OrnsteinUhlenbeckPopulationCentralMeasures.java

  1. package org.drip.sample.ckls;

  3. import org.drip.dynamics.meanreverting.R1OrnsteinUhlenbeckStochasticEvolver;
  4. import org.drip.dynamics.process.R1StochasticEvolver;
  5. import org.drip.measure.statistics.PopulationCentralMeasures;
  6. import org.drip.numerical.common.FormatUtil;
  7. import org.drip.service.env.EnvManager;

  9. /*
  10.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  11.  */


  14. /*!
  15.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  16.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  17.  * 
  18.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  19.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  20.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  21.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  22.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  23.  *      and computational support.
  24.  *  
  25.  *      https://lakshmidrip.github.io/DROP/
  26.  *  
  27.  *  DROP is composed of three modules:
  28.  *  
  29.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  30.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  31.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  32.  * 
  33.  *  DROP Product Core implements libraries for the following:
  34.  *  - Fixed Income Analytics
  35.  *  - Loan Analytics
  36.  *  - Transaction Cost Analytics
  37.  * 
  38.  *  DROP Portfolio Core implements libraries for the following:
  39.  *  - Asset Allocation Analytics
  40.  *  - Asset Liability Management Analytics
  41.  *  - Capital Estimation Analytics
  42.  *  - Exposure Analytics
  43.  *  - Margin Analytics
  44.  *  - XVA Analytics
  45.  * 
  46.  *  DROP Computational Core implements libraries for the following:
  47.  *  - Algorithm Support
  48.  *  - Computation Support
  49.  *  - Function Analysis
  50.  *  - Model Validation
  51.  *  - Numerical Analysis
  52.  *  - Numerical Optimizer
  53.  *  - Spline Builder
  54.  *  - Statistical Learning
  55.  * 
  56.  *  Documentation for DROP is Spread Over:
  57.  * 
  58.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  59.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  60.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  61.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  62.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  63.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  64.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  65.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
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  67.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  68.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  69.  * 
  70.  *  Licensed under the Apache License, Version 2.0 (the "License");
  71.  *      you may not use this file except in compliance with the License.
  72.  *   
  73.  *  You may obtain a copy of the License at
  74.  *      http://www.apache.org/licenses/LICENSE-2.0
  75.  *  
  76.  *  Unless required by applicable law or agreed to in writing, software
  77.  *      distributed under the License is distributed on an "AS IS" BASIS,
  78.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  79.  *  
  80.  *  See the License for the specific language governing permissions and
  81.  *      limitations under the License.
  82.  */

  84. /**
  85.  * <i>OrnsteinUhlenbeckPopulationCentralMeasures</i> illustrates the Aging of Population Central Measures,
  86.  *  both Temporal and Steady-State, of an Evolving R<sup>1</sup> Ornstein-Uhlenbeck Process. The References
  87.  * are:
  88.  *  
  89.  *  <br><br>
  90.  *  <ul>
  91.  *      <li>
  92.  *          Bogoliubov, N. N., and D. P. Sankevich (1994): N. N. Bogoliubov and Statistical Mechanics
  93.  *              <i>Russian Mathematical Surveys</i> <b>49 (5)</b> 19-49
  94.  *      </li>
  95.  *      <li>
  96.  *          Holubec, V., K. Kroy, and S. Steffenoni (2019): Physically Consistent Numerical Solver for
  97.  *              Time-dependent Fokker-Planck Equations <i>Physical Review E</i> <b>99 (4)</b> 032117
  98.  *      </li>
  99.  *      <li>
  100.  *          Kadanoff, L. P. (2000): <i>Statistical Physics: Statics, Dynamics, and Re-normalization</i>
  101.  *              <b>World Scientific</b>
  102.  *      </li>
  103.  *      <li>
  104.  *          Ottinger, H. C. (1996): <i>Stochastic Processes in Polymeric Fluids</i> <b>Springer-Verlag</b>
  105.  *              Berlin-Heidelberg
  106.  *      </li>
  107.  *      <li>
  108.  *          Wikipedia (2019): Fokker-Planck Equation
  109.  *              https://en.wikipedia.org/wiki/Fokker%E2%80%93Planck_equation
  110.  *      </li>
  111.  *  </ul>
  112.  *
  113.  *  <br><br>
  114.  *  <ul>
  115.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ProductCore.md">Product Core Module</a></li>
  116.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FixedIncomeAnalyticsLibrary.md">Fixed Income Analytics</a></li>
  117.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">DROP API Construction and Usage</a></li>
  118.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/ckls/README.md">Analysis of CKLS Process Variants</a></li>
  119.  *  </ul>
  120.  *
  121.  * @author Lakshmi Krishnamurthy
  122.  */

  124. public class OrnsteinUhlenbeckPopulationCentralMeasures
  125. {

  127.     private static final void TemporalCentralMeasures (
  128.         final double meanReversionSpeed,
  129.         final double volatility,
  130.         final double[] tArray)
  131.         throws Exception
  132.     {
  133.         R1StochasticEvolver r1StochasticEvolver = R1OrnsteinUhlenbeckStochasticEvolver.Wiener (
  134.             meanReversionSpeed,
  135.             volatility,
  136.             0.01
  137.         );

