ModelMTMDistribution11a.java

  1. package org.drip.sample.anfuso2017;

  3. import org.drip.measure.gaussian.R1UnivariateNormal;
  4. import org.drip.numerical.common.FormatUtil;
  5. import org.drip.service.env.EnvManager;
  6. import org.drip.validation.evidence.Sample;
  7. import org.drip.validation.hypothesis.ProbabilityIntegralTransform;

  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>ModelMTMDistribution11a</i> illustrates the Model MTM Distributions laid out in Table 11a of Anfuso,
  85.  * Karyampas, and Nawroth (2017).
  86.  *
  87.  *  <br><br>
  88.  *  <ul>
  89.  *      <li>
  90.  *          Anfuso, F., D. Karyampas, and A. Nawroth (2017): A Sound Basel III Compliant Framework for
  91.  *              Back-testing Credit Exposure Models
  92.  *              https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2264620 <b>eSSRN</b>
  93.  *      </li>
  94.  *      <li>
  95.  *          Diebold, F. X., T. A. Gunther, and A. S. Tay (1998): Evaluating Density Forecasts with
  96.  *              Applications to Financial Risk Management, International Economic Review 39 (4) 863-883
  97.  *      </li>
  98.  *      <li>
  99.  *          Kenyon, C., and R. Stamm (2012): Discounting, LIBOR, CVA, and Funding: Interest Rate and Credit
  100.  *              Pricing, Palgrave Macmillan
  101.  *      </li>
  102.  *      <li>
  103.  *          Wikipedia (2018): Probability Integral Transform
  104.  *              https://en.wikipedia.org/wiki/Probability_integral_transform
  105.  *      </li>
  106.  *      <li>
  107.  *          Wikipedia (2019): p-value https://en.wikipedia.org/wiki/P-value
  108.  *      </li>
  109.  *  </ul>
  110.  *
  111.  *  <br><br>
  112.  *  <ul>
  113.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  114.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ModelValidationAnalyticsLibrary.md">Model Validation Analytics Library</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/anfuso2017/README.md">Anfuso, Karyampas, and Nawroth (2013) Replications</a></li>
  117.  *  </ul>
  118.  * <br><br>
  119.  *
  120.  * @author Lakshmi Krishnamurthy
  121.  */

  123. public class ModelMTMDistribution11a
  124. {

  126.     private static final double UnivariateRandom (
  127.         final double mean,
  128.         final double sigma)
  129.         throws Exception
  130.     {
  131.         return new R1UnivariateNormal (
  132.             mean,
  133.             sigma
  134.         ).random();
  135.     }

  137.     private static final Sample GenerateSample (
  138.         final double mean,
  139.         final double sigma,
  140.         final int drawCount)
  141.         throws Exception
  142.     {
  143.         double[] univariateRandomArray = new double[drawCount];

  145.         for (int drawIndex = 0; drawIndex < drawCount; ++drawIndex)
  146.         {
  147.             univariateRandomArray[drawIndex] = UnivariateRandom (
  148.                 mean,
  149.                 sigma
  150.             );
  151.         }

  153.         return new Sample (univariateRandomArray);
  154.     }

  156.     private static final void ProbabilityPlot (
  157.         final ProbabilityIntegralTransform pitTooHighVolatility,
  158.         final ProbabilityIntegralTransform pitCorrectVolatility,
  159.         final ProbabilityIntegralTransform pitTooLowVolatility,
  160.         final double xLeft,
  161.         final double xRight,
  162.         final double xWidth)
  163.         throws Exception
  164.     {
  165.         double leftProbabilityTooHighVolatility = 0.;
  166.         double leftProbabilityCorrectVolatility = 0.;
  167.         double leftProbabilityTooLowVolatility = 0.;

  169.         for (double x = xLeft; x <= xRight; x += xWidth)
  170.         {
  171.             double probabilityTooHighVolatility = pitTooHighVolatility.pValue (x);

  173.             double probabilityCorrectVolatility = pitCorrectVolatility.pValue (x);

  175.             double probabilityTooLowVolatility = pitTooLowVolatility.pValue (x);

  177.             System.out.println (
  178.                 "\t| " +
  179.                 FormatUtil.FormatDouble (x, 1, 2, 1.) + " | " +
  180.                 FormatUtil.FormatDouble (probabilityTooHighVolatility - leftProbabilityTooHighVolatility, 1, 8, 1.) + " | " +
  181.                 FormatUtil.FormatDouble (probabilityCorrectVolatility - leftProbabilityCorrectVolatility, 1, 8, 1.) + " | " +
  182.                 FormatUtil.FormatDouble (probabilityTooLowVolatility - leftProbabilityTooLowVolatility, 1, 8, 1.) + " ||"
  183.             );

  185.             leftProbabilityTooHighVolatility = probabilityTooHighVolatility;
  186.             leftProbabilityCorrectVolatility = probabilityCorrectVolatility;
  187.             leftProbabilityTooLowVolatility = probabilityTooLowVolatility;
  188.         }
  189.     }

  191.     public static final void main (
  192.         final String[] argumentArray)
  193.         throws Exception
  194.     {
  195.         EnvManager.InitEnv ("");

  197.         int drawCount = 1000000;
  198.         double mean = 0.;
  199.         double volatilityTooHigh = 3.;
  200.         double volatilityCorrect = 2.;
  201.         double volatilityTooLow = 1.;
  202.         double xLeft = -7.00;
  203.         double xRight = 7.00;
  204.         double xWidth = 0.50;

  206.         Sample sampleVolatilityTooHigh = GenerateSample (
  207.             mean,
  208.             volatilityTooHigh,
  209.             drawCount
  210.         );

  212.         Sample sampleVolatilityCorrect = GenerateSample (
  213.             mean,
  214.             volatilityCorrect,
  215.             drawCount
  216.         );

  218.         Sample sampleVolatilityTooLow = GenerateSample (
  219.             mean,
  220.             volatilityTooLow,
  221.             drawCount
  222.         );

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

  226.         System.out.println ("\t|        MODEL MTM DISTRIBUTION COMPARISON        ||");

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

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

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

  234.         System.out.println ("\t|          - p-Value (Volatility Too High)        ||");

  236.         System.out.println ("\t|          - p-Value (Volatility Correct)         ||");

  238.         System.out.println ("\t|          - p-Value (Volatility Too Low)         ||");

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

  242.         ProbabilityPlot (
  243.             sampleVolatilityTooHigh.nativeProbabilityIntegralTransform(),
  244.             sampleVolatilityCorrect.nativeProbabilityIntegralTransform(),
  245.             sampleVolatilityTooLow.nativeProbabilityIntegralTransform(),
  246.             xLeft,
  247.             xRight,
  248.             xWidth
  249.         );

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

  253.         EnvManager.TerminateEnv();
  254.     }
  255. }
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