CVMCorrelationBacktesting7e.java

package org.drip.sample.anfuso2017;

import java.util.ArrayList;
import java.util.List;

import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
import org.drip.state.identifier.EntityEquityLabel;
import org.drip.state.identifier.FXLabel;
import org.drip.validation.distance.GapLossWeightFunction;
import org.drip.validation.distance.GapTestOutcome;
import org.drip.validation.distance.GapTestSetting;
import org.drip.validation.evidence.Ensemble;
import org.drip.validation.evidence.Sample;
import org.drip.validation.evidence.TestStatisticEvaluator;
import org.drip.validation.hypothesis.HistogramTestOutcome;
import org.drip.validation.hypothesis.HistogramTestSetting;
import org.drip.validation.hypothesis.ProbabilityIntegralTransformTest;
import org.drip.validation.quantile.PlottingPositionGeneratorHeuristic;
import org.drip.validation.riskfactorjoint.NormalSampleCohort;
import org.drip.validation.riskfactorsingle.DiscriminatoryPowerAnalyzer;

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

/*!
 * Copyright (C) 2020 Lakshmi Krishnamurthy
 * Copyright (C) 2019 Lakshmi Krishnamurthy
 * 
 *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
 *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
 *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
 *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
 *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
 *      and computational support.
 *  
 *      https://lakshmidrip.github.io/DROP/
 *  
 *  DROP is composed of three modules:
 *  
 *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
 *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
 *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
 * 
 *  DROP Product Core implements libraries for the following:
 *  - Fixed Income Analytics
 *  - Loan Analytics
 *  - Transaction Cost Analytics
 * 
 *  DROP Portfolio Core implements libraries for the following:
 *  - Asset Allocation Analytics
 *  - Asset Liability Management Analytics
 *  - Capital Estimation Analytics
 *  - Exposure Analytics
 *  - Margin Analytics
 *  - XVA Analytics
 * 
 *  DROP Computational Core implements libraries for the following:
 *  - Algorithm Support
 *  - Computation Support
 *  - Function Analysis
 *  - Model Validation
 *  - Numerical Analysis
 *  - Numerical Optimizer
 *  - Spline Builder
 *  - Statistical Learning
 * 
 *  Documentation for DROP is Spread Over:
 * 
 *  - Main                     => https://lakshmidrip.github.io/DROP/
 *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
 *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
 *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
 *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
 *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
 *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
 *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
 *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
 *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
 *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
 * 
 *  Licensed under the Apache License, Version 2.0 (the "License");
 *      you may not use this file except in compliance with the License.
 *   
 *  You may obtain a copy of the License at
 *      http://www.apache.org/licenses/LICENSE-2.0
 *  
 *  Unless required by applicable law or agreed to in writing, software
 *      distributed under the License is distributed on an "AS IS" BASIS,
 *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  
 *  See the License for the specific language governing permissions and
 *      limitations under the License.
 */

/**
 * <i>CVMCorrelationBacktesting7e</i> demonstrates the Horizon Multi-Factor Gap PIT Quantiles set out in
 * Table 7e of Anfuso, Karyampas, and Nawroth (2017).
 *
 *  <br><br>
 *  <ul>
 *      <li>
 *          Anfuso, F., D. Karyampas, and A. Nawroth (2017): A Sound Basel III Compliant Framework for
 *              Back-testing Credit Exposure Models
 *              https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2264620 <b>eSSRN</b>
 *      </li>
 *      <li>
 *          Diebold, F. X., T. A. Gunther, and A. S. Tay (1998): Evaluating Density Forecasts with
 *              Applications to Financial Risk Management, International Economic Review 39 (4) 863-883
 *      </li>
 *      <li>
 *          Kenyon, C., and R. Stamm (2012): Discounting, LIBOR, CVA, and Funding: Interest Rate and Credit
 *              Pricing, Palgrave Macmillan
 *      </li>
 *      <li>
 *          Wikipedia (2018): Probability Integral Transform
 *              https://en.wikipedia.org/wiki/Probability_integral_transform
 *      </li>
 *      <li>
 *          Wikipedia (2019): p-value https://en.wikipedia.org/wiki/P-value
 *      </li>
 *  </ul>
 *
 *  <br><br>
 *  <ul>
 *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
 *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ModelValidationAnalyticsLibrary.md">Model Validation Analytics Library</a></li>
 *      <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>
 *      <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>
 *  </ul>
 * <br><br>
 *
 * @author Lakshmi Krishnamurthy
 */

public class CVMCorrelationBacktesting7e
{

    private static final double[][] CorrelationMatrix (
        final double correlation)
    {
        return new double[][]
        {
            {1.,          correlation},
            {correlation, 1.         }
        };
    }