  139.         java.lang.String dump = "\t| [" + FormatUtil.FormatDouble (meanReversionSpeed, 1, 1, 1.) + "," +
  140.             FormatUtil.FormatDouble (volatility, 1, 1, 1.) + "] =>";

  142.         for (double t : tArray)
  143.         {
  144.             PopulationCentralMeasures populationCentralMeasures =
  145.                 r1StochasticEvolver.temporalPopulationCentralMeasures (
  146.                     meanReversionSpeed,
  147.                     t
  148.                 );

  150.             dump = dump + " {" + FormatUtil.FormatDouble (
  151.                 populationCentralMeasures.mean(), 1, 4, 1.
  152.             ) + " |" + FormatUtil.FormatDouble (
  153.                 populationCentralMeasures.variance(), 1, 4, 1.
  154.             ) + "}";
  155.         }

  157.         System.out.println (dump);
  158.     }

  160.     private static final void SteadyStateCentralMeasures (
  161.         final double meanReversionSpeed,
  162.         final double volatility)
  163.         throws Exception
  164.     {
  165.         PopulationCentralMeasures populationCentralMeasures = R1OrnsteinUhlenbeckStochasticEvolver.Wiener (
  166.             meanReversionSpeed,
  167.             volatility,
  168.             0.01
  169.         ).steadyStatePopulationCentralMeasures (
  170.             meanReversionSpeed
  171.         );

  173.         System.out.println (
  174.             "\t| [" + FormatUtil.FormatDouble (
  175.                 meanReversionSpeed, 1, 1, 1.
  176.             ) + "," + FormatUtil.FormatDouble (
  177.                 volatility, 1, 1, 1.
  178.             ) + "] =>" + " {" + FormatUtil.FormatDouble (
  179.                 populationCentralMeasures.mean(), 1, 4, 1.
  180.             ) + " |" + FormatUtil.FormatDouble (
  181.                 populationCentralMeasures.variance(), 1, 4, 1.
  182.             ) + "}"
  183.         );
  184.     }

  186.     public static final void main (
  187.         final String[] argumentArray)
  188.         throws Exception
  189.     {
  190.         EnvManager.InitEnv (
  191.             ""
  192.         );
  193.         double[] tArray =
  194.         {
  195.              1.0,
  196.              2.0,
  197.              3.0,
  198.              4.0,
  199.              5.0,
  200.              6.0,
  201.              7.0,
  202.         };
  203.         double[] volatilityArray =
  204.         {
  205.              0.5,
  206.              1.0,
  207.              1.5,
  208.              2.0,
  209.              2.5,
  210.         };
  211.         double[] meanReversionSpeedArray =
  212.         {
  213.              0.5,
  214.              1.0,
  215.              1.5,
  216.              2.0,
  217.              2.5,
  218.         };

  220.         System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------------------------||");

  222.         System.out.println ("\t|                                          ORNSTEIN-UHLENBECK FOKKER-PLANCK PDF TEMPORAL CENTRAL MEASURES                                           ||");

  224.         System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------------------------||");

  226.         System.out.println ("\t|        L -> R:                                                                                                                                    ||");

  228.         System.out.println ("\t|                - Mean Reversion Level                                                                                                             ||");

  230.         System.out.println ("\t|                - Volatility                                                                                                                       ||");

  232.         System.out.println ("\t|                - Row of PDF {Mean | Variance} Tuple over t                                                                                        ||");

  234.         System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------------------------||");

  236.         for (double meanReversionSpeed : meanReversionSpeedArray)
  237.         {
  238.             for (double volatility : volatilityArray)
  239.             {
  240.                 TemporalCentralMeasures (
  241.                     meanReversionSpeed,
  242.                     volatility,
  243.                     tArray
  244.                 );
  245.             }
  246.         }

  248.         System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------------------------||");

  250.         System.out.println();

  252.         System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------------------------||");

  254.         System.out.println ("\t|                                        ORNSTEIN-UHLENBECK FOKKER-PLANCK PDF STEADY STATE CENTRAL MEASURES                                         ||");

  256.         System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------------------------||");

  258.         System.out.println ("\t|        L -> R:                                                                                                                                    ||");

  260.         System.out.println ("\t|                - Mean Reversion Level                                                                                                             ||");

  262.         System.out.println ("\t|                - Volatility                                                                                                                       ||");

  264.         System.out.println ("\t|                - PDF {Mean | Variance} Tuple                                                                                                      ||");

  266.         System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------------------------||");

  268.         for (double meanReversionSpeed : meanReversionSpeedArray)
  269.         {
  270.             for (double volatility : volatilityArray)
  271.             {
  272.                 SteadyStateCentralMeasures (
  273.                     meanReversionSpeed,
  274.                     volatility
  275.                 );
  276.             }
  277.         }

  279.         System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------------------------||");

  281.         EnvManager.TerminateEnv();
  282.     }
  283. }
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