AndersenPykhtinSokolSegment.java

  1. package org.drip.exposure.regression;

  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>AndersenPykhtinSokolSegment</i> generates the Segment Regression Based Exposures off of the
  80.  * corresponding Pillar Vertexes using the Pykhtin (2009) Scheme with the Andersen, Pykhtin, and Sokol (2017)
  81.  * Adjustments applied. The References are:
  82.  *  
  83.  * <br><br>
  84.  *      <ul>
  85.  *          <li>
  86.  *              Andersen, L. B. G., M. Pykhtin, and A. Sokol (2017): Re-thinking Margin Period of Risk
  87.  *                  https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2902737 <b>eSSRN</b>
  88.  *          </li>
  89.  *          <li>
  90.  *              Andersen, L. B. G., M. Pykhtin, and A. Sokol (2017): Credit Exposure in the Presence of
  91.  *                  Initial Margin https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2806156 <b>eSSRN</b>
  92.  *          </li>
  93.  *          <li>
  94.  *              Albanese, C., and L. Andersen (2014): Accounting for OTC Derivatives: Funding Adjustments and
  95.  *                  the Re-Hypothecation Option https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2482955
  96.  *                  <b>eSSRN</b>
  97.  *          </li>
  98.  *          <li>
  99.  *              Burgard, C., and M. Kjaer (2017): Derivatives Funding, Netting, and Accounting
  100.  *                  https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2534011 <b>eSSRN</b>
  101.  *          </li>
  102.  *          <li>
  103.  *              Piterbarg, V. (2010): Funding Beyond Discounting: Collateral Agreements and Derivatives
  104.  *                  Pricing <i>Risk</i> <b>21 (2)</b> 97-102
  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/ExposureAnalyticsLibrary.md">Exposure Analytics</a></li>
  112.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/exposure/README.md">Exposure Group Level Collateralized/Uncollateralized Exposure</a></li>
  113.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/exposure/regression/README.md">Regression Based Path Exposure Generation</a></li>
  114.  *  </ul>
  115.  *  
  116.  * @author Lakshmi Krishnamurthy
  117.  */

  119. public class AndersenPykhtinSokolSegment
  120. {
  121.     private int _epochDate = -1;
  122.     private org.drip.exposure.regression.PillarVertex _leftPillar = null;
  123.     private org.drip.exposure.regression.PillarVertex _rightPillar = null;
  124.     private org.drip.function.definition.R1ToR1 _rightPillarLocalVolatility = null;

  126.     /**
  127.      * AndersenPykhtinSokolSegment Constructor
  128.      * 
  129.      * @param epochDate The Path Epoch Date
  130.      * @param leftPillar The Left Pillar Vertex
  131.      * @param rightPillar The Right Pillar Vertex
  132.      * @param rightPillarLocalVolatility The Right Pillar Local Volatility
  133.      * 
  134.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  135.      */

  137.     public AndersenPykhtinSokolSegment (
  138.         final int epochDate,
  139.         final org.drip.exposure.regression.PillarVertex leftPillar,
  140.         final org.drip.exposure.regression.PillarVertex rightPillar,
  141.         final org.drip.function.definition.R1ToR1 rightPillarLocalVolatility)
  142.         throws java.lang.Exception
  143.     {
  144.         if (null == (_leftPillar = leftPillar) ||
  145.             null == (_rightPillar = rightPillar) ||
  146.             _leftPillar.date() >= _rightPillar.date() ||
  147.             null == (_rightPillarLocalVolatility = rightPillarLocalVolatility))
  148.         {
  149.             throw new java.lang.Exception ("AndersenPykhtinSokolSegment Constructor => Invalid Inputs");
  150.         }

  152.         _epochDate = epochDate;
  153.     }

  155.     /**
  156.      * Retrieve the Epoch Date
  157.      * 
  158.      * @return The Epoch Date
  159.      */

  161.     public int epochDate()
  162.     {
  163.         return _epochDate;
  164.     }

  166.     /**
  167.      * Retrieve the Left Pillar Vertex
  168.      * 
  169.      * @return The Left Pillar Vertex
  170.      */

  172.     public org.drip.exposure.regression.PillarVertex leftPillar()
  173.     {
  174.         return _leftPillar;
  175.     }

  177.     /**
  178.      * Retrieve the Right Pillar Vertex
  179.      * 
  180.      * @return The Right Pillar Vertex
  181.      */

  183.     public org.drip.exposure.regression.PillarVertex rightPillar()
  184.     {
  185.         return _rightPillar;
  186.     }

  188.     /**
  189.      * Retrieve the Right Pillar Local Volatility
  190.      * 
  191.      * @return The Right Pillar Local Volatility
  192.      */

  194.     public org.drip.function.definition.R1ToR1 rightPillarLocalVolatility()
  195.     {
  196.         return _rightPillarLocalVolatility;
  197.     }

  199.     /**
  200.      * Generate the Dense (Complete) Segment Exposures
  201.      * 
  202.      * @param denseExposureTrajectory The Dense Exposure Trajectory
  203.      * @param wanderTrajectory The Wander Date Trajectory
  204.      * 
  205.      * @return The Dense (Complete) Segment Exposures
  206.      */

  208.     public boolean denseExposureTrajectoryUpdate (
  209.         final double[] denseExposureTrajectory,
  210.         final double[] wanderTrajectory)
  211.     {
  212.         if (null == denseExposureTrajectory || null == wanderTrajectory)
  213.         {
  214.             return false;
  215.         }

  217.         int leftPillarDate = _leftPillar.date();

  219.         int rightPillarDate = _rightPillar.date();

  221.         double leftPillarExposure = _leftPillar.exposure();

  223.         double rightPillarExposure = _rightPillar.exposure();

  225.         int dateWidth = rightPillarDate - leftPillarDate;
  226.         double urgency = 1. / dateWidth;
  227.         double localVolatility = java.lang.Double.NaN;
  228.         double localDrift = (rightPillarExposure - leftPillarExposure) * urgency;
  229.         denseExposureTrajectory[leftPillarDate - _epochDate] = leftPillarExposure;
  230.         denseExposureTrajectory[rightPillarDate - _epochDate] = rightPillarExposure;

  232.         try
  233.         {
  234.             localVolatility = _rightPillarLocalVolatility.evaluate (rightPillarExposure);
  235.         }
  236.         catch (java.lang.Exception e)
  237.         {
  238.             e.printStackTrace();

  240.             return false;
  241.         }

  243.         for (int dateIndex = dateWidth - 1; dateIndex > 0; --dateIndex)
  244.         {
  245.             int epochIndex = leftPillarDate + dateIndex - _epochDate;

  247.             denseExposureTrajectory[epochIndex] = rightPillarExposure - localDrift * (dateWidth - dateIndex)
  248.                 + localVolatility * urgency * wanderTrajectory[epochIndex] * java.lang.Math.sqrt (dateIndex *
  249.                     (dateWidth - dateIndex));
  250.         }

  252.         return true;
  253.     }
  254. }
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