LocalVolatilityGenerationControl.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>LocalVolatilityGenerationControl</i> holds the Parameters the control the Calculation of the Local
  80.  * Volatility in the Pykhtin (2009) Brownian Bridge Calibration. 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 LocalVolatilityGenerationControl
  119. {

  121.     /**
  122.      * The Pyhktin (2009) Empirical Floor
  123.      */

  125.     public static final int PYKHTIN_2009_EMPIRICAL_FLOOR = 20;

  127.     /**
  128.      * The Pyhktin (2009) Empirical Ceiling Factor
  129.      */

  131.     public static final double PYKHTIN_2009_EMPIRICAL_CEILING_FACTOR = 0.05;

  133.     /**
  134.      * The Local Volatility Smooth Floor Bias
  135.      */

  137.     public static final double LOCAL_VOLATILITY_SMOOTHING_FLOOR_BIAS = 0.90;

  139.     private double[] _uniformCPDArray = null;
  140.     private int _localVolatilityIndexShift = -1;
  141.     private double[] _impliedBrownianVariateArray = null;
  142.     private org.drip.spline.params.SegmentCustomBuilderControl[] _segmentCustomBuilderControlArray = null;

  144.     /**
  145.      * Construct a Standard Instance of LocalVolatilityGenerationControl
  146.      * 
  147.      * @param ensembleSize Size of the Distribution Ensemble
  148.      * 
  149.      * @return Standard Instance of LocalVolatilityGenerationControl
  150.      */

  152.     public static final LocalVolatilityGenerationControl Standard (
  153.         final int ensembleSize)
  154.     {
  155.         if (PYKHTIN_2009_EMPIRICAL_FLOOR > ensembleSize)
  156.         {
  157.             return null;
  158.         }

  160.         double[] uniformCPDArray = new double[ensembleSize];
  161.         double[] impliedBrownianVariateArray = new double[ensembleSize];
  162.         int localVolatilityIndexShift = (int) (LOCAL_VOLATILITY_SMOOTHING_FLOOR_BIAS *
  163.             PYKHTIN_2009_EMPIRICAL_FLOOR + (1 - LOCAL_VOLATILITY_SMOOTHING_FLOOR_BIAS) * ensembleSize);

  165.         if (PYKHTIN_2009_EMPIRICAL_FLOOR > localVolatilityIndexShift)
  166.         {
  167.             return null;
  168.         }

  170.         for (int realizationCoordinate = 0;
  171.             realizationCoordinate < ensembleSize;
  172.             ++realizationCoordinate)
  173.         {
  174.             try
  175.             {
  176.                 impliedBrownianVariateArray[realizationCoordinate] =
  177.                     org.drip.measure.gaussian.NormalQuadrature.InverseCDF
  178.                         (uniformCPDArray[realizationCoordinate] = (((double) realizationCoordinate) + 0.5) /
  179.                             ((double) ensembleSize));
  180.             }
  181.             catch (java.lang.Exception e)
  182.             {
  183.                 e.printStackTrace();

  185.                 return null;
  186.             }
  187.         }

  189.         try
  190.         {
  191.             org.drip.spline.params.SegmentCustomBuilderControl[] segmentCustomBuilderControlArray = new
  192.                 org.drip.spline.params.SegmentCustomBuilderControl[ensembleSize - 1];
  193.             org.drip.spline.params.SegmentCustomBuilderControl segmentCustomBuilderControl = new
  194.                 org.drip.spline.params.SegmentCustomBuilderControl (
  195.                     org.drip.spline.stretch.MultiSegmentSequenceBuilder.BASIS_SPLINE_POLYNOMIAL,
  196.                     new org.drip.spline.basis.PolynomialFunctionSetParams (2),
  197.                     org.drip.spline.params.SegmentInelasticDesignControl.Create (
  198.                         0,
  199.                         2
  200.                     ),
  201.                     new org.drip.spline.params.ResponseScalingShapeControl (
  202.                         true,
  203.                         new org.drip.function.r1tor1.QuadraticRationalShapeControl (0.)
  204.                     ),
  205.                     null
  206.                 );

