CurvatureResponseCornishFischer.java

  1. package org.drip.simm.foundation;

  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.  * Copyright (C) 2018 Lakshmi Krishnamurthy
  11.  * 
  12.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  13.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  14.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  15.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  16.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  17.  *      and computational support.
  18.  *  
  19.  *      https://lakshmidrip.github.io/DROP/
  20.  *  
  21.  *  DROP is composed of three modules:
  22.  *  
  23.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  24.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  25.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  26.  * 
  27.  *  DROP Product Core implements libraries for the following:
  28.  *  - Fixed Income Analytics
  29.  *  - Loan Analytics
  30.  *  - Transaction Cost Analytics
  31.  * 
  32.  *  DROP Portfolio Core implements libraries for the following:
  33.  *  - Asset Allocation Analytics
  34.  *  - Asset Liability Management Analytics
  35.  *  - Capital Estimation Analytics
  36.  *  - Exposure Analytics
  37.  *  - Margin Analytics
  38.  *  - XVA Analytics
  39.  * 
  40.  *  DROP Computational Core implements libraries for the following:
  41.  *  - Algorithm Support
  42.  *  - Computation Support
  43.  *  - Function Analysis
  44.  *  - Model Validation
  45.  *  - Numerical Analysis
  46.  *  - Numerical Optimizer
  47.  *  - Spline Builder
  48.  *  - Statistical Learning
  49.  * 
  50.  *  Documentation for DROP is Spread Over:
  51.  * 
  52.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  53.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  54.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  55.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  56.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  57.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  58.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  59.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  60.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  61.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  62.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  63.  * 
  64.  *  Licensed under the Apache License, Version 2.0 (the "License");
  65.  *      you may not use this file except in compliance with the License.
  66.  *   
  67.  *  You may obtain a copy of the License at
  68.  *      http://www.apache.org/licenses/LICENSE-2.0
  69.  *  
  70.  *  Unless required by applicable law or agreed to in writing, software
  71.  *      distributed under the License is distributed on an "AS IS" BASIS,
  72.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  73.  *  
  74.  *  See the License for the specific language governing permissions and
  75.  *      limitations under the License.
  76.  */

  78. /**
  79.  * <i>CurvatureResponseCornishFischer</i> computes the Curvature Co-variance Scaling Factor using the
  80.  * Cumulative Curvature Sensitivities. The References are:
  81.  * 
  82.  * <br><br>
  83.  *  <ul>
  84.  *      <li>
  85.  *          Andersen, L. B. G., M. Pykhtin, and A. Sokol (2017): Credit Exposure in the Presence of Initial
  86.  *              Margin https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2806156 <b>eSSRN</b>
  87.  *      </li>
  88.  *      <li>
  89.  *          Albanese, C., S. Caenazzo, and O. Frankel (2017): Regression Sensitivities for Initial Margin
  90.  *              Calculations https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2763488 <b>eSSRN</b>
  91.  *      </li>
  92.  *      <li>
  93.  *          Anfuso, F., D. Aziz, P. Giltinan, and K. Loukopoulus (2017): A Sound Modeling and Back-testing
  94.  *              Framework for Forecasting Initial Margin Requirements
  95.  *                  https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2716279 <b>eSSRN</b>
  96.  *      </li>
  97.  *      <li>
  98.  *          Caspers, P., P. Giltinan, R. Lichters, and N. Nowaczyk (2017): Forecasting Initial Margin
  99.  *              Requirements - A Model Evaluation https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2911167
  100.  *                  <b>eSSRN</b>
  101.  *      </li>
  102.  *      <li>
  103.  *          International Swaps and Derivatives Association (2017): SIMM v2.0 Methodology
  104.  *              https://www.isda.org/a/oFiDE/isda-simm-v2.pdf
  105.  *      </li>
  106.  *  </ul>
  107.  * 
  108.  * <br><br>
  109.  *  <ul>
  110.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/PortfolioCore.md">Portfolio Core Module</a></li>
  111.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/MarginAnalyticsLibrary.md">Initial and Variation Margin Analytics</a></li>
  112.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/simm/README.md">Initial Margin Analytics based on ISDA SIMM and its Variants</a></li>
  113.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/simm/foundation/README.md">Foundation Utilities for ISDA SIMM</a></li>
  114.  *  </ul>
  115.  * <br><br>
  116.  * 
  117.  * @author Lakshmi Krishnamurthy
  118.  */

