MTMVolatilityComparison11b.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.distance.GapLossWeightFunction;
  7. import org.drip.validation.distance.GapTestOutcome;
  8. import org.drip.validation.distance.GapTestSetting;
  9. import org.drip.validation.evidence.Ensemble;
  10. import org.drip.validation.evidence.Sample;
  11. import org.drip.validation.evidence.TestStatisticEvaluator;
  12. import org.drip.validation.hypothesis.HistogramTestOutcome;
  13. import org.drip.validation.hypothesis.HistogramTestSetting;
  14. import org.drip.validation.hypothesis.ProbabilityIntegralTransformTest;
  15. import org.drip.validation.quantile.PlottingPositionGeneratorHeuristic;
  16. import org.drip.validation.riskfactorsingle.DiscriminatoryPowerAnalyzer;

  18. /*
  19.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  20.  */

  22. /*!
  23.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  24.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  25.  * 
  26.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  27.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  28.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  29.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  30.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  31.  *      and computational support.
  32.  *  
  33.  *      https://lakshmidrip.github.io/DROP/
  34.  *  
  35.  *  DROP is composed of three modules:
  36.  *  
  37.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  38.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  39.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  40.  * 
  41.  *  DROP Product Core implements libraries for the following:
  42.  *  - Fixed Income Analytics
  43.  *  - Loan Analytics
  44.  *  - Transaction Cost Analytics
  45.  * 
  46.  *  DROP Portfolio Core implements libraries for the following:
  47.  *  - Asset Allocation Analytics
  48.  *  - Asset Liability Management Analytics
  49.  *  - Capital Estimation Analytics
  50.  *  - Exposure Analytics
  51.  *  - Margin Analytics
  52.  *  - XVA Analytics
  53.  * 
  54.  *  DROP Computational Core implements libraries for the following:
  55.  *  - Algorithm Support
  56.  *  - Computation Support
  57.  *  - Function Analysis
  58.  *  - Model Validation
  59.  *  - Numerical Analysis
  60.  *  - Numerical Optimizer
  61.  *  - Spline Builder
  62.  *  - Statistical Learning
  63.  * 
  64.  *  Documentation for DROP is Spread Over:
  65.  * 
  66.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  67.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  68.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  69.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  70.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  71.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  72.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  73.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  74.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  75.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  76.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  77.  * 
  78.  *  Licensed under the Apache License, Version 2.0 (the "License");
  79.  *      you may not use this file except in compliance with the License.
  80.  *   
  81.  *  You may obtain a copy of the License at
  82.  *      http://www.apache.org/licenses/LICENSE-2.0
  83.  *  
  84.  *  Unless required by applicable law or agreed to in writing, software
  85.  *      distributed under the License is distributed on an "AS IS" BASIS,
  86.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  87.  *  
  88.  *  See the License for the specific language governing permissions and
  89.  *      limitations under the License.
  90.  */

  92. /**
  93.  * <i>MTMVolatilityComparison11b</i> illustrates the Impact on Gap Distribution of Hypothesis Parameters as
  94.  * laid out in Table 11b of Anfuso, Karyampas, and Nawroth (2017).
  95.  *
  96.  *  <br><br>
  97.  *  <ul>
  98.  *      <li>
  99.  *          Anfuso, F., D. Karyampas, and A. Nawroth (2017): A Sound Basel III Compliant Framework for
  100.  *              Back-testing Credit Exposure Models
  101.  *              https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2264620 <b>eSSRN</b>
  102.  *      </li>
  103.  *      <li>
  104.  *          Diebold, F. X., T. A. Gunther, and A. S. Tay (1998): Evaluating Density Forecasts with
  105.  *              Applications to Financial Risk Management, International Economic Review 39 (4) 863-883
  106.  *      </li>
  107.  *      <li>
  108.  *          Kenyon, C., and R. Stamm (2012): Discounting, LIBOR, CVA, and Funding: Interest Rate and Credit
  109.  *              Pricing, Palgrave Macmillan
  110.  *      </li>
  111.  *      <li>
  112.  *          Wikipedia (2018): Probability Integral Transform
  113.  *              https://en.wikipedia.org/wiki/Probability_integral_transform
  114.  *      </li>
  115.  *      <li>
  116.  *          Wikipedia (2019): p-value https://en.wikipedia.org/wiki/P-value
  117.  *      </li>
  118.  *  </ul>
  119.  *
  120.  *  <br><br>
  121.  *  <ul>
  122.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  123.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ModelValidationAnalyticsLibrary.md">Model Validation Analytics Library</a></li>
  124.  *      <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>
  125.  *      <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>
  126.  *  </ul>
  127.  * <br><br>
  128.  *
  129.  * @author Lakshmi Krishnamurthy
  130.  */

  132. public class MTMVolatilityComparison11b
  133. {

  135.     private static final double UnivariateRandom (
  136.         final double mean,
  137.         final double sigma)
  138.         throws Exception
  139.     {
  140.         return new R1UnivariateNormal (
  141.             mean,
  142.             sigma
  143.         ).random();
  144.     }

  146.     private static final Sample GenerateSample (
  147.         final double mean,
  148.         final double sigma,
  149.         final int drawCount)
  150.         throws Exception
  151.     {
  152.         double[] univariateRandomArray = new double[drawCount];

  154.         for (int drawIndex = 0; drawIndex < drawCount; ++drawIndex)
  155.         {
  156.             univariateRandomArray[drawIndex] = UnivariateRandom (
  157.                 mean,
  158.                 sigma
  159.             );
  160.         }

  162.         return new Sample (univariateRandomArray);
  163.     }

  165.     private static final Sample[] GenerateSampleArray (
  166.         final double mean,
  167.         final double sigma,
  168.         final int drawCount,
  169.         final int sampleCount)
  170.         throws Exception
  171.     {
  172.         Sample[] sampleArray = new Sample[sampleCount];

  174.         for (int sampleIndex = 0; sampleIndex < sampleCount; ++sampleIndex)
  175.         {
  176.             sampleArray[sampleIndex] = GenerateSample (
  177.                 mean,
  178.                 sigma,
  179.                 drawCount
  180.             );
  181.         }

  183.         return sampleArray;
  184.     }

  186.     private static final Ensemble GenerateEnsemble (
  187.         final double mean,
  188.         final double sigma,
  189.         final int drawCount,
  190.         final int sampleCount)
  191.         throws Exception
  192.     {
  193.         return new Ensemble (
  194.             GenerateSampleArray (
  195.                 mean,
  196.                 sigma,
  197.                 drawCount,
  198.                 sampleCount
  199.             ),
  200.             new TestStatisticEvaluator[]
  201.             {
  202.                 new TestStatisticEvaluator()
  203.                 {
  204.                     public double evaluate (
  205.                         final double[] drawArray)
  206.                         throws Exception
  207.                     {
  208.                         return 1.;
  209.                     }
  210.                 }
  211.             }
  212.         );
  213.     }

  215.     private static final void DistanceTest (
  216.         final GapTestOutcome gapTestOutcome,
  217.         final int orderStatisticsCount)
  218.         throws Exception
  219.     {
  220.         HistogramTestOutcome histogram = new ProbabilityIntegralTransformTest (
  221.             gapTestOutcome.probabilityIntegralTransformWeighted()
  222.         ).histogramTest (
  223.             HistogramTestSetting.AnfusoKaryampasNawroth2017 (
  224.                 PlottingPositionGeneratorHeuristic.NIST2013 (orderStatisticsCount)
  225.             )
  226.         );

  228.         double[] pValueIncrementalArray = histogram.pValueIncrementalArray();

  230.         double[] gapArray = histogram.testStatisticArray();

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

  234.         System.out.println ("\t| CPT Integrand Distribution ||");

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

  238.         for (int histogramIndex = 0; histogramIndex <= orderStatisticsCount + 1; ++histogramIndex)
  239.         {
  240.             System.out.println (
  241.                 "\t|" +
  242.                 FormatUtil.FormatDouble (gapArray[histogramIndex], 1, 9, 1.) + " | " +
  243.                 FormatUtil.FormatDouble (pValueIncrementalArray[histogramIndex], 1, 9, 1.) + " ||"
  244.             );
  245.         }

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

  250.     public static final void main (
  251.         final String[] argumentArray)
  252.         throws Exception
  253.     {
  254.         EnvManager.InitEnv ("");

  256.         int drawCount = 100000;
  257.         int sampleCount = 10;
  258.         double mean = 0.;
  259.         double sampleVolatility = 2.;
  260.         int orderStatisticsCount = 20;
  261.         double hypothesis1Volatility = 1.;
  262.         double hypothesis2Volatility = 3.;

  264.         Sample sample = GenerateSample (
  265.             mean,
  266.             sampleVolatility,
  267.             drawCount
  268.         );

  270.         DiscriminatoryPowerAnalyzer discriminatoryPowerAnalysis = DiscriminatoryPowerAnalyzer.FromSample (
  271.             sample,
  272.             GapTestSetting.ConservativePortfolioLossTest (GapLossWeightFunction.CramersVonMises())
  273.         );

  275.         DistanceTest (
  276.             discriminatoryPowerAnalysis.gapTest (
  277.                 GenerateEnsemble (
  278.                     mean,
  279.                     hypothesis1Volatility,
  280.                     drawCount,
  281.                     sampleCount
  282.                 )
  283.             ),
  284.             orderStatisticsCount
  285.         );

  287.         DistanceTest (
  288.             discriminatoryPowerAnalysis.gapTest (
  289.                 GenerateEnsemble (
  290.                     mean,
  291.                     hypothesis2Volatility,
  292.                     drawCount,
  293.                     sampleCount
  294.                 )
  295.             ),
  296.             orderStatisticsCount
  297.         );

  299.         EnvManager.TerminateEnv();
  300.     }
  301. }
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