OrnsteinUhlenbeckSteadyStatePDF.java

  1. package org.drip.sample.kolmogorov;

  3. import org.drip.dynamics.kolmogorov.R1FokkerPlanckOrnsteinUhlenbeck;
  4. import org.drip.dynamics.meanreverting.CKLSParameters;
  5. import org.drip.function.definition.R1ToR1;
  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.  * 
  16.  *  This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
  17.  *      calculations, valuation adjustment, and portfolio construction within and across fixed income,
  18.  *      credit, commodity, equity, FX, and structured products.
  19.  *  
  20.  *      https://lakshmidrip.github.io/DROP/
  21.  *  
  22.  *  DROP is composed of three modules:
  23.  *  
  24.  *  - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
  25.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  26.  *  - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
  27.  * 
  28.  *  DROP Analytics Core implements libraries for the following:
  29.  *  - Fixed Income Analytics
  30.  *  - Asset Backed Analytics
  31.  *  - XVA Analytics
  32.  *  - Exposure and Margin Analytics
  33.  * 
  34.  *  DROP Portfolio Core implements libraries for the following:
  35.  *  - Asset Allocation Analytics
  36.  *  - Transaction Cost Analytics
  37.  * 
  38.  *  DROP Numerical Core implements libraries for the following:
  39.  *  - Statistical Learning Library
  40.  *  - Numerical Optimizer Library
  41.  *  - Machine Learning Library
  42.  *  - Spline Builder Library
  43.  * 
  44.  *  Documentation for DROP is Spread Over:
  45.  * 
  46.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  47.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  48.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  49.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  50.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  51.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  52.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  53.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  54.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  55.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  56.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  57.  * 
  58.  *  Licensed under the Apache License, Version 2.0 (the "License");
  59.  *      you may not use this file except in compliance with the License.
  60.  *   
  61.  *  You may obtain a copy of the License at
  62.  *      http://www.apache.org/licenses/LICENSE-2.0
  63.  *  
  64.  *  Unless required by applicable law or agreed to in writing, software
  65.  *      distributed under the License is distributed on an "AS IS" BASIS,
  66.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  67.  *  
  68.  *  See the License for the specific language governing permissions and
  69.  *      limitations under the License.
  70.  */

  72. /**
  73.  * <i>OrnsteinUhlenbeckSteadyStatePDF</i> illustrates the Steady-State Distribution of an Evolving
  74.  *  R<sup>1</sup> Ornstein-Uhlenbeck Process. The References are:
  75.  *  
  76.  *  <br><br>
  77.  *  <ul>
  78.  *      <li>
  79.  *          Bogoliubov, N. N., and D. P. Sankevich (1994): N. N. Bogoliubov and Statistical Mechanics
  80.  *              <i>Russian Mathematical Surveys</i> <b>49 (5)</b> 19-49
  81.  *      </li>
  82.  *      <li>
  83.  *          Holubec, V., K. Kroy, and S. Steffenoni (2019): Physically Consistent Numerical Solver for
  84.  *              Time-dependent Fokker-Planck Equations <i>Physical Review E</i> <b>99 (4)</b> 032117
  85.  *      </li>
  86.  *      <li>
  87.  *          Kadanoff, L. P. (2000): <i>Statistical Physics: Statics, Dynamics, and Re-normalization</i>
  88.  *              <b>World Scientific</b>
  89.  *      </li>
  90.  *      <li>
  91.  *          Ottinger, H. C. (1996): <i>Stochastic Processes in Polymeric Fluids</i> <b>Springer-Verlag</b>
  92.  *              Berlin-Heidelberg
  93.  *      </li>
  94.  *      <li>
  95.  *          Wikipedia (2019): Fokker-Planck Equation
  96.  *              https://en.wikipedia.org/wiki/Fokker%E2%80%93Planck_equation
  97.  *      </li>
  98.  *  </ul>
  99.  *
  100.  *  <br><br>
  101.  *  <ul>
  102.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/AnalyticsCore.md">Analytics Core Module</a></li>
  103.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FixedIncomeAnalyticsLibrary.md">Fixed Income Analytics</a></li>
  104.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/dynamics/README.md">Dynamics</a></li>
  105.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/dynamics/lmm/README.md">LIBOR Market Model</a></li>
  106.  *  </ul>
  107.  *
  108.  * @author Lakshmi Krishnamurthy
  109.  */

  111. public class OrnsteinUhlenbeckSteadyStatePDF
  112. {

  114.     private static final void SteadyStateDistribution (
  115.         final double meanReversionSpeed,
  116.         final double volatility,
  117.         final double[] xArray)
  118.         throws Exception
  119.     {
  120.         R1ToR1 steadyStatePDF = new R1FokkerPlanckOrnsteinUhlenbeck (
  121.             CKLSParameters.OrnsteinUhlenbeck (
  122.                 meanReversionSpeed,
  123.                 volatility
  124.             )
  125.         ).steadyStatePDF();

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

  130.         for (double x : xArray)
  131.         {
  132.             dump = dump + " " + FormatUtil.FormatDouble (
  133.                 steadyStatePDF.evaluate (
  134.                     x
  135.                 ), 1, 6, 1.
  136.             ) + " |";
  137.         }

  139.         System.out.println (dump + "|");
  140.     }

  142.     public static final void main (
  143.         final String[] argumentArray)
  144.         throws Exception
  145.     {
  146.         EnvManager.InitEnv (
  147.             ""
  148.         );
  149.         double[] xArray =
  150.         {
  151.             -2.5,
  152.             -2.0,
  153.             -1.5,
  154.             -1.0,
  155.             -0.5,
  156.              0.0,
  157.              0.5,
  158.              1.0,
  159.              1.5,
  160.              2.0,
  161.              2.5,
  162.         };
  163.         double[] volatilityArray =
  164.         {
  165.              0.5,
  166.              1.0,
  167.              1.5,
  168.              2.0,
  169.              2.5,
  170.         };
  171.         double[] meanReversionSpeedArray =
  172.         {
  173.              0.5,
  174.              1.0,
  175.              1.5,
  176.              2.0,
  177.              2.5,
  178.         };

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

  182.         System.out.println ("\t|                                          ORNSTEIN-UHLENBECK FOKKER-PLANCK PDF STEADY STATE DISTRIBUTION                                           ||");

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

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

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

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

  192.         System.out.println ("\t|                - Row of PDF Values over x                                                                                                         ||");

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

  196.         for (double meanReversionSpeed : meanReversionSpeedArray)
  197.         {
  198.             for (double volatility : volatilityArray)
  199.             {
  200.                 SteadyStateDistribution (
  201.                     meanReversionSpeed,
  202.                     volatility,
  203.                     xArray
  204.                 );
  205.             }
  206.         }

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

  210.         EnvManager.TerminateEnv();
  211.     }
  212. }
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