  208.             for (int realizationCoordinate = 0;
  209.                 realizationCoordinate < ensembleSize - 1;
  210.                 ++realizationCoordinate)
  211.             {
  212.                 segmentCustomBuilderControlArray[realizationCoordinate] = segmentCustomBuilderControl;
  213.             }

  215.             return new LocalVolatilityGenerationControl (
  216.                 localVolatilityIndexShift,
  217.                 uniformCPDArray,
  218.                 impliedBrownianVariateArray,
  219.                 segmentCustomBuilderControlArray
  220.             );
  221.         }
  222.         catch (java.lang.Exception e)
  223.         {
  224.             e.printStackTrace();
  225.         }

  227.         return null;
  228.     }

  230.     /**
  231.      * LocalVolatilityGenerationControl Constructor
  232.      * 
  233.      * @param localVolatilityIndexShift The Local Volatility Index Shift
  234.      * @param uniformCPDArray The Uniform Cumulative Probability Density Array
  235.      * @param impliedBrownianVariateArray The Implied Brownian Variate Array
  236.      * @param segmentCustomBuilderControlArray Array of Segment Builder Control
  237.      * 
  238.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  239.      */

  241.     public LocalVolatilityGenerationControl (
  242.         final int localVolatilityIndexShift,
  243.         final double[] uniformCPDArray,
  244.         final double[] impliedBrownianVariateArray,
  245.         final org.drip.spline.params.SegmentCustomBuilderControl[] segmentCustomBuilderControlArray)
  246.         throws java.lang.Exception
  247.     {
  248.         if (0 >= (_localVolatilityIndexShift = localVolatilityIndexShift) ||
  249.             null == (_uniformCPDArray = uniformCPDArray) ||
  250.             null == (_impliedBrownianVariateArray = impliedBrownianVariateArray) ||
  251.             null == (_segmentCustomBuilderControlArray = segmentCustomBuilderControlArray))
  252.         {
  253.             throw new java.lang.Exception ("LocalVolatilityGenerationControl Constructor => Invalid Inputs");
  254.         }

  256.         int uniformCPDArraySize = _uniformCPDArray.length;

  258.         if (0 == uniformCPDArraySize ||
  259.             uniformCPDArraySize != _impliedBrownianVariateArray.length ||
  260.             uniformCPDArraySize != _segmentCustomBuilderControlArray.length + 1)
  261.         {
  262.             throw new java.lang.Exception ("LocalVolatilityGenerationControl Constructor => Invalid Inputs");
  263.         }
  264.     }

  266.     /**
  267.      * Retrieve the Local Volatility Index Shift
  268.      * 
  269.      * @return The Local Volatility Index Shift
  270.      */

  272.     public int localVolatilityIndexShift()
  273.     {
  274.         return _localVolatilityIndexShift;
  275.     }

  277.     /**
  278.      * Retrieve the Uniform Cumulative Probability Density Array
  279.      * 
  280.      * @return The Uniform Cumulative Probability Density Array
  281.      */

  283.     public double[] uniformCPDArray()
  284.     {
  285.         return _uniformCPDArray;
  286.     }

  288.     /**
  289.      * Retrieve the Implied Brownian Variate Array
  290.      * 
  291.      * @return The Implied Brownian Variate Array
  292.      */

  294.     public double[] impliedBrownianVariateArray()
  295.     {
  296.         return _impliedBrownianVariateArray;
  297.     }

  299.     /**
  300.      * Retrieve the Custom Segment Builder Control Array
  301.      * 
  302.      * @return The Custom Segment Builder Control Array
  303.      */

  305.     public org.drip.spline.params.SegmentCustomBuilderControl[] segmentCustomBuilderControlArray()
  306.     {
  307.         return _segmentCustomBuilderControlArray;
  308.     }
  309. }
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