VasicekPopulationCentralMeasures.java

  1. package org.drip.sample.ckls;

  3. import org.drip.dynamics.meanreverting.R1VasicekStochasticEvolver;
  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.  */

  13. /*!
  14.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  15.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  16.  * 
  17.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  18.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  19.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  20.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  21.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  22.  *      and computational support.
  23.  *  
  24.  *      https://lakshmidrip.github.io/DROP/
  25.  *  
  26.  *  DROP is composed of three modules:
  27.  *  
  28.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  29.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  30.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  31.  * 
  32.  *  DROP Product Core implements libraries for the following:
  33.  *  - Fixed Income Analytics
  34.  *  - Loan Analytics
  35.  *  - Transaction Cost Analytics
  36.  * 
  37.  *  DROP Portfolio Core implements libraries for the following:
  38.  *  - Asset Allocation Analytics
  39.  *  - Asset Liability Management Analytics
  40.  *  - Capital Estimation Analytics
  41.  *  - Exposure Analytics
  42.  *  - Margin Analytics
  43.  *  - XVA Analytics
  44.  * 
  45.  *  DROP Computational Core implements libraries for the following:
  46.  *  - Algorithm Support
  47.  *  - Computation Support
  48.  *  - Function Analysis
  49.  *  - Model Validation
  50.  *  - Numerical Analysis
  51.  *  - Numerical Optimizer
  52.  *  - Spline Builder
  53.  *  - Statistical Learning
  54.  * 
  55.  *  Documentation for DROP is Spread Over:
  56.  * 
  57.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  58.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  59.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  60.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  61.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  62.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  63.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  64.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  65.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  66.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  67.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  68.  * 
  69.  *  Licensed under the Apache License, Version 2.0 (the "License");
  70.  *      you may not use this file except in compliance with the License.
  71.  *   
  72.  *  You may obtain a copy of the License at
  73.  *      http://www.apache.org/licenses/LICENSE-2.0
  74.  *  
  75.  *  Unless required by applicable law or agreed to in writing, software
  76.  *      distributed under the License is distributed on an "AS IS" BASIS,
  77.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  78.  *  
  79.  *  See the License for the specific language governing permissions and
  80.  *      limitations under the License.
  81.  */

  83. /**
  84.  * <i>VasicekPopulationCentralMeasures</i> illustrates the Aging of Population Central Measures, both
  85.  *  Temporal and Steady-State, of an Evolving R<sup>1</sup> Vasiceck Process. The References are:
  86.  *  
  87.  *  <br><br>
  88.  *  <ul>
  89.  *      <li>
  90.  *          Bogoliubov, N. N., and D. P. Sankevich (1994): N. N. Bogoliubov and Statistical Mechanics
  91.  *              <i>Russian Mathematical Surveys</i> <b>49 (5)</b> 19-49
  92.  *      </li>
  93.  *      <li>
  94.  *          Holubec, V., K. Kroy, and S. Steffenoni (2019): Physically Consistent Numerical Solver for
  95.  *              Time-dependent Fokker-Planck Equations <i>Physical Review E</i> <b>99 (4)</b> 032117
  96.  *      </li>
  97.  *      <li>
  98.  *          Kadanoff, L. P. (2000): <i>Statistical Physics: Statics, Dynamics, and Re-normalization</i>
  99.  *              <b>World Scientific</b>
  100.  *      </li>
  101.  *      <li>
  102.  *          Ottinger, H. C. (1996): <i>Stochastic Processes in Polymeric Fluids</i> <b>Springer-Verlag</b>
  103.  *              Berlin-Heidelberg
  104.  *      </li>
  105.  *      <li>
  106.  *          Wikipedia (2019): Fokker-Planck Equation
  107.  *              https://en.wikipedia.org/wiki/Fokker%E2%80%93Planck_equation
  108.  *      </li>
  109.  *  </ul>
  110.  *
  111.  *  <br><br>
  112.  *  <ul>
  113.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ProductCore.md">Product Core Module</a></li>
  114.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FixedIncomeAnalyticsLibrary.md">Fixed Income Analytics</a></li>
  115.  *      <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>
  116.  *      <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>
  117.  *  </ul>
  118.  *
  119.  * @author Lakshmi Krishnamurthy
  120.  */