  120. public class CurvatureResponseCornishFischer implements org.drip.simm.foundation.CurvatureResponse
  121. {

  123.     /**
  124.      * ISDA SIMM VaR Curvature Cut-off
  125.      */

  127.     public static final double CURVATURE_VAR_CUT_OFF = 0.995;

  129.     private double _varCutoff = java.lang.Double.NaN;
  130.     private double _lambdaPlateauPeak = java.lang.Double.NaN;

  132.     /**
  133.      * Construct the Standard Instance of CurvatureResponseCornishFischer
  134.      * 
  135.      * @return The Standard Instance of CurvatureResponseCornishFischer
  136.      */

  138.     public static final CurvatureResponseCornishFischer Standard()
  139.     {
  140.         try
  141.         {
  142.             return new CurvatureResponseCornishFischer (CURVATURE_VAR_CUT_OFF);
  143.         }
  144.         catch (java.lang.Exception e)
  145.         {
  146.             e.printStackTrace();
  147.         }

  149.         return null;
  150.     }

  152.     /**
  153.      * CurvatureResponseCornishFischer Constructor
  154.      * 
  155.      * @param varCutoff VaR Cut-off
  156.      * 
  157.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  158.      */

  160.     public CurvatureResponseCornishFischer (
  161.         final double varCutoff)
  162.         throws java.lang.Exception
  163.     {
  164.         if (!org.drip.numerical.common.NumberUtil.IsValid (_varCutoff = varCutoff) ||
  165.                 0. > _varCutoff || 1. < _varCutoff)
  166.         {
  167.             throw new java.lang.Exception ("CurvatureResponseCornishFischer Constructor => Invalid Inputs");
  168.         }

  170.         double tailVariate = org.drip.measure.gaussian.NormalQuadrature.InverseCDF (_varCutoff);

  172.         _lambdaPlateauPeak = tailVariate * tailVariate - 1.;
  173.     }

  175.     /**
  176.      * Retrieve the VaR Cut-off
  177.      * 
  178.      * @return The VaR Cut-off
  179.      */

  181.     public double varCutoff()
  182.     {
  183.         return _varCutoff;
  184.     }

  186.     /**
  187.      * Retrieve the Lambda Plateau Peak
  188.      * 
  189.      * @return The Lambda Plateau Peak
  190.      */

  192.     public double lambdaPlateauPeak()
  193.     {
  194.         return _lambdaPlateauPeak;
  195.     }

  197.     /**
  198.      * Compute the Lambda from the Curvature Sensitivities
  199.      * 
  200.      * @param cumulativeRiskFactorSensitivity Cumulative Risk Factor Sensitivity
  201.      * @param cumulativeRiskFactorSensitivityPositive Cumulative Risk Factor Sensitivity Positive
  202.      * 
  203.      * @return The Lambda
  204.      * 
  205.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  206.      */

  208.     @Override public double lambda (
  209.         final double cumulativeRiskFactorSensitivity,
  210.         final double cumulativeRiskFactorSensitivityPositive)
  211.         throws java.lang.Exception
  212.     {
  213.         if (!org.drip.numerical.common.NumberUtil.IsValid (cumulativeRiskFactorSensitivity) ||
  214.             !org.drip.numerical.common.NumberUtil.IsValid (cumulativeRiskFactorSensitivityPositive) ||
  215.                 0. > cumulativeRiskFactorSensitivityPositive)
  216.         {
  217.             throw new java.lang.Exception ("CurvatureResponseCornishFischer::lambda => Invalid Inputs");
  218.         }

  220.         double theta = java.lang.Math.min (
  221.             0. == cumulativeRiskFactorSensitivityPositive ? 0. :
  222.                 cumulativeRiskFactorSensitivity / cumulativeRiskFactorSensitivityPositive,
  223.             0.
  224.         );

  226.         return _lambdaPlateauPeak * (1. + theta) - theta;
  227.     }
  228. }
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