    private static final void DistanceTest (
        final GapTestOutcome gapTestOutcome,
        final int orderStatisticsCount,
        final double pValueThreshold)
        throws Exception
    {
        HistogramTestOutcome histogram = new ProbabilityIntegralTransformTest (
            gapTestOutcome.probabilityIntegralTransformWeighted()
        ).histogramTest (
            HistogramTestSetting.AnfusoKaryampasNawroth2017 (
                PlottingPositionGeneratorHeuristic.NIST2013 (orderStatisticsCount)
            )
        );

        double[] pValueIncrementalArray = histogram.pValueIncrementalArray();

        double[] pValueCumulativeArray = histogram.pValueCumulativeArray();

        double thresholdTestStatistic = histogram.thresholdTestStatistic();

        double[] gapArray = histogram.testStatisticArray();

        double distance = gapTestOutcome.distance();

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

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

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

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

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

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

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

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

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

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

        for (int histogramIndex = 0; histogramIndex <= orderStatisticsCount + 1; ++histogramIndex)
        {
            System.out.println (
                "\t|" +
                FormatUtil.FormatDouble (gapArray[histogramIndex], 1, 8, 1.) + " | " +
                FormatUtil.FormatDouble (pValueCumulativeArray[histogramIndex], 1, 8, 1.) + " | " +
                FormatUtil.FormatDouble (pValueIncrementalArray[histogramIndex], 1, 8, 1.) + " | " +
                FormatUtil.FormatDouble (distance, 1, 8, 1.) + " | " +
                FormatUtil.FormatDouble (thresholdTestStatistic, 1, 8, 1.) + " ||"
            );
        }

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

    private static final Ensemble Hypothesis (
        final List<String> labelList,
        final double[] annualStateMeanArray,
        final double[] annualStateVolatilityArray,
        final double[][] correlationMatrix,
        final int vertexCount,
        final int sampleCount,
        final double horizon,
        final String label1,
        final String label2)
        throws Exception
    {
        Sample[] sampleArray = new Sample[sampleCount];

        for (int sampleIndex = 0; sampleIndex < sampleCount; ++sampleIndex)
        {
            sampleArray[sampleIndex] = NormalSampleCohort.Correlated (
                labelList,
                annualStateMeanArray,
                annualStateVolatilityArray,
                correlationMatrix,
                vertexCount,
                horizon
            ).reduce (
                label1,
                label2
            );
        }

        return new Ensemble (
            sampleArray,
            new TestStatisticEvaluator[]
            {
                new TestStatisticEvaluator()
                {
                    public double evaluate (
                        final double[] drawArray)
                        throws Exception
                    {
                        return 1.;
                    }
                }
            }
        );
    }

    public static final void main (
        final String[] argumentArray)
        throws Exception
    {
        EnvManager.InitEnv ("");

        int sampleCount = 26;
        int vertexCount = 390;
        int orderStatisticsCount = 20;
        String currency = "USD";
        double horizon = 3. / 12.;
        double correlation = 0.50;
        double pValueThreshold = 0.95;
        String equityEntity = "SNP500";
        String fxCurrencyPair = "CHF/USD";
        double[] annualStateMeanArray =
        {
            0.06,
            0.01
        };
        double[] annualStateVolatilityArray =
        {
            0.1,
            0.1
        };

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

        String snp500Label = EntityEquityLabel.Standard (
            equityEntity,
            currency
        ).fullyQualifiedName();

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

        labelList.add (snp500Label);

        labelList.add (chfusdLabel);

        Sample sample = NormalSampleCohort.Correlated (
            labelList,
            annualStateMeanArray,
            annualStateVolatilityArray,
            CorrelationMatrix (correlation),
            vertexCount,
            horizon
        ).reduce (
            snp500Label,
            chfusdLabel
        );

        DiscriminatoryPowerAnalyzer discriminatoryPowerAnalysis = DiscriminatoryPowerAnalyzer.FromSample (
            sample,
            GapTestSetting.RiskFactorLossTest (GapLossWeightFunction.CramersVonMises())
        );

        Ensemble hypothesis = Hypothesis (
            labelList,
            annualStateMeanArray,
            annualStateVolatilityArray,
            CorrelationMatrix (correlation),
            vertexCount,
            sampleCount,
            horizon,
            snp500Label,
            chfusdLabel
        );

        GapTestOutcome gapTestOutcome = discriminatoryPowerAnalysis.gapTest (hypothesis);

        DistanceTest (
            gapTestOutcome,
            orderStatisticsCount,
            pValueThreshold
        );

        EnvManager.TerminateEnv();
    }
}