BurgardKjaerOperator.java

  1. package org.drip.xva.pde;

  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.  * Copyright (C) 2017 Lakshmi Krishnamurthy
  12.  * 
  13.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  14.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  15.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  16.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  17.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  18.  *      and computational support.
  19.  *  
  20.  *      https://lakshmidrip.github.io/DROP/
  21.  *  
  22.  *  DROP is composed of three modules:
  23.  *  
  24.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  25.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  26.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  27.  * 
  28.  *  DROP Product Core implements libraries for the following:
  29.  *  - Fixed Income Analytics
  30.  *  - Loan Analytics
  31.  *  - Transaction Cost Analytics
  32.  * 
  33.  *  DROP Portfolio Core implements libraries for the following:
  34.  *  - Asset Allocation Analytics
  35.  *  - Asset Liability Management Analytics
  36.  *  - Capital Estimation Analytics
  37.  *  - Exposure Analytics
  38.  *  - Margin Analytics
  39.  *  - XVA Analytics
  40.  * 
  41.  *  DROP Computational Core implements libraries for the following:
  42.  *  - Algorithm Support
  43.  *  - Computation Support
  44.  *  - Function Analysis
  45.  *  - Model Validation
  46.  *  - Numerical Analysis
  47.  *  - Numerical Optimizer
  48.  *  - Spline Builder
  49.  *  - Statistical Learning
  50.  * 
  51.  *  Documentation for DROP is Spread Over:
  52.  * 
  53.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  54.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  55.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  56.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  57.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  58.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  59.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  60.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  61.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  62.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  63.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  64.  * 
  65.  *  Licensed under the Apache License, Version 2.0 (the "License");
  66.  *      you may not use this file except in compliance with the License.
  67.  *   
  68.  *  You may obtain a copy of the License at
  69.  *      http://www.apache.org/licenses/LICENSE-2.0
  70.  *  
  71.  *  Unless required by applicable law or agreed to in writing, software
  72.  *      distributed under the License is distributed on an "AS IS" BASIS,
  73.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  74.  *  
  75.  *  See the License for the specific language governing permissions and
  76.  *      limitations under the License.
  77.  */

  79. /**
  80.  * <i>BurgardKjaerOperator</i> sets up the Parabolic Differential Equation PDE based on the Ito Evolution
  81.  * Differential for the Reference Underlier Asset, as laid out in Burgard and Kjaer (2014). The References
  82.  * are:
  83.  *
  84.  *  <br><br>
  85.  *  <ul>
  86.  *      <li>
  87.  *          Burgard, C., and M. Kjaer (2014): PDE Representations of Derivatives with Bilateral Counter-party
  88.  *              Risk and Funding Costs <i>Journal of Credit Risk</i> <b>7 (3)</b> 1-19
  89.  *      </li>
  90.  *      <li>
  91.  *          Cesari, G., J. Aquilina, N. Charpillon, X. Filipovic, G. Lee, and L. Manda (2009): <i>Modeling,
  92.  *              Pricing, and Hedging Counter-party Credit Exposure - A Technical Guide</i> <b>Springer
  93.  *              Finance</b> New York
  94.  *      </li>
  95.  *      <li>
  96.  *          Gregory, J. (2009): Being Two-faced over Counter-party Credit Risk <i>Risk</i> <b>20 (2)</b>
  97.  *              86-90
  98.  *      </li>
  99.  *      <li>
  100.  *          Li, B., and Y. Tang (2007): <i>Quantitative Analysis, Derivatives Modeling, and Trading
  101.  *              Strategies in the Presence of Counter-party Credit Risk for the Fixed Income Market</i>
  102.  *              <b>World Scientific Publishing</b> Singapore
  103.  *      </li>
  104.  *      <li>
  105.  *          Piterbarg, V. (2010): Funding Beyond Discounting: Collateral Agreements and Derivatives Pricing
  106.  *              <i>Risk</i> <b>21 (2)</b> 97-102
  107.  *      </li>
  108.  *  </ul>
  109.  *
  110.  *  <br><br>
  111.  *  <ul>
  112.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/PortfolioCore.md">Portfolio Core Module</a></li>
  113.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/XVAAnalyticsLibrary.md">XVA Analytics Library</a></li>
  114.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/xva/README.md">Valuation Adjustments that account for Collateral, CC Credit/Debt and Funding Overhead</a></li>
  115.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/xva/pde/README.md">Burgard Kjaer PDE Evolution Scheme</a></li>
  116.  *  </ul>
  117.  * <br><br>
  118.  * 
  119.  * @author Lakshmi Krishnamurthy
  120.  */

  122. public class BurgardKjaerOperator
  123. {
  124.     private org.drip.xva.definition.PDEEvolutionControl _pdeEvolutionControl = null;
  125.     private org.drip.exposure.evolver.PrimarySecurityDynamicsContainer _tradeablesContainer = null;

