CVMDiscriminatoryPowerAnalysis3a.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.riskfactorsingle.DiscriminatoryPowerAnalyzer;

  14. /*
  15.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  16.  */

  18. /*!
  19.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  20.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  21.  * 
  22.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  23.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  24.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  25.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  26.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  27.  *      and computational support.
  28.  *  
  29.  *      https://lakshmidrip.github.io/DROP/
  30.  *  
  31.  *  DROP is composed of three modules:
  32.  *  
  33.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  34.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  35.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  36.  * 
  37.  *  DROP Product Core implements libraries for the following:
  38.  *  - Fixed Income Analytics
  39.  *  - Loan Analytics
  40.  *  - Transaction Cost Analytics
  41.  * 
  42.  *  DROP Portfolio Core implements libraries for the following:
  43.  *  - Asset Allocation Analytics
  44.  *  - Asset Liability Management Analytics
  45.  *  - Capital Estimation Analytics
  46.  *  - Exposure Analytics
  47.  *  - Margin Analytics
  48.  *  - XVA Analytics
  49.  * 
  50.  *  DROP Computational Core implements libraries for the following:
  51.  *  - Algorithm Support
  52.  *  - Computation Support
  53.  *  - Function Analysis
  54.  *  - Model Validation
  55.  *  - Numerical Analysis
  56.  *  - Numerical Optimizer
  57.  *  - Spline Builder
  58.  *  - Statistical Learning
  59.  * 
  60.  *  Documentation for DROP is Spread Over:
  61.  * 
  62.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  63.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  64.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  65.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  66.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  67.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  68.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  69.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  70.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  71.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  72.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  73.  * 
  74.  *  Licensed under the Apache License, Version 2.0 (the "License");
  75.  *      you may not use this file except in compliance with the License.
  76.  *   
  77.  *  You may obtain a copy of the License at
  78.  *      http://www.apache.org/licenses/LICENSE-2.0
  79.  *  
  80.  *  Unless required by applicable law or agreed to in writing, software
  81.  *      distributed under the License is distributed on an "AS IS" BASIS,
  82.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  83.  *  
  84.  *  See the License for the specific language governing permissions and
  85.  *      limitations under the License.
  86.  */

  88. /**
  89.  * <i>CVMDiscriminatoryPowerAnalysis3a</i> demonstrates the Discriminatory Power Analysis illustrated in
  90.  * Table 3a of Anfuso, Karyampas, and Nawroth (2013).
  91.  *
  92.  *  <br><br>
  93.  *  <ul>
  94.  *      <li>
  95.  *          Anfuso, F., D. Karyampas, and A. Nawroth (2017): A Sound Basel III Compliant Framework for
  96.  *              Back-testing Credit Exposure Models
  97.  *              https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2264620 <b>eSSRN</b>
  98.  *      </li>
  99.  *      <li>
  100.  *          Diebold, F. X., T. A. Gunther, and A. S. Tay (1998): Evaluating Density Forecasts with
  101.  *              Applications to Financial Risk Management, International Economic Review 39 (4) 863-883
  102.  *      </li>
  103.  *      <li>
  104.  *          Kenyon, C., and R. Stamm (2012): Discounting, LIBOR, CVA, and Funding: Interest Rate and Credit
  105.  *              Pricing, Palgrave Macmillan
  106.  *      </li>
  107.  *      <li>
  108.  *          Wikipedia (2018): Probability Integral Transform
  109.  *              https://en.wikipedia.org/wiki/Probability_integral_transform
  110.  *      </li>
  111.  *      <li>
  112.  *          Wikipedia (2019): p-value https://en.wikipedia.org/wiki/P-value
  113.  *      </li>
  114.  *  </ul>
  115.  *
  116.  *  <br><br>
  117.  *  <ul>
  118.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  119.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ModelValidationAnalyticsLibrary.md">Model Validation Analytics Library</a></li>
  120.  *      <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>
  121.  *      <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>
  122.  *  </ul>
  123.  * <br><br>
  124.  *
  125.  * @author Lakshmi Krishnamurthy
  126.  */

  128. public class CVMDiscriminatoryPowerAnalysis3a
  129. {

  131.     private static final double UnivariateRandom (
  132.         final double mean,
  133.         final double sigma)
  134.         throws Exception
  135.     {
  136.         return new R1UnivariateNormal (
  137.             mean,
  138.             sigma
  139.         ).random();
  140.     }

