ADDiscriminatoryPowerAggregation6b.java

package org.drip.sample.anfuso2017;

import java.util.Map;

import org.drip.analytics.support.CaseInsensitiveHashMap;
import org.drip.analytics.support.Helper;
import org.drip.measure.gaussian.R1UnivariateNormal;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
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.ProbabilityIntegralTransform;
import org.drip.validation.riskfactorsingle.DiscriminatoryPowerAnalyzerAggregate;
import org.drip.validation.riskfactorsingle.EventAggregationWeightFunction;
import org.drip.validation.riskfactorsingle.GapTestOutcomeAggregate;
import org.drip.validation.riskfactorsingle.HypothesisOutcomeAggregate;
import org.drip.validation.riskfactorsingle.HypothesisOutcomeSuiteAggregate;
import org.drip.validation.riskfactorsingle.HypothesisSuiteAggregate;

/*
 * -*- 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>ADDiscriminatoryPowerAggregation6a</i> demonstrates Multi-Horizon Discriminatory Power Aggregation
 * illustrated in Table 6b 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 ADDiscriminatoryPowerAggregation6b
{

    private static final double UnivariateRandom (
        final double mean,
        final double volatility)
        throws Exception
    {
        return new R1UnivariateNormal (
            mean,
            volatility
        ).random();
    }

    private static final Sample GenerateSample (
        final double annualMean,
        final double annualVolatility,
        final String horizonTenor,
        final int drawCount)
        throws Exception
    {
        double[] univariateRandomArray = new double[drawCount];

        double horizonYF = Helper.TenorToYearFraction (horizonTenor);

        double horizonYFSQRT = Math.sqrt (horizonYF);

        for (int drawIndex = 0; drawIndex < drawCount; ++drawIndex)
        {
            univariateRandomArray[drawIndex] = UnivariateRandom (
                annualMean * horizonYF,
                annualVolatility * horizonYFSQRT
            );
        }

        return new Sample (univariateRandomArray);
    }

    private static final Map<String, ProbabilityIntegralTransform> EventSamplePITMap (
        final double annualMean,
        final double annualVolatility,
        final String[] horizonTenorArray,
        final int drawCount)
        throws Exception
    {
        Map<String, ProbabilityIntegralTransform> eventSamplePITMap = new
            CaseInsensitiveHashMap<ProbabilityIntegralTransform>();

        for (int horizonIndex = 0; horizonIndex < horizonTenorArray.length; ++horizonIndex)
        {
            eventSamplePITMap.put (
                horizonTenorArray[horizonIndex],
                GenerateSample (
                    annualMean,
                    annualVolatility,
                    horizonTenorArray[horizonIndex],
                    drawCount
                ).nativeProbabilityIntegralTransform()
            );
        }

        return eventSamplePITMap;
    }

    private static final Sample[] GenerateSampleArray (
        final double annualMean,
        final double annualVolatility,
        final String horizonTenor,
        final int drawCount,
        final int sampleCount)
        throws Exception
    {
        Sample[] sampleArray = new Sample[sampleCount];

        for (int sampleIndex = 0; sampleIndex < sampleCount; ++sampleIndex)
        {
            sampleArray[sampleIndex] = GenerateSample (
                annualMean,
                annualVolatility,
                horizonTenor,
                drawCount
            );
        }

        return sampleArray;
    }

    private static final Ensemble GenerateEnsemble (
        final double hypothesisAnnualMean,
        final double hypothesisAnnualVolatility,
        final String horizonTenor,
        final int drawCount,
        final int sampleCount)
        throws Exception
    {
        return new Ensemble (
            GenerateSampleArray (
                hypothesisAnnualMean,
                hypothesisAnnualVolatility,
                horizonTenor,
                drawCount,
                sampleCount
            ),
            new TestStatisticEvaluator[]
            {
                new TestStatisticEvaluator()
                {
                    public double evaluate (
                        final double[] drawArray)
                        throws Exception
                    {
                        return 1.;
                    }
                }
            }
        );
    }

    private static final HypothesisSuiteAggregate HypothesisEventMap (
        final double[] hypothesisAnnualMeanArray,
        final double[] hypothesisAnnualVolatilityArray,
        final String[] horizonTenorArray,
        final int drawCount,
        final int sampleCount)
        throws Exception
    {
        HypothesisSuiteAggregate hypothesisSuiteAggregate = new HypothesisSuiteAggregate();

        for (double hypothesisAnnualMean : hypothesisAnnualMeanArray)
        {
            for (double hypothesisAnnualVolatility : hypothesisAnnualVolatilityArray)
            {
                String hypothesisID = "HYPOTHESIS_" +
                    FormatUtil.FormatDouble (hypothesisAnnualMean, 2, 4, 1.) + "_" +
                    FormatUtil.FormatDouble (hypothesisAnnualVolatility, 2, 4, 1.);

                for (String horizonTenor : horizonTenorArray)
                {
                    hypothesisSuiteAggregate.add (
                        hypothesisID,
                        horizonTenor,
                        GenerateEnsemble (
                            hypothesisAnnualMean,
                            hypothesisAnnualVolatility,
                            horizonTenor,
                            drawCount,
                            sampleCount
                        )
                    );
                }
            }
        }

        return hypothesisSuiteAggregate;
    }

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

        int drawCount = 390;
        int sampleCount = 1000;
        double sampleAnnualMean = 0.;
        double sampleAnnualVolatility = 0.1;
        String[] horizonTenorArray =
        {
            "3M",
            "6M",
            "1Y"
        };
        double[] hypothesisAnnualMeanArray = {
            -0.050,
            -0.025,
             0.000,
             0.025,
             0.050
        };
        double[] hypothesisAnnualVolatilityArray = {
            0.050,
            0.075,
            0.100,
            0.125,
            0.150
        };

        EventAggregationWeightFunction eventAggregationWeightFunction =
            EventAggregationWeightFunction.AnfusoKaryampasNawroth();

        Map<String, ProbabilityIntegralTransform> eventSamplePITMap = EventSamplePITMap (
            sampleAnnualMean,
            sampleAnnualVolatility,
            horizonTenorArray,
            drawCount
        );

        DiscriminatoryPowerAnalyzerAggregate discriminatoryPowerAnalyzerAggregate = new
            DiscriminatoryPowerAnalyzerAggregate (
                eventSamplePITMap,
                GapTestSetting.RiskFactorLossTest (
                    GapLossWeightFunction.AndersonDarling()
                ),
                eventAggregationWeightFunction
            );

        HypothesisSuiteAggregate hypothesisSuiteAggregate = HypothesisEventMap (
            hypothesisAnnualMeanArray,
            hypothesisAnnualVolatilityArray,
            horizonTenorArray,
            drawCount,
            sampleCount
        );

        HypothesisOutcomeSuiteAggregate hypothesisOutcomeSuiteAggregate =
            discriminatoryPowerAnalyzerAggregate.hypothesisGapTest (hypothesisSuiteAggregate);

        Map<String, GapTestOutcomeAggregate> hypothesisOutcomeAggregateMap =
            hypothesisOutcomeSuiteAggregate.hypothesisOutcomeAggregate();

        HypothesisOutcomeAggregate leadingHypothesis = hypothesisOutcomeSuiteAggregate.leadingHypothesis();

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

        System.out.println ("\t|                     Disciminatory Power Analysis Multi Horizon Distance Test                      ||");

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

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

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

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

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

        System.out.println ("\t|            - Horizon Gap Outcomes [ Horizon1 = Distance1 | ... ]                                  ||");

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

        for (Map.Entry<String, GapTestOutcomeAggregate> gapTestOutcomeAggregateEntry :
            hypothesisOutcomeAggregateMap.entrySet())
        {
            GapTestOutcomeAggregate gapTestOutcomeAggregate = gapTestOutcomeAggregateEntry.getValue();

            String gapTestOutcomeAggregateDisplay = "\t| " + gapTestOutcomeAggregateEntry.getKey() + " => " +
                FormatUtil.FormatDouble (gapTestOutcomeAggregate.distance(), 1, 6, 1.) + " | [";

            for (Map.Entry<String, GapTestOutcome> gapTestOutcomeEntry :
                gapTestOutcomeAggregate.eventOutcomeMap().entrySet())
            {
                gapTestOutcomeAggregateDisplay = gapTestOutcomeAggregateDisplay + " " +
                    gapTestOutcomeEntry.getKey() + " = " +
                    FormatUtil.FormatDouble (gapTestOutcomeEntry.getValue().distance(), 1, 6, 1.) + " |";
            }

            System.out.println (gapTestOutcomeAggregateDisplay + "] ||");
        }

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

        System.out.println();

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

        System.out.println ("\t|            Leading Hypothesis Disciminatory Power Analysis Multi Horizon Distance Test            ||");

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

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

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

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

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

        System.out.println ("\t|            - Horizon Gap Outcomes [ Horizon1 = Distance1 | ... ]                                  ||");

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

        GapTestOutcomeAggregate gapTestOutcomeAggregate = leadingHypothesis.gapTestOutcomeAggregate();

        String gapTestOutcomeAggregateDisplay = "\t| " + leadingHypothesis.hypothesisID() + " => " +
            FormatUtil.FormatDouble (gapTestOutcomeAggregate.distance(), 1, 6, 1.) + " | [";

        for (Map.Entry<String, GapTestOutcome> gapTestOutcomeEntry :
            gapTestOutcomeAggregate.eventOutcomeMap().entrySet())
        {
            gapTestOutcomeAggregateDisplay = gapTestOutcomeAggregateDisplay + " " +
                gapTestOutcomeEntry.getKey() + " = " +
                FormatUtil.FormatDouble (gapTestOutcomeEntry.getValue().distance(), 1, 6, 1.) + " |";
        }

        System.out.println (gapTestOutcomeAggregateDisplay + "] ||");

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

        EnvManager.TerminateEnv();
    }
}