NormalSampleCohort.java

  1. package org.drip.validation.riskfactorjoint;

  3. /*
  4.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  5.  */

  7. /*!
  8.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  9.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  10.  * 
  11.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  12.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  13.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  14.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  15.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  16.  *      and computational support.
  17.  *  
  18.  *      https://lakshmidrip.github.io/DROP/
  19.  *  
  20.  *  DROP is composed of three modules:
  21.  *  
  22.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  23.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  24.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  25.  * 
  26.  *  DROP Product Core implements libraries for the following:
  27.  *  - Fixed Income Analytics
  28.  *  - Loan Analytics
  29.  *  - Transaction Cost Analytics
  30.  * 
  31.  *  DROP Portfolio Core implements libraries for the following:
  32.  *  - Asset Allocation Analytics
  33.  *  - Asset Liability Management Analytics
  34.  *  - Capital Estimation Analytics
  35.  *  - Exposure Analytics
  36.  *  - Margin Analytics
  37.  *  - XVA Analytics
  38.  * 
  39.  *  DROP Computational Core implements libraries for the following:
  40.  *  - Algorithm Support
  41.  *  - Computation Support
  42.  *  - Function Analysis
  43.  *  - Model Validation
  44.  *  - Numerical Analysis
  45.  *  - Numerical Optimizer
  46.  *  - Spline Builder
  47.  *  - Statistical Learning
  48.  * 
  49.  *  Documentation for DROP is Spread Over:
  50.  * 
  51.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  52.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  53.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  54.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  55.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  56.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  57.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  58.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  59.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  60.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  61.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  62.  * 
  63.  *  Licensed under the Apache License, Version 2.0 (the "License");
  64.  *      you may not use this file except in compliance with the License.
  65.  *   
  66.  *  You may obtain a copy of the License at
  67.  *      http://www.apache.org/licenses/LICENSE-2.0
  68.  *  
  69.  *  Unless required by applicable law or agreed to in writing, software
  70.  *      distributed under the License is distributed on an "AS IS" BASIS,
  71.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  72.  *  
  73.  *  See the License for the specific language governing permissions and
  74.  *      limitations under the License.
  75.  */

  77. /**
  78.  * <i>NormalSampleCohort</i> holds the Joint Realizations from a Multivariate Normal Distribution and its
  79.  * Reduction to a Synthetic Single Risk Factor.
  80.  *
  81.  *  <br><br>
  82.  *  <ul>
  83.  *      <li>
  84.  *          Anfuso, F., D. Karyampas, and A. Nawroth (2017): A Sound Basel III Compliant Framework for
  85.  *              Back-testing Credit Exposure Models
  86.  *              https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2264620 <b>eSSRN</b>
  87.  *      </li>
  88.  *      <li>
  89.  *          Diebold, F. X., T. A. Gunther, and A. S. Tay (1998): Evaluating Density Forecasts with
  90.  *              Applications to Financial Risk Management <i>International Economic Review</i> <b>39 (4)</b>
  91.  *              863-883
  92.  *      </li>
  93.  *      <li>
  94.  *          Kenyon, C., and R. Stamm (2012): <i>Discounting, LIBOR, CVA, and Funding: Interest Rate and
  95.  *              Credit Pricing</i> <b>Palgrave Macmillan</b>
  96.  *      </li>
  97.  *      <li>
  98.  *          Wikipedia (2018): Probability Integral Transform
  99.  *              https://en.wikipedia.org/wiki/Probability_integral_transform
  100.  *      </li>
  101.  *      <li>
  102.  *          Wikipedia (2019): p-value https://en.wikipedia.org/wiki/P-value
  103.  *      </li>
  104.  *  </ul>
  105.  *
  106.  *  <br><br>
  107.  *  <ul>
  108.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  109.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ModelValidationAnalyticsLibrary.md">Model Validation Analytics Library</a></li>
  110.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/validation/README.md">Risk Factor and Hypothesis Validation, Evidence Processing, and Model Testing</a></li>
  111.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/validation/riskfactorjoint/README.md">Joint Risk Factor Aggregate Tests</a></li>
  112.  *  </ul>
  113.  * <br><br>
  114.  *
  115.  * @author Lakshmi Krishnamurthy
  116.  */

