ExpectedPositiveExposure12.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;

  7. /*
  8.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  9.  */

  11. /*!
  12.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  13.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  14.  * 
  15.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  16.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  17.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  18.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  19.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  20.  *      and computational support.
  21.  *  
  22.  *      https://lakshmidrip.github.io/DROP/
  23.  *  
  24.  *  DROP is composed of three modules:
  25.  *  
  26.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  27.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  28.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  29.  * 
  30.  *  DROP Product Core implements libraries for the following:
  31.  *  - Fixed Income Analytics
  32.  *  - Loan Analytics
  33.  *  - Transaction Cost Analytics
  34.  * 
  35.  *  DROP Portfolio Core implements libraries for the following:
  36.  *  - Asset Allocation Analytics
  37.  *  - Asset Liability Management Analytics
  38.  *  - Capital Estimation Analytics
  39.  *  - Exposure Analytics
  40.  *  - Margin Analytics
  41.  *  - XVA Analytics
  42.  * 
  43.  *  DROP Computational Core implements libraries for the following:
  44.  *  - Algorithm Support
  45.  *  - Computation Support
  46.  *  - Function Analysis
  47.  *  - Model Validation
  48.  *  - Numerical Analysis
  49.  *  - Numerical Optimizer
  50.  *  - Spline Builder
  51.  *  - Statistical Learning
  52.  * 
  53.  *  Documentation for DROP is Spread Over:
  54.  * 
  55.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  56.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  57.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  58.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  59.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  60.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  61.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  62.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  63.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  64.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  65.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  66.  * 
  67.  *  Licensed under the Apache License, Version 2.0 (the "License");
  68.  *      you may not use this file except in compliance with the License.
  69.  *   
  70.  *  You may obtain a copy of the License at
  71.  *      http://www.apache.org/licenses/LICENSE-2.0
  72.  *  
  73.  *  Unless required by applicable law or agreed to in writing, software
  74.  *      distributed under the License is distributed on an "AS IS" BASIS,
  75.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  76.  *  
  77.  *  See the License for the specific language governing permissions and
  78.  *      limitations under the License.
  79.  */

  81. /**
  82.  * <i>ExpectedPositiveExposure12</i> computes the Expected Positive Exposure as a Function of the MTM
  83.  * Volatility as laid out in Table 12 of Anfuso, Karyampas, and Nawroth (2017).
  84.  *
  85.  *  <br><br>
  86.  *  <ul>
  87.  *      <li>
  88.  *          Anfuso, F., D. Karyampas, and A. Nawroth (2017): A Sound Basel III Compliant Framework for
  89.  *              Back-testing Credit Exposure Models
  90.  *              https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2264620 <b>eSSRN</b>
  91.  *      </li>
  92.  *      <li>
  93.  *          Diebold, F. X., T. A. Gunther, and A. S. Tay (1998): Evaluating Density Forecasts with
  94.  *              Applications to Financial Risk Management, International Economic Review 39 (4) 863-883
  95.  *      </li>
  96.  *      <li>
  97.  *          Kenyon, C., and R. Stamm (2012): Discounting, LIBOR, CVA, and Funding: Interest Rate and Credit
  98.  *              Pricing, Palgrave Macmillan
  99.  *      </li>
  100.  *      <li>
  101.  *          Wikipedia (2018): Probability Integral Transform
  102.  *              https://en.wikipedia.org/wiki/Probability_integral_transform
  103.  *      </li>
  104.  *      <li>
  105.  *          Wikipedia (2019): p-value https://en.wikipedia.org/wiki/P-value
  106.  *      </li>
  107.  *  </ul>
  108.  *
  109.  *  <br><br>
  110.  *  <ul>
  111.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  112.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ModelValidationAnalyticsLibrary.md">Model Validation Analytics Library</a></li>
  113.  *      <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>
  114.  *      <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>
  115.  *  </ul>
  116.  * <br><br>
  117.  *
  118.  * @author Lakshmi Krishnamurthy
  119.  */

  121. public class ExpectedPositiveExposure12
  122. {

  124.     private static final double ExpectedPositiveRealization (
  125.         final double mean,
  126.         final double sigma,
  127.         final int drawCount)
  128.         throws Exception
  129.     {
  130.         double expectedPositiveRealization = 0.;

  132.         for (int drawIndex = 0; drawIndex < drawCount; ++drawIndex)
  133.         {
  134.             double realization = new R1UnivariateNormal (
  135.                 mean,
  136.                 sigma
  137.             ).random();

  139.             expectedPositiveRealization = expectedPositiveRealization +
  140.                 (realization > 0. ? realization : 0.);
  141.         }

  143.         return expectedPositiveRealization / drawCount;
  144.     }

  146.     private static final void ExpectedPositiveRealization (
  147.         final double mean,
  148.         final double[] sigmaArray,
  149.         final int drawCount)
  150.         throws Exception
  151.     {
  152.         for (double sigma : sigmaArray)
  153.         {
  154.             System.out.println (
  155.                 "\t| " +
  156.                 FormatUtil.FormatDouble (mean, 1, 1, 1.) + " | " +
  157.                 FormatUtil.FormatDouble (sigma, 1, 2, 1.) + " | " +
  158.                 FormatUtil.FormatDouble (
  159.                     ExpectedPositiveRealization (
  160.                         mean,
  161.                         sigma,
  162.                         drawCount
  163.                     ), 1, 4, 1.
  164.                 ) + " ||"
  165.             );
  166.         }

  168.         System.out.println ("\t|------------------------||");
  169.     }

  171.     public static final void main (
  172.         final String[] argumentArray)
  173.         throws Exception
  174.     {
  175.         EnvManager.InitEnv ("");

  177.         int drawCount = 100000;
  178.         double[] meanArray =
  179.         {
  180.             -5.0,
  181.              0.0,
  182.              5.0
  183.         };
  184.         double[] sigmaArray = {
  185.             1.0,
  186.             2.0,
  187.             3.0,
  188.             4.0,
  189.             5.0
  190.         };

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

  194.         System.out.println ("\t|  EPE for Model Params  ||");

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

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

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

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

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

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

  208.         for (double mean : meanArray)
  209.         {
  210.             ExpectedPositiveRealization (
  211.                 mean,
  212.                 sigmaArray,
  213.                 drawCount
  214.             );
  215.         }

  217.         EnvManager.TerminateEnv();
  218.     }
  219. }
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