ADCorrelationBacktesting7c.java

  1. package org.drip.sample.anfuso2017;

  3. import java.util.ArrayList;
  4. import java.util.List;

  6. import org.drip.numerical.common.FormatUtil;
  7. import org.drip.service.env.EnvManager;
  8. import org.drip.state.identifier.EntityEquityLabel;
  9. import org.drip.state.identifier.FXLabel;
  10. import org.drip.validation.distance.GapLossWeightFunction;
  11. import org.drip.validation.distance.GapTestOutcome;
  12. import org.drip.validation.distance.GapTestSetting;
  13. import org.drip.validation.evidence.Ensemble;
  14. import org.drip.validation.evidence.Sample;
  15. import org.drip.validation.evidence.TestStatisticEvaluator;
  16. import org.drip.validation.hypothesis.HistogramTestOutcome;
  17. import org.drip.validation.hypothesis.HistogramTestSetting;
  18. import org.drip.validation.hypothesis.ProbabilityIntegralTransformTest;
  19. import org.drip.validation.quantile.PlottingPositionGenerator;
  20. import org.drip.validation.quantile.PlottingPositionGeneratorHeuristic;
  21. import org.drip.validation.riskfactorjoint.NormalSampleCohort;
  22. import org.drip.validation.riskfactorsingle.DiscriminatoryPowerAnalyzer;

  24. /*
  25.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  26.  */

  28. /*!
  29.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  30.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  31.  * 
  32.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  33.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  34.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  35.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  36.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  37.  *      and computational support.
  38.  *  
  39.  *      https://lakshmidrip.github.io/DROP/
  40.  *  
  41.  *  DROP is composed of three modules:
  42.  *  
  43.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  44.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  45.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  46.  * 
  47.  *  DROP Product Core implements libraries for the following:
  48.  *  - Fixed Income Analytics
  49.  *  - Loan Analytics
  50.  *  - Transaction Cost Analytics
  51.  * 
  52.  *  DROP Portfolio Core implements libraries for the following:
  53.  *  - Asset Allocation Analytics
  54.  *  - Asset Liability Management Analytics
  55.  *  - Capital Estimation Analytics
  56.  *  - Exposure Analytics
  57.  *  - Margin Analytics
  58.  *  - XVA Analytics
  59.  * 
  60.  *  DROP Computational Core implements libraries for the following:
  61.  *  - Algorithm Support
  62.  *  - Computation Support
  63.  *  - Function Analysis
  64.  *  - Model Validation
  65.  *  - Numerical Analysis
  66.  *  - Numerical Optimizer
  67.  *  - Spline Builder
  68.  *  - Statistical Learning
  69.  * 
  70.  *  Documentation for DROP is Spread Over:
  71.  * 
  72.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  73.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  74.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  75.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  76.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  77.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  78.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  79.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  80.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  81.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  82.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  83.  * 
  84.  *  Licensed under the Apache License, Version 2.0 (the "License");
  85.  *      you may not use this file except in compliance with the License.
  86.  *   
  87.  *  You may obtain a copy of the License at
  88.  *      http://www.apache.org/licenses/LICENSE-2.0
  89.  *  
  90.  *  Unless required by applicable law or agreed to in writing, software
  91.  *      distributed under the License is distributed on an "AS IS" BASIS,
  92.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  93.  *  
  94.  *  See the License for the specific language governing permissions and
  95.  *      limitations under the License.
  96.  */

  98. /**
  99.  * <i>ADCorrelationBacktesting7c</i> demonstrates the Horizon Multi-Factor Gap PIT Quantiles set out in Table
  100.  * 7c of Anfuso, Karyampas, and Nawroth (2017).
  101.  *
  102.  *  <br><br>
  103.  *  <ul>
  104.  *      <li>
  105.  *          Anfuso, F., D. Karyampas, and A. Nawroth (2017): A Sound Basel III Compliant Framework for
  106.  *              Back-testing Credit Exposure Models
  107.  *              https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2264620 <b>eSSRN</b>
  108.  *      </li>
  109.  *      <li>
  110.  *          Diebold, F. X., T. A. Gunther, and A. S. Tay (1998): Evaluating Density Forecasts with
  111.  *              Applications to Financial Risk Management, International Economic Review 39 (4) 863-883
  112.  *      </li>
  113.  *      <li>
  114.  *          Kenyon, C., and R. Stamm (2012): Discounting, LIBOR, CVA, and Funding: Interest Rate and Credit
  115.  *              Pricing, Palgrave Macmillan
  116.  *      </li>
  117.  *      <li>
  118.  *          Wikipedia (2018): Probability Integral Transform
  119.  *              https://en.wikipedia.org/wiki/Probability_integral_transform
  120.  *      </li>
  121.  *      <li>
  122.  *          Wikipedia (2019): p-value https://en.wikipedia.org/wiki/P-value
  123.  *      </li>
  124.  *  </ul>
  125.  *
  126.  *  <br><br>
  127.  *  <ul>
  128.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  129.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ModelValidationAnalyticsLibrary.md">Model Validation Analytics Library</a></li>
  130.  *      <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>
  131.  *      <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>
  132.  *  </ul>
  133.  * <br><br>
  134.  *
  135.  * @author Lakshmi Krishnamurthy
  136.  */

  138. public class ADCorrelationBacktesting7c
  139. {

  141.     private static final double[][] CorrelationMatrix (
  142.         final double correlation)
  143.     {
  144.         return new double[][]
  145.         {
  146.             {1.,          correlation},
  147.             {correlation, 1.         }
  148.         };
  149.     }