  118. public class NormalSampleCohort implements org.drip.validation.riskfactorjoint.SampleCohort
  119. {
  120.     private double _horizon = java.lang.Double.NaN;
  121.     private org.drip.measure.stochastic.LabelRdVertex _labelRdVertex = null;
  122.     private org.drip.measure.stochastic.LabelCovariance _latentStateLabelCovariance = null;

  124.     /**
  125.      * Generate a Correlated NormalSampleCohort
  126.      * 
  127.      * @param labelList Label List
  128.      * @param annualMeanArray Array of Annual Means
  129.      * @param annualVolatilityArray Array of Annual Volatilities
  130.      * @param correlationMatrix Correlation Matrix
  131.      * @param vertexCount Vertex Count
  132.      * @param horizon Horizon
  133.      * 
  134.      * @return NormalSampleCohort Instance
  135.      */

  137.     public static final NormalSampleCohort Correlated (
  138.         final java.util.List<java.lang.String> labelList,
  139.         final double[] annualMeanArray,
  140.         final double[] annualVolatilityArray,
  141.         final double[][] correlationMatrix,
  142.         final int vertexCount,
  143.         final double horizon)
  144.     {
  145.         if (!org.drip.numerical.common.NumberUtil.IsValid (horizon))
  146.         {
  147.             return null;
  148.         }

  150.         org.drip.measure.discrete.CorrelatedPathVertexDimension correlatedPathVertexDimension = null;

  152.         try
  153.         {
  154.             correlatedPathVertexDimension = new org.drip.measure.discrete.CorrelatedPathVertexDimension (
  155.                 new org.drip.measure.crng.RandomNumberGenerator(),
  156.                 correlationMatrix,
  157.                 vertexCount,
  158.                 1,
  159.                 false,
  160.                 null
  161.             );
  162.         }
  163.         catch (java.lang.Exception e)
  164.         {
  165.             e.printStackTrace();

  167.             return null;
  168.         }

  170.         org.drip.measure.discrete.VertexRd[] vertexRdArray =
  171.             correlatedPathVertexDimension.straightMultiPathVertexRd();

  173.         if (null == vertexRdArray || null == vertexRdArray[0])
  174.         {
  175.             return null;
  176.         }

  178.         double[][] realization = vertexRdArray[0].flatform();

  180.         if (null == realization)
  181.         {
  182.             return null;
  183.         }

  185.         double horizonSQRT = Math.sqrt (horizon);

  187.         for (int vertexIndex = 0; vertexIndex < vertexCount; ++vertexIndex)
  188.         {
  189.             for (int entityIndex = 0; entityIndex < correlationMatrix.length; ++entityIndex)
  190.             {
  191.                 realization[vertexIndex][entityIndex] =
  192.                     realization[vertexIndex][entityIndex] * annualVolatilityArray[entityIndex] * horizonSQRT +
  193.                     annualMeanArray[entityIndex] * horizon;
  194.             }
  195.         }

  197.         try
  198.         {
  199.             return new NormalSampleCohort (
  200.                 new org.drip.measure.stochastic.LabelRdVertex (
  201.                     labelList,
  202.                     realization
  203.                 ),
  204.                 new org.drip.measure.stochastic.LabelCovariance (
  205.                     labelList,
  206.                     annualMeanArray,
  207.                     annualVolatilityArray,
  208.                     correlationMatrix
  209.                 ),
  210.                 horizon
  211.             );
  212.         }
  213.         catch (java.lang.Exception e)
  214.         {
  215.             e.printStackTrace();
  216.         }

  218.         return null;
  219.     }

  221.     /**
  222.      * NormalSampleCohort Constructor
  223.      * 
  224.      * @param labelRdVertex R<sup>d</sup> Labeled Vertex
  225.      * @param latentStateLabelCovariance R<sup>d</sup> Labeled Covariance
  226.      * @param horizon Horizon
  227.      * 
  228.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  229.      */

  231.     public NormalSampleCohort (
  232.         final org.drip.measure.stochastic.LabelRdVertex labelRdVertex,
  233.         final org.drip.measure.stochastic.LabelCovariance latentStateLabelCovariance,
  234.         final double horizon)
  235.         throws java.lang.Exception
  236.     {
  237.         if (null == (_labelRdVertex = labelRdVertex) ||
  238.             null == (_latentStateLabelCovariance = latentStateLabelCovariance) ||
  239.             !org.drip.numerical.common.NumberUtil.IsValid (_horizon = horizon) || _horizon <= 0.)
  240.         {
  241.             throw new java.lang.Exception ("NormalSampleCohort Constructor => Invalid Inputs");
  242.         }
  243.     }

  245.     /**
  246.      * Retrieve the Latent State Label Covariance
  247.      * 
  248.      * @return The Latent State Label Covariance
  249.      */

  251.     public org.drip.measure.stochastic.LabelCorrelation latentStateLabelCovariance()
  252.     {
  253.         return _latentStateLabelCovariance;
  254.     }

  256.     /**
  257.      * Retrieve the Sample Horizon
  258.      * 
  259.      * @return The Sample Horizon
  260.      */

  262.     public double horizon()
  263.     {
  264.         return _horizon;
  265.     }

  267.     @Override public java.util.List<java.lang.String> latentStateLabelList()
  268.     {
  269.         return _latentStateLabelCovariance.labelList();
  270.     }

  272.     @Override public org.drip.measure.stochastic.LabelRdVertex vertexRd()
  273.     {
  274.         return _labelRdVertex;
  275.     }

  277.     @Override public org.drip.validation.evidence.Sample reduce (
  278.         final java.lang.String label1,
  279.         final java.lang.String label2)
  280.     {
  281.         double annualMean1 = java.lang.Double.NaN;
  282.         double annualMean2 = java.lang.Double.NaN;
  283.         double correlation = java.lang.Double.NaN;
  284.         double annualPrecision1 = java.lang.Double.NaN;
  285.         double annualPrecision2 = java.lang.Double.NaN;
  286.         double annualVolatility1 = java.lang.Double.NaN;
  287.         double annualVolatility2 = java.lang.Double.NaN;

  289.         try
  290.         {
  291.             correlation = _latentStateLabelCovariance.entry (
  292.                 label1,
  293.                 label2
  294.             );

  296.             annualMean1 = _latentStateLabelCovariance.mean (label1);

  298.             annualMean2 = _latentStateLabelCovariance.mean (label2);

  300.             annualPrecision1 = (1. / (annualVolatility1 = _latentStateLabelCovariance.volatility (label1)));

  302.             annualPrecision2 = (1. / (annualVolatility2 = _latentStateLabelCovariance.volatility (label2)));
  303.         }
  304.         catch (java.lang.Exception e)
  305.         {
  306.             e.printStackTrace();

  308.             return null;
  309.         }

  311.         double[] vertexR1_1 = _labelRdVertex.vertexR1 (label1);

  313.         double[] vertexR1_2 = _labelRdVertex.vertexR1 (label2);

  315.         if (null == vertexR1_1 || null == vertexR1_2)
  316.         {
  317.             return null;
  318.         }

  320.         int cohortCount = vertexR1_1.length;
  321.         double[] cohortRealization = new double[cohortCount];
  322.         double cohortScale = java.lang.Math.exp (_horizon * (0.5 * (annualVolatility1 + annualVolatility2) -
  323.             (1. + correlation) - (annualMean1 * annualPrecision1 + annualMean2 * annualPrecision2)));

  325.         for (int cohortIndex = 0; cohortIndex < cohortCount; ++cohortIndex)
  326.         {
  327.             cohortRealization[cohortIndex] = cohortScale * java.lang.Math.pow (
  328.                 vertexR1_1[cohortIndex],
  329.                 annualPrecision1
  330.             ) * java.lang.Math.pow (
  331.                 vertexR1_2[cohortIndex],
  332.                 annualPrecision2
  333.             );
  334.         }

  336.         try
  337.         {
  338.             return new org.drip.validation.evidence.Sample (cohortRealization);
  339.         }
  340.         catch (java.lang.Exception e)
  341.         {
  342.             e.printStackTrace();
  343.         }

  345.         return null;
  346.     }
  347. }
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