolio Transactions <i>Journal of
  93.  *              Risk</i> <b>3 (2)</b> 5-39
  94.  *      </li>
  95.  *      <li>
  96.  *          Brunnermeier, L. K., and L. H. Pedersen (2005): Predatory Trading <i>Journal of Finance</i> <b>60
  97.  *              (4)</b> 1825-1863
  98.  *      </li>
  99.  *      <li>
  100.  *          Almgren, R., and J. Lorenz (2006): Bayesian Adaptive Trading with a Daily Cycle <i>Journal of
  101.  *              Trading</i> <b>1 (4)</b> 38-46
  102.  *      </li>
  103.  *      <li>
  104.  *          Kissell, R., and R. Malamut (2007): Algorithmic Decision Making Framework <i>Journal of
  105.  *              Trading</i> <b>1 (1)</b> 12-21
  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/cost/README.md">Linear Temporary Market Impact Cost</a></li>
  115.  *  </ul>
  116.  * 
  117.  * @author Lakshmi Krishnamurthy
  118.  */

  120. public class LinearTemporaryImpact {
  121.     private double _dblSpotTime = java.lang.Double.NaN;
  122.     private double _dblFinishTime = java.lang.Double.NaN;
  123.     private double _dblSpotHoldings = java.lang.Double.NaN;
  124.     private double _dblGrossPriceChange = java.lang.Double.NaN;
  125.     private double _dblTransactionCostGain = java.lang.Double.NaN;
  126.     private double _dblStaticTransactionCost = java.lang.Double.NaN;
  127.     private double _dblInstantaneousTradeRate = java.lang.Double.NaN;
  128.     private org.drip.execution.bayesian.PriorConditionalCombiner _pcc = null;
  129.     private org.drip.execution.impact.TransactionFunctionLinear _tflTemporary = null;
  130.     private org.drip.execution.optimum.EfficientTradingTrajectoryContinuous _ectt = null;

  132.     /**
  133.      * Generate an Unconstrained LinearTemporaryImpact Instance
  134.      * 
  135.      * @param dblSpotTime Spot Time
  136.      * @param dblFinishTime Finish Time
  137.      * @param dblSpotHoldings Spot Holdings
  138.      * @param pcc The Prior/Conditional Combiner
  139.      * @param dblGrossPriceChange The Gross Price Change
  140.      * @param tflTemporary The Temporary Linear Impact Function
  141.      * 
  142.      * @return The Unconstrained LinearTemporaryImpact Instance
  143.      */

  145.     public static final LinearTemporaryImpact Unconstrained (
  146.         final double dblSpotTime,
  147.         final double dblFinishTime,
  148.         final double dblSpotHoldings,
  149.         final org.drip.execution.bayesian.PriorConditionalCombiner pcc,
  150.         final double dblGrossPriceChange,
  151.         final org.drip.execution.impact.TransactionFunctionLinear tflTemporary)
  152.     {
  153.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblSpotTime) ||
  154.             !org.drip.numerical.common.NumberUtil.IsValid (dblFinishTime) ||
  155.                 !org.drip.numerical.common.NumberUtil.IsValid (dblSpotHoldings) || null == pcc || null ==
  156.                     tflTemporary)
  157.             return null;

  159.         final double dblHorizon = dblFinishTime - dblSpotTime;

  161.         org.drip.measure.gaussian.R1UnivariateNormal r1unPosterior = pcc.posteriorDriftDistribution
  162.             (dblGrossPriceChange);

  164.         if (null == r1unPosterior) return null;

  166.         final double dblScaledDrift = 0.25 * r1unPosterior.mean() / tflTemporary.slope();

  168.         org.drip.function.definition.R1ToR1 r1ToR1Holdings = new org.drip.function.definition.R1ToR1 (null) {
  169.             @Override public double evaluate (
  170.                 final double dblTau)
  171.                 throws java.lang.Exception
  172.             {
  173.                 if (0. >= dblHorizon) return 0.;