  151.     private static final void DistanceTest (
  152.         final GapTestOutcome gapTestOutcome,
  153.         final PlottingPositionGenerator plottingPositionGenerator)
  154.         throws Exception
  155.     {
  156.         HistogramTestOutcome histogram = new ProbabilityIntegralTransformTest (
  157.             gapTestOutcome.probabilityIntegralTransformWeighted()
  158.         ).histogramTest (
  159.             HistogramTestSetting.AnfusoKaryampasNawroth2017 (
  160.                 plottingPositionGenerator
  161.             )
  162.         );

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

  166.         double[] pValueCumulativeArray = histogram.pValueCumulativeArray();

  168.         double thresholdTestStatistic = histogram.thresholdTestStatistic();

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

  172.         double distance = gapTestOutcome.distance();

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

  176.         System.out.println ("\t|             Anderson Darling Correlation Distance Test             ||");

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

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

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

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

  186.         System.out.println ("\t|        - Incremental p-Value                                       ||");

  188.         System.out.println ("\t|        - Ensemble Weighted Distance                                ||");

  190.         System.out.println ("\t|        - p-Value Threshold Distance                                ||");

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

  194.         for (int histogramIndex = 0;
  195.             histogramIndex <= plottingPositionGenerator.orderStatisticCount() + 1;
  196.             ++histogramIndex)
  197.         {
  198.             System.out.println (
  199.                 "\t|" +
  200.                 FormatUtil.FormatDouble (gapArray[histogramIndex], 1, 8, 1.) + " | " +
  201.                 FormatUtil.FormatDouble (pValueCumulativeArray[histogramIndex], 1, 8, 1.) + " | " +
  202.                 FormatUtil.FormatDouble (pValueIncrementalArray[histogramIndex], 1, 8, 1.) + " | " +
  203.                 FormatUtil.FormatDouble (distance, 1, 8, 1.) + " | " +
  204.                 FormatUtil.FormatDouble (thresholdTestStatistic, 1, 8, 1.) + " ||"
  205.             );
  206.         }

  208.         System.out.println ("\t|--------------------------------------------------------------------||");
  209.     }

  211.     private static final Ensemble Hypothesis (
  212.         final List<String> labelList,
  213.         final double[] annualStateMeanArray,
  214.         final double[] annualStateVolatilityArray,
  215.         final double[][] correlationMatrix,
  216.         final int vertexCount,
  217.         final int sampleCount,
  218.         final double horizon,
  219.         final String label1,
  220.         final String label2)
  221.         throws Exception
  222.     {
  223.         Sample[] sampleArray = new Sample[sampleCount];

  225.         for (int sampleIndex = 0; sampleIndex < sampleCount; ++sampleIndex)
  226.         {
  227.             sampleArray[sampleIndex] = NormalSampleCohort.Correlated (
  228.                 labelList,
  229.                 annualStateMeanArray,
  230.                 annualStateVolatilityArray,
  231.                 correlationMatrix,
  232.                 vertexCount,
  233.                 horizon
  234.             ).reduce (
  235.                 label1,
  236.                 label2
  237.             );
  238.         }

  240.         return new Ensemble (
  241.             sampleArray,
  242.             new TestStatisticEvaluator[]
  243.             {
  244.                 new TestStatisticEvaluator()
  245.                 {
  246.                     public double evaluate (
  247.                         final double[] drawArray)
  248.                         throws Exception
  249.                     {
  250.                         return 1.;
  251.                     }
  252.                 }
  253.             }
  254.         );
  255.     }

  257.     public static final void main (
  258.         final String[] argumentArray)
  259.         throws Exception
  260.     {
  261.         EnvManager.InitEnv ("");

  263.         int sampleCount = 26;
  264.         int vertexCount = 390;
  265.         String currency = "USD";
  266.         double horizon = 12. / 12.;
  267.         double correlation = 0.50;
  268.         int orderStatisticsCount = 20;
  269.         String equityEntity = "SNP500";
  270.         String fxCurrencyPair = "CHF/USD";
  271.         double[] annualStateMeanArray =
  272.         {
  273.             0.06,
  274.             0.01
  275.         };
  276.         double[] annualStateVolatilityArray =
  277.         {
  278.             0.1,
  279.             0.1
  280.         };

  282.         List<String> labelList = new ArrayList<String>();

  284.         String snp500Label = EntityEquityLabel.Standard (
  285.             equityEntity,
  286.             currency
  287.         ).fullyQualifiedName();

  289.         String chfusdLabel = FXLabel.Standard (fxCurrencyPair).fullyQualifiedName();

  291.         labelList.add (snp500Label);

  293.         labelList.add (chfusdLabel);

  295.         Sample sample = NormalSampleCohort.Correlated (
  296.             labelList,
  297.             annualStateMeanArray,
  298.             annualStateVolatilityArray,
  299.             CorrelationMatrix (correlation),
  300.             vertexCount,
  301.             horizon
  302.         ).reduce (
  303.             snp500Label,
  304.             chfusdLabel
  305.         );

  307.         DiscriminatoryPowerAnalyzer discriminatoryPowerAnalysis = DiscriminatoryPowerAnalyzer.FromSample (
  308.             sample,
  309.             GapTestSetting.RiskFactorLossTest (
  310.                 GapLossWeightFunction.AndersonDarling()
  311.             )
  312.         );

  314.         Ensemble hypothesis = Hypothesis (
  315.             labelList,
  316.             annualStateMeanArray,
  317.             annualStateVolatilityArray,
  318.             CorrelationMatrix (correlation),
  319.             vertexCount,
  320.             sampleCount,
  321.             horizon,
  322.             snp500Label,
  323.             chfusdLabel
  324.         );

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

  328.         DistanceTest (
  329.             gapTestOutcome,
  330.             PlottingPositionGeneratorHeuristic.NIST2013 (orderStatisticsCount)
  331.         );

  333.         EnvManager.TerminateEnv();
  334.     }
  335. }
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