  127.     /**
  128.      * BurgardKjaerOperator Constructor
  129.      * 
  130.      * @param tradeablesContainer The Universe of Tradeable Assets
  131.      * @param pdeEvolutionControl The XVA Control Settings
  132.      * 
  133.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  134.      */

  136.     public BurgardKjaerOperator (
  137.         final org.drip.exposure.evolver.PrimarySecurityDynamicsContainer tradeablesContainer,
  138.         final org.drip.xva.definition.PDEEvolutionControl pdeEvolutionControl)
  139.         throws java.lang.Exception
  140.     {
  141.         if (null == (_tradeablesContainer = tradeablesContainer) ||
  142.             null == (_pdeEvolutionControl = pdeEvolutionControl))
  143.         {
  144.             throw new java.lang.Exception ("BurgardKjaerOperator Constructor => Invalid Inputs");
  145.         }
  146.     }

  148.     /**
  149.      * Retrieve the Universe of Trade-able Assets
  150.      * 
  151.      * @return The Universe of Trade-able Assets
  152.      */

  154.     public org.drip.exposure.evolver.PrimarySecurityDynamicsContainer tradeablesContainer()
  155.     {
  156.         return _tradeablesContainer;
  157.     }

  159.     /**
  160.      * Retrieve the XVA Control Settings
  161.      * 
  162.      * @return The XVA Control Settings
  163.      */

  165.     public org.drip.xva.definition.PDEEvolutionControl pdeEvolutionControl()
  166.     {
  167.         return _pdeEvolutionControl;
  168.     }

  170.     /**
  171.      * Generate the Derivative Value Time Increment using the Burgard Kjaer Scheme
  172.      * 
  173.      * @param marketEdge The Market Edge
  174.      * @param initialTrajectoryVertex The Evolution Trajectory Vertex
  175.      * @param collateral The Off-setting Collateral
  176.      * 
  177.      * @return The Time Increment using the Burgard Kjaer Scheme
  178.      */

  180.     public org.drip.xva.pde.BurgardKjaerEdgeRun edgeRun (
  181.         final org.drip.exposure.universe.MarketEdge marketEdge,
  182.         final org.drip.xva.derivative.EvolutionTrajectoryVertex initialTrajectoryVertex,
  183.         final double collateral)
  184.     {
  185.         if (null == marketEdge ||
  186.             null == initialTrajectoryVertex ||
  187.             !org.drip.numerical.common.NumberUtil.IsValid (collateral))
  188.         {
  189.             return null;
  190.         }

  192.         org.drip.exposure.universe.MarketVertex finalMarketVertex = marketEdge.finish();

  194.         org.drip.exposure.universe.MarketVertexEntity finalDealerMarketVertex = finalMarketVertex.dealer();

  196.         org.drip.exposure.universe.MarketVertexEntity finalClientMarketVertex = finalMarketVertex.client();

  198.         org.drip.xva.derivative.PositionGreekVertex initialPositionGreekVertex =
  199.             initialTrajectoryVertex.positionGreekVertex();

  201.         double initialDerivativeXVAValue = initialPositionGreekVertex.derivativeXVAValue();

  203.         double gainOnDealerDefault = initialTrajectoryVertex.gainOnDealerDefault();

  205.         double dealerSeniorDefaultIntensity = finalDealerMarketVertex.hazardRate();

  207.         double clientDefaultIntensity = finalClientMarketVertex.hazardRate();

  209.         double dealerGainOnClientDefault = initialTrajectoryVertex.gainOnClientDefault();

  211.         double gainOnClientDefault = clientDefaultIntensity * dealerGainOnClientDefault;

  213.         try
  214.         {
  215.             double initialPortfolioValue = finalMarketVertex.latentStateValue
  216.                 (_tradeablesContainer.assetList().get (0).label());

  218.             double portfolioValueBump = _pdeEvolutionControl.sensitivityShiftFactor() *
  219.                 initialPortfolioValue;

  221.             double[] bumpedThetaArray = new org.drip.xva.pde.ParabolicDifferentialOperator
  222.                 (_tradeablesContainer.assetList().get (0)).thetaUpDown (
  223.                     initialTrajectoryVertex,
  224.                     initialPortfolioValue,
  225.                     portfolioValueBump
  226.                 );

  228.             if (null == bumpedThetaArray || 3 != bumpedThetaArray.length)
  229.             {
  230.                 return null;
  231.             }

  233.             return new org.drip.xva.pde.BurgardKjaerEdgeRun (
  234.                 portfolioValueBump,
  235.                 -1. * bumpedThetaArray[0],
  236.                 -1. * bumpedThetaArray[1],
  237.                 -1. * bumpedThetaArray[2],
  238.                 finalMarketVertex.csaReplicator() * collateral,
  239.                 (dealerSeniorDefaultIntensity + clientDefaultIntensity) * initialDerivativeXