PykhtinPillarDynamics.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>PykhtinPillarDynamics</i> generates the Dynamics off of the Pillar Vertex Exposure Realizations to be
  80.  * used in eventual Exposure Regression 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 PykhtinPillarDynamics
  119. {
  120.     private java.util.List<java.lang.Double> _exposureList = null;

  122.     /**
  123.      * Construct an Instance of PykhtinPillarDynamics from the Exposure Array
  124.      * 
  125.      * @param exposureArray The Exposure Array
  126.      * 
  127.      * @return The VertexRealization Instance
  128.      */

  130.     public static final PykhtinPillarDynamics Standard (
  131.         final double[] exposureArray)
  132.     {
  133.         if (null == exposureArray)
  134.         {
  135.             return null;
  136.         }

  138.         java.util.List<java.lang.Double> exposureList = new java.util.ArrayList<java.lang.Double>();

  140.         int exposureCount = exposureArray.length;

  142.         if (0 == exposureCount)
  143.         {
  144.             return null;
  145.         }

  147.         for (double exposure : exposureArray)
  148.         {
  149.             if (!org.drip.numerical.common.NumberUtil.IsValid (exposure))
  150.             {
  151.                 return null;
  152.             }

  154.             exposureList.add (exposure);
  155.         }

  157.         java.util.Collections.sort (exposureList);

  159.         try
  160.         {
  161.             return new PykhtinPillarDynamics (exposureList);
  162.         }
  163.         catch (java.lang.Exception e)
  164.         {
  165.             e.printStackTrace();
  166.         }

  168.         return null;
  169.     }

  171.     protected PykhtinPillarDynamics (
  172.         final java.util.List<java.lang.Double> exposureList)
  173.         throws java.lang.Exception
  174.     {
  175.         if (null == (_exposureList = exposureList) || 0 == _exposureList.size())
  176.         {
  177.             throw new java.lang.Exception ("PykhtinPillarVertexDynamics Constructor => Invalid Inputs");
  178.         }
  179.     }

  181.     /**
  182.      * Retrieve the Exposure Set
  183.      * 
  184.      * @return The Exposure Set
  185.      */

  187.     public java.util.List<java.lang.Double> exposureList()
  188.     {
  189.         return _exposureList;
  190.     }

  192.     /**
  193.      * Retrieve the Pykhtin Pillar Vertex Array
  194.      * 
  195.      * @param localVolatilityGenerationControl The Local Volatility Generation Control
  196.      * 
  197.      * @return The Pykhtin Pillar Vertex Array
  198.      */

  200.     public org.drip.exposure.regression.PykhtinPillar[] pillarVertexArray (
  201.         final org.drip.exposure.regression.LocalVolatilityGenerationControl localVolatilityGenerationControl)
  202.     {
  203.         if (null == localVolatilityGenerationControl)
  204.         {
  205.             return null;
  206.         }

  208.         int realizationCount = _exposureList.size();

  210.         double[] uniformCPDArray = localVolatilityGenerationControl.uniformCPDArray();

  212.         int localVolatilityIndexShift = localVolatilityGenerationControl.localVolatilityIndexShift();

  214.         double[] impliedBrownianVariateArray = localVolatilityGenerationControl.impliedBrownianVariateArray();

  216.         int realizationIndex = 0;
  217.         double[] exposureArray = new double[realizationCount];
  218.         int localVolatilityIndexFloor = localVolatilityIndexShift;
  219.         double[] localVolatilityArray = new double[realizationCount];
  220.         int localVolatilityIndexCeiling = realizationCount - localVolatilityIndexShift;
  221.         org.drip.exposure.regression.PykhtinPillar[] pillarVertexArray = new
  222.             org.drip.exposure.regression.PykhtinPillar[realizationCount];

  224.         for (double exposure : _exposureList)
  225.         {
  226.             exposureArray[realizationIndex++] = exposure;
  227.         }

  229.         for (int realizationCoordinate = localVolatilityIndexFloor;
  230.             realizationCoordinate < localVolatilityIndexCeiling;
  231.             ++realizationCoordinate)
  232.         {
  233.             localVolatilityArray[realizationCoordinate] =
  234.                 (exposureArray[realizationCoordinate - localVolatilityIndexShift] -
  235.                     exposureArray[realizationCoordinate + localVolatilityIndexShift]) /
  236.                 (impliedBrownianVariateArray[realizationCoordinate - localVolatilityIndexShift] -
  237.                     impliedBrownianVariateArray[realizationCoordinate + localVolatilityIndexShift]);
  238.         }