  175.                 if (!org.drip.numerical.common.NumberUtil.IsValid (dblTau))
  176.                     throw new java.lang.Exception
  177.                         ("LinearTemporaryImpact::Holdings::evaluate => Invalid Inputs");

  179.                 if (dblTau <= dblSpotTime) return dblSpotHoldings;

  181.                 if (dblTau >= dblFinishTime) return 0.;

  183.                 return (dblFinishTime - dblTau) * (dblSpotHoldings / (dblFinishTime - dblSpotTime) -
  184.                     dblScaledDrift * (dblTau - dblSpotTime));
  185.             }
  186.         };

  188.         try {
  189.             return new LinearTemporaryImpact (dblSpotTime, dblFinishTime, dblSpotHoldings, pcc,
  190.                 dblGrossPriceChange, tflTemporary, dblFinishTime - dblSpotTime, r1ToR1Holdings, 0 >=
  191.                     dblHorizon ? 0. : dblSpotHoldings / dblHorizon + dblScaledDrift * dblHorizon);
  192.         } catch (java.lang.Exception e) {
  193.             e.printStackTrace();
  194.         }

  196.         return null;
  197.     }

  199.     protected LinearTemporaryImpact (
  200.         final double dblSpotTime,
  201.         final double dblFinishTime,
  202.         final double dblSpotHoldings,
  203.         final org.drip.execution.bayesian.PriorConditionalCombiner pcc,
  204.         final double dblGrossPriceChange,
  205.         final org.drip.execution.impact.TransactionFunctionLinear tflTemporary,
  206.         final double dblCharacteristicTime,
  207.         final org.drip.function.definition.R1ToR1 r1ToR1Holdings,
  208.         final double dblInstantaneousTradeRate)
  209.         throws java.lang.Exception
  210.     {
  211.         if (!org.drip.numerical.common.NumberUtil.IsValid (_dblSpotTime = dblSpotTime) ||
  212.             !org.drip.numerical.common.NumberUtil.IsValid (_dblFinishTime = dblFinishTime) ||
  213.                 !org.drip.numerical.common.NumberUtil.IsValid (_dblSpotHoldings = dblSpotHoldings) || null ==
  214.                     (_pcc = pcc) || !org.drip.numerical.common.NumberUtil.IsValid (_dblGrossPriceChange =
  215.                         dblGrossPriceChange) || null == (_tflTemporary = tflTemporary) || null ==
  216.                             r1ToR1Holdings || !org.drip.numerical.common.NumberUtil.IsValid
  217.                                 (_dblInstantaneousTradeRate = dblInstantaneousTradeRate))
  218.             throw new java.lang.Exception ("LinearTemporaryImpact Constructor => Invalid Inputs");

  220.         final double dblLiquidityCoefficient = _tflTemporary.slope();

  222.         double dblDriftEstimate = _pcc.posteriorDriftDistribution (_dblGrossPriceChange).mean();

  224.         final double dblExecutionTime = _dblFinishTime - _dblSpotTime;
  225.         _dblStaticTransactionCost = _dblSpotHoldings * _dblSpotHoldings * dblLiquidityCoefficient /
  226.             dblExecutionTime + 0.5 * _dblSpotHoldings * dblDriftEstimate * dblExecutionTime -
  227.                 dblExecutionTime * dblExecutionTime * dblExecutionTime * dblDriftEstimate * dblDriftEstimate
  228.                     / (48. * dblLiquidityCoefficient);

  230.         double dblDriftConfidence = _pcc.prior().confidence();

  232.         final double dblPriceVolatility = _pcc.conditional().priceVolatility();

  234.         org.drip.function.definition.R1ToR1 r1ToR1HoldingsSquared = new org.drip.function.definition.R1ToR1
  235.             (null) {
  236.             @Override public double evaluate (
  237.                 final double dblTime)
  238.                 throws java.lang.Exception
  239.             {
  240.                 double dblHoldings = r1ToR1Holdings.evaluate (dblTime);