  142.     private static final Sample GenerateSample (
  143.         final double mean,
  144.         final double sigma,
  145.         final int drawCount)
  146.         throws Exception
  147.     {
  148.         double[] univariateRandomArray = new double[drawCount];

  150.         for (int drawIndex = 0; drawIndex < drawCount; ++drawIndex)
  151.         {
  152.             univariateRandomArray[drawIndex] = UnivariateRandom (
  153.                 mean,
  154.                 sigma
  155.             );
  156.         }

  158.         return new Sample (univariateRandomArray);
  159.     }

  161.     private static final Sample[] GenerateSampleArray (
  162.         final double mean,
  163.         final double sigma,
  164.         final int drawCount,
  165.         final int sampleCount)
  166.         throws Exception
  167.     {
  168.         Sample[] sampleArray = new Sample[sampleCount];

  170.         for (int sampleIndex = 0; sampleIndex < sampleCount; ++sampleIndex)
  171.         {
  172.             sampleArray[sampleIndex] = GenerateSample (
  173.                 mean,
  174.                 sigma,
  175.                 drawCount
  176.             );
  177.         }

  179.         return sampleArray;
  180.     }

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

  211.     private static final double DistanceTest (
  212.         final GapTestOutcome gapTestOutcome)
  213.         throws Exception
  214.     {
  215.         return gapTestOutcome.distance();
  216.     }

  218.     public static final void main (
  219.         final String[] argumentArray)
  220.         throws Exception
  221.     {
  222.         EnvManager.InitEnv ("");

  224.         int drawCount = 3780;
  225.         int sampleCount = 100;
  226.         double horizon = 1. / 12;
  227.         double sampleAnnualMean = 0.;
  228.         double sampleAnnualVolatility = 0.1;
  229.         double[] hypothesisAnnualMeanArray = {
  230.             -0.050,
  231.             -0.025,
  232.              0.000,
  233.              0.025,
  234.              0.050
  235.         };
  236.         double[] hypothesisAnnualVolatilityArray = {
  237.             0.050,
  238.             0.075,
  239.             0.100,
  240.             0.125,
  241.             0.150
  242.         };

  244.         double hypothesisHorizonSQRT = Math.sqrt (horizon);

  246.         Sample sample = GenerateSample (
  247.             sampleAnnualMean,
  248.             sampleAnnualVolatility * hypothesisHorizonSQRT,
  249.             drawCount
  250.         );

  252.         DiscriminatoryPowerAnalyzer discriminatoryPowerAnalysis = DiscriminatoryPowerAnalyzer.FromSample (
  253.             sample,
  254.             GapTestSetting.RiskFactorLossTest (
  255.                 GapLossWeightFunction.AndersonDarling()
  256.             )
  257.         );

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

  261.         System.out.println ("\t|     DISCRIMINANT GRID SCAN     ||");

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

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

  267.         System.out.println ("\t|        - Hypothesis Mean       ||");

  269.         System.out.println ("\t|        - Hypothesis Sigma      ||");

  271.         System.out.println ("\t|        - Distance Metric       ||");

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

  275.         for (double hypothesisAnnualMean : hypothesisAnnualMeanArray)
  276.         {
  277.             for (double hypothesisAnnualVolatility : hypothesisAnnualVolatilityArray)
  278.             {
  279.                 Ensemble hypothesis = GenerateEnsemble (
  280.                     hypothesisAnnualMean * horizon,
  281.                     hypothesisAnnualVolatility * hypothesisHorizonSQRT,
  282.                     drawCount,
  283.                     sampleCount
  284.                 );

  286.                 GapTestOutcome gapTestOutcome = discriminatoryPowerAnalysis.gapTest (hypothesis);

  288.                 System.out.println (
  289.                     "\t| " +
  290.                     FormatUtil.FormatDouble (hypothesisAnnualMean, 1, 3, 1.) + " | " +
  291.                     FormatUtil.FormatDouble (hypothesisAnnualVolatility, 1, 3, 1.) + " => " +
  292.                     FormatUtil.FormatDouble (DistanceTest (gapTestOutcome), 1, 8, 1.) + " ||"
  293.                 );
  294.             }
  295.         }

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

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