  122. public class VasicekPopulationCentralMeasures
  123. {

  125.     private static final void TemporalCentralMeasures (
  126.         final double meanReversionSpeed,
  127.         final double meanReversionLevel,
  128.         final double volatility,
  129.         final double[] tArray)
  130.         throws Exception
  131.     {
  132.         R1StochasticEvolver r1StochasticEvolver = R1VasicekStochasticEvolver.Wiener (
  133.             meanReversionSpeed,
  134.             meanReversionLevel,
  135.             volatility,
  136.             0.01
  137.         );

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

  144.         for (double t : tArray)
  145.         {
  146.             PopulationCentralMeasures populationCentralMeasures =
  147.                 r1StochasticEvolver.temporalPopulationCentralMeasures (
  148.                     meanReversionSpeed,
  149.                     t
  150.                 );

  152.             dump = dump + " {" + FormatUtil.FormatDouble (
  153.                 populationCentralMeasures.mean(), 1, 4, 1.
  154.             ) + " |" + FormatUtil.FormatDouble (
  155.                 populationCentralMeasures.variance(), 1, 4, 1.
  156.             ) + "}";
  157.         }

  159.         System.out.println (dump);
  160.     }

  162.     private static final void SteadyStateCentralMeasures (
  163.         final double meanReversionSpeed,
  164.         final double meanReversionLevel,
  165.         final double volatility)
  166.         throws Exception
  167.     {
  168.         PopulationCentralMeasures populationCentralMeasures = R1VasicekStochasticEvolver.Wiener (
  169.             meanReversionSpeed,
  170.             meanReversionLevel,
  171.             volatility,
  172.             0.01
  173.         ).steadyStatePopulationCentralMeasures (
  174.             meanReversionSpeed
  175.         );

  177.         System.out.println (
  178.             "\t| [" + FormatUtil.FormatDouble (
  179.                 meanReversionSpeed, 1, 1, 1.
  180.             ) + "," + FormatUtil.FormatDouble (
  181.                 meanReversionLevel, 1, 1, 1.
  182.             ) + "," + FormatUtil.FormatDouble (
  183.                 volatility, 1, 1, 1.
  184.             ) + "] =>" + " {" + FormatUtil.FormatDouble (
  185.                 populationCentralMeasures.mean(), 1, 4, 1.
  186.             ) + " |" + FormatUtil.FormatDouble (
  187.                 populationCentralMeasures.variance(), 1, 4, 1.
  188.             ) + "}"
  189.         );
  190.     }

  192.     public static final void main (
  193.         final String[] argumentArray)
  194.         throws Exception
  195.     {
  196.         EnvManager.InitEnv (
  197.             ""
  198.         );
  199.         double[] tArray =
  200.         {
  201.              1.0,
  202.              2.0,
  203.              3.0,
  204.              4.0,
  205.              5.0,
  206.              6.0,
  207.              7.0,
  208.         };
  209.         double[] volatilityArray =
  210.         {
  211.              0.5,
  212.              1.0,
  213.              1.5,
  214.              2.0,
  215.              2.5,
  216.         };
  217.         double[] meanReversionLevelArray =
  218.         {
  219.              0.5,
  220.              1.0,
  221.              1.5,
  222.         };
  223.         double[] meanReversionSpeedArray =
  224.         {
  225.              0.5,
  226.              1.0,
  227.              1.5,
  228.              2.0,
  229.              2.5,
  230.         };

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

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

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

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

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

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

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

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

  248.         for (double meanReversionSpeed : meanReversionSpeedArray)
  249.         {
  250.             for (double meanReversionLevel : meanReversionLevelArray)
  251.             {
  252.                 for (double volatility : volatilityArray)
  253.                 {
  254.                     TemporalCentralMeasures (
  255.                         meanReversionSpeed,
  256.                         meanReversionLevel,
  257.                         volatility,
  258.                         tArray
  259.                     );
  260.                 }
  261.             }
  262.         }

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

  266.         System.out.println();

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

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

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

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

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

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

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

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

  284.         for (double meanReversionSpeed : meanReversionSpeedArray)
  285.         {
  286.             for (double meanReversionLevel : meanReversionLevelArray)
  287.             {
  288.                 for (double volatility : volatilityArray)
  289.                 {
  290.                     SteadyStateCentralMeasures (
  291.                         meanReversionSpeed,
  292.                         meanReversionLevel,
  293.                         volatility
  294.                     );
  295.                 }
  296.             }
  297.         }

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

  301.         EnvManager.TerminateEnv();
  302.     }
  303. }
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