  242.                 return dblHoldings * dblHoldings;
  243.             }
  244.         };

  246.         final double dblRho = dblPriceVolatility * dblPriceVolatility / (dblDriftConfidence *
  247.             dblDriftConfidence * dblExecutionTime);

  249.         org.drip.function.definition.R1ToR1 r1ToR1Quadrature = new org.drip.function.definition.R1ToR1 (null)
  250.         {
  251.             @Override public double evaluate (
  252.                 final double dblDelta)
  253.                 throws java.lang.Exception
  254.             {
  255.                 if (!org.drip.numerical.common.NumberUtil.IsValid (dblDelta))
  256.                     throw new java.lang.Exception
  257.                         ("LinearTemporaryImpact::r1ToR1Quadrature::evaluate => Invalid Inputs");

  259.                 double dblRemainingTime = 1. - dblDelta;
  260.                 double dblDimensionlessTime = dblDelta + dblRho;
  261.                 return dblRemainingTime * dblRemainingTime * dblRemainingTime / (dblDimensionlessTime *
  262.                     dblDimensionlessTime);
  263.             }
  264.         };

  266.         _dblTransactionCostGain = dblPriceVolatility * dblPriceVolatility * dblExecutionTime *
  267.             dblExecutionTime / (48. * linearTemporaryImpact().slope()) * r1ToR1Quadrature.integrate (0., 1.);

  269.         org.drip.function.definition.R1ToR1 r1ToR1TradeRate = new org.drip.function.definition.R1ToR1 (null)
  270.         {
  271.             @Override public double evaluate (
  272.                 final double dblS)
  273.                 throws java.lang.Exception
  274.             {
  275.                 return r1ToR1Holdings.derivative (dblS, 1);
  276.             }
  277.         };

  279.         final org.drip.function.definition.R1ToR1 r1ToR1TransactionCostExpectationRate = new
  280.             org.drip.function.definition.R1ToR1 (null) {
  281.             @Override public double evaluate (
  282.                 final double dblTime)
  283.                 throws java.lang.Exception
  284.             {
  285.                 double dblTradeRate = r1ToR1Holdings.derivative (dblTime, 1);

  287.                 return dblLiquidityCoefficient * dblLiquidityCoefficient * dblTradeRate * dblTradeRate;
  288.             }
  289.         };

  291.         org.drip.function.definition.R1ToR1 r1ToR1TransactionCostExpectation = new
  292.             org.drip.function.definition.R1ToR1 (null) {
  293.             @Override public double evaluate (
  294.                 final double dblTime)
  295.                 throws java.lang.Exception
  296.             {
  297.                 return r1ToR1TransactionCostExpectationRate.integrate (dblTime, dblExecutionTime);
  298.             }
  299.         };

  301.         final org.drip.function.definition.R1ToR1 r1ToR1TransactionCostVarianceRate = new
  302.             org.drip.function.definition.R1ToR1 (null) {
  303.             @Override public double evaluate (
  304.                 final double dblTime)
  305.                 throws java.lang.Exception
  306.             {
  307.                 double dblHoldings = r1ToR1Holdings.evaluate (dblTime);

  309.                 return dblPriceVolatility * dblPriceVolatility * dblHoldings * dblHoldings;
  310.             }
  311.         };

  313.         org.drip.function.definition.R1ToR1 r1ToR1TransactionCostVariance = new
  314.             org.drip.function.definition.R1ToR1 (null) {
  315.             @Override public double evaluate (
  316.                 final double dblTime)
  317.                 throws java.lang.Exception
  318.             {
  319.                 return r1ToR1TransactionCostVarianceRate.integrate (dblTime, dblExecutionTime);
  320.             }
  321.         };