  240.         for (int realizationCoordinate = 0;
  241.             realizationCoordinate < localVolatilityIndexFloor;
  242.             ++realizationCoordinate)
  243.         {
  244.             localVolatilityArray[realizationCoordinate] = localVolatilityArray[localVolatilityIndexFloor];
  245.         }

  247.         for (int realizationCoordinate = localVolatilityIndexCeiling;
  248.             realizationCoordinate < realizationCount;
  249.             ++realizationCoordinate)
  250.         {
  251.             localVolatilityArray[realizationCoordinate] =
  252.                 localVolatilityArray[localVolatilityIndexCeiling - 1];
  253.         }

  255.         for (int realizationCoordinate = 0; realizationCoordinate < realizationCount;
  256.             ++realizationCoordinate)
  257.         {
  258.             try
  259.             {
  260.                 pillarVertexArray[realizationCoordinate] =
  261.                     new org.drip.exposure.regression.PykhtinPillar (
  262.                         exposureArray[realizationCoordinate],
  263.                         realizationCoordinate,
  264.                         uniformCPDArray[realizationCoordinate],
  265.                         impliedBrownianVariateArray[realizationCoordinate],
  266.                         localVolatilityArray[realizationCoordinate]
  267.                     );

  269.                 ++realizationIndex;
  270.             }
  271.             catch (java.lang.Exception e)
  272.             {
  273.                 e.printStackTrace();

  275.                 return null;
  276.             }
  277.         }

  279.         return pillarVertexArray;
  280.     }

  282.     /**
  283.      * Generate a Local Volatility R^1 To R^1
  284.      * 
  285.      * @param localVolatilityGenerationControl The Local Volatility Generation Control
  286.      * @param pillarVertexArray The Array of Pykhtin Pillar Vertexes
  287.      * 
  288.      * @return The Local Volatility R^1 To R^1
  289.      */

  291.     public org.drip.function.definition.R1ToR1 localVolatilityR1ToR1 (
  292.         final org.drip.exposure.regression.LocalVolatilityGenerationControl localVolatilityGenerationControl,
  293.         final org.drip.exposure.regression.PykhtinPillar[] pillarVertexArray)
  294.     {
  295.         if (null == localVolatilityGenerationControl)
  296.         {
  297.             return null;
  298.         }

  300.         int vertexCount = pillarVertexArray.length;
  301.         double[] exposureArray = new double[vertexCount];
  302.         double[] localVolatilityArray = new double[vertexCount];

  304.         for (int vertexIndex = 0; vertexIndex < vertexCount; ++vertexIndex)
  305.         {
  306.             exposureArray[vertexIndex] = pillarVertexArray[vertexIndex].exposure();

  308.             localVolatilityArray[vertexIndex] = pillarVertexArray[vertexIndex].localVolatility();
  309.         }

  311.         org.drip.spline.stretch.MultiSegmentSequence multiSegmentSequence =
  312.             org.drip.spline.stretch.MultiSegmentSequenceBuilder.CreateCalibratedStretchEstimator (
  313.                 "LocalVolatilityR1ToR1_" + org.drip.numerical.common.StringUtil.GUID(),
  314.                 exposureArray,
  315.                 localVolatilityArray,
  316.                 localVolatilityGenerationControl.segmentCustomBuilderControlArray(),
  317.                 null,
  318.                 org.drip.spline.stretch.BoundarySettings.NaturalStandard(),
  319.                 org.drip.spline.stretch.MultiSegmentSequence.CALIBRATE
  320.             );

  322.         return null == multiSegmentSequence ? null : multiSegmentSequence.toAU();
  323.     }

  325.     /**
  326.      * Generate a Local Volatility R^1 To R^1
  327.      * 
  328.      * @param localVolatilityGenerationControl The Local Volatility Generation Control
  329.      * 
  330.      * @return The Local Volatility R^1 To R^1
  331.      */

  333.     public org.drip.function.definition.R1ToR1 localVolatilityR1ToR1 (
  334.         final org.drip.exposure.regression.LocalVolatilityGenerationControl localVolatilityGenerationControl)
  335.     {
  336.         return localVolatilityR1ToR1 (
  337.             localVolatilityGenerationControl,
  338.             pillarVertexArray (localVolatilityGenerationControl)
  339.         );
  340.     }
  341. }
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