PykhtinBrownianBridgeSegment.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>PykhtinBrownianBridgeSegment</i> generates the Segment Regression Based Exposures off of the
  80.  * corresponding Pillar Vertexes using the Pykhtin (2009) Scheme. The References are:
  81.  *  
  82.  * <br><br>
  83.  *      <ul>
  84.  *          <li>
  85.  *              Andersen, L. B. G., M. Pykhtin, and A. Sokol (2017): Re-thinking Margin Period of Risk
  86.  *                  https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2902737 <b>eSSRN</b>
  87.  *          </li>
  88.  *          <li>
  89.  *              Andersen, L. B. G., M. Pykhtin, and A. Sokol (2017): Credit Exposure in the Presence of
  90.  *                  Initial Margin https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2806156 <b>eSSRN</b>
  91.  *          </li>
  92.  *          <li>
  93.  *              Albanese, C., and L. Andersen (2014): Accounting for OTC Derivatives: Funding Adjustments and
  94.  *                  the Re-Hypothecation Option https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2482955
  95.  *                  <b>eSSRN</b>
  96.  *          </li>
  97.  *          <li>
  98.  *              Burgard, C., and M. Kjaer (2017): Derivatives Funding, Netting, and Accounting
  99.  *                  https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2534011 <b>eSSRN</b>
  100.  *          </li>
  101.  *          <li>
  102.  *              Piterbarg, V. (2010): Funding Beyond Discounting: Collateral Agreements and Derivatives
  103.  *                  Pricing <i>Risk</i> <b>21 (2)</b> 97-102
  104.  *          </li>
  105.  *      </ul>
  106.  *
  107.  *  <br><br>
  108.  *  <ul>
  109.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/PortfolioCore.md">Portfolio Core Module</a></li>
  110.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ExposureAnalyticsLibrary.md">Exposure Analytics</a></li>
  111.  *      <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>
  112.  *      <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>
  113.  *  </ul>
  114.  * 
  115.  * @author Lakshmi Krishnamurthy
  116.  */

  118. public class PykhtinBrownianBridgeSegment
  119. {
  120.     private org.drip.exposure.regression.PillarVertex _leftPillar = null;
  121.     private org.drip.exposure.regression.PillarVertex _rightPillar = null;
  122.     private org.drip.function.definition.R1ToR1 _rightPillarLocalVolatility = null;

  124.     /**
  125.      * PykhtinBrownianBridgeSegment Constructor
  126.      * 
  127.      * @param leftPillar The Left Pillar Vertex
  128.      * @param rightPillar The Right Pillar Vertex
  129.      * @param rightPillarLocalVolatility The Right Pillar Local Volatility
  130.      * 
  131.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  132.      */

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

  149.     /**
  150.      * Retrieve the Left Pillar Vertex
  151.      * 
  152.      * @return The Left Pillar Vertex
  153.      */

  155.     public org.drip.exposure.regression.PillarVertex leftPillar()
  156.     {
  157.         return _leftPillar;
  158.     }

  160.     /**
  161.      * Retrieve the Right Pillar Vertex
  162.      * 
  163.      * @return The Right Pillar Vertex
  164.      */

  166.     public org.drip.exposure.regression.PillarVertex rightPillar()
  167.     {
  168.         return _rightPillar;
  169.     }

  171.     /**
  172.      * Retrieve the Right Pillar Local Volatility
  173.      * 
  174.      * @return The Right Pillar Local Volatility
  175.      */

  177.     public org.drip.function.definition.R1ToR1 rightPillarLocalVolatility()
  178.     {
  179.         return _rightPillarLocalVolatility;
  180.     }

  182.     /**
  183.      * Generate the Dense (Complete) Segment Exposures
  184.      * 
  185.      * @param denseExposureTrajectory The Dense Exposure Trajectory
  186.      * @param wanderTrajectory The Wander Date Trajectory
  187.      * 
  188.      * @return The Dense (Complete) Segment Exposures
  189.      */

  191.     public boolean denseExposureTrajectoryUpdate (
  192.         final java.util.Map<java.lang.Integer, java.lang.Double> denseExposureTrajectory,
  193.         final java.util.Map<java.lang.Integer, java.lang.Double> wanderTrajectory)
  194.     {
  195.         if (null == denseExposureTrajectory || null == wanderTrajectory)
  196.         {
  197.             return false;
  198.         }

  200.         int leftPillarDate = _leftPillar.date();

  202.         int rightPillarDate = _rightPillar.date();

  204.         double leftPillarExposure = _leftPillar.exposure();

  206.         double rightPillarExposure = _rightPillar.exposure();

  208.         int dateWidth = rightPillarDate - leftPillarDate;
  209.         double urgency = 1. / dateWidth;
  210.         double localVolatility = java.lang.Double.NaN;
  211.         double localDrift = (rightPillarExposure - leftPillarExposure) * urgency;

  213.         denseExposureTrajectory.put (
  214.             leftPillarDate,
  215.             leftPillarExposure
  216.         );

  218.         denseExposureTrajectory.put (
  219.             rightPillarDate,
  220.             rightPillarExposure
  221.         );

  223.         try
  224.         {
  225.             localVolatility = _rightPillarLocalVolatility.evaluate (rightPillarExposure);
  226.         }
  227.         catch (java.lang.Exception e)
  228.         {
  229.             e.printStackTrace();

  231.             return false;
  232.         }

  234.         for (int dateIndex = dateWidth - 1; dateIndex > 0; --dateIndex)
  235.         {
  236.             int date = leftPillarDate + dateIndex;

  238.             if (!wanderTrajectory.containsKey (date))
  239.             {
  240.                 return false;
  241.             }

  243.             denseExposureTrajectory.put (
  244.                 date,
  245.                 rightPillarExposure - localDrift * (dateWidth - dateIndex) + localVolatility * urgency *
  246.                     wanderTrajectory.get (date) * java.lang.Math.sqrt (dateIndex * (dateWidth - dateIndex))
  247.             );
  248.         }

  250.         return true;
  251.     }
  252. }
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