  323.         _ectt = new org.drip.execution.optimum.EfficientTradingTrajectoryContinuous (dblExecutionTime,
  324.             _dblStaticTransactionCost + _dblTransactionCostGain, dblPriceVolatility * dblPriceVolatility *
  325.                 r1ToR1HoldingsSquared.integrate (_dblSpotTime, _dblFinishTime), dblCharacteristicTime,
  326.                     dblLiquidityCoefficient * _dblSpotHoldings / (dblExecutionTime * dblLiquidityCoefficient
  327.                         * java.lang.Math.sqrt (dblExecutionTime)), r1ToR1Holdings, r1ToR1TradeRate,
  328.                             r1ToR1TransactionCostExpectation, r1ToR1TransactionCostVariance);
  329.     }

  331.     /**
  332.      * Retrieve the Spot Time
  333.      * 
  334.      * @return The Spot Time
  335.      */

  337.     public double spotTime()
  338.     {
  339.         return _dblSpotTime;
  340.     }

  342.     /**
  343.      * Retrieve the Finish Time
  344.      * 
  345.      * @return The Finish Time
  346.      */

  348.     public double finishTime()
  349.     {
  350.         return _dblFinishTime;
  351.     }

  353.     /**
  354.      * Retrieve the Spot Holdings
  355.      * 
  356.      * @return The Spot Holdings
  357.      */

  359.     public double spotHoldings()
  360.     {
  361.         return _dblSpotHoldings;
  362.     }

  364.     /**
  365.      * Retrieve the Prior/Conditional Distributions Combiner
  366.      * 
  367.      * @return The Prior/Conditional Distributions Combiner
  368.      */

  370.     public org.drip.execution.bayesian.PriorConditionalCombiner combiner()
  371.     {
  372.         return _pcc;
  373.     }

  375.     /**
  376.      * Retrieve the Gross Price Change
  377.      * 
  378.      * @return The Gross Price Change
  379.      */

  381.     public double grossPriceChange()
  382.     {
  383.         return _dblGrossPriceChange;
  384.     }

  386.     /**
  387.      * Retrieve the Drift Expectation Estimate
  388.      * 
  389.      * @return The Drift Expectation Estimate
  390.      */

  392.     public double driftExpectationEstimate()
  393.     {
  394.         return _pcc.posteriorDriftDistribution (_dblGrossPriceChange).mean();
  395.     }

  397.     /**
  398.      * Retrieve the Drift Volatility Estimate
  399.      * 
  400.      * @return The Drift Volatility Estimate
  401.      */

  403.     public double driftVolatilityEstimate()
  404.     {
  405.         return java.lang.Math.sqrt (_pcc.posteriorDriftDistribution (_dblGrossPriceChange).variance());
  406.     }

  408.     /**
  409.      * Retrieve the Linear Temporary Market Impact Function
  410.      * 
  411.      * @return The Linear Temporary Market Impact Function
  412.      */

  414.     public org.drip.execution.impact.TransactionFunctionLinear linearTemporaryImpact()
  415.     {
  416.         return _tflTemporary;
  417.     }

  419.     /**
  420.      * Retrieve the Holdings Trajectory
  421.      * 
  422.      * @return The Holdings Trajectory
  423.      */

  425.     public org.drip.execution.optimum.EfficientTradingTrajectoryContinuous trajectory()
  426.     {
  427.         return _ectt;
  428.     }

  430.     /**
  431.      * Retrieve the Instantaneous Trade Rate
  432.      * 
  433.      * @return The Instantaneous Trade Rate
  434.      */

  436.     public double instantaneousTradeRate()
  437.     {
  438.         return _dblInstantaneousTradeRate;
  439.     }

  441.     /**
  442.      * Estimate of the Static Transaction Cost
  443.      * 
  444.      * @return The Static Transaction Cost Estimate
  445.      */

  447.     public double staticTransactionCost()
  448.     {
  449.         return _dblStaticTransactionCost;
  450.     }

  452.     /**
  453.      * Estimate the Transaction Cost Gain available from the Bayesian Drift
  454.      * 
  455.      * @return The Transaction Cost Gain available from the Bayesian Drift
  456.      */

  458.     public double transactionCostGain()
  459.     {
  460.         return _dblTransactionCostGain;
  461.     }
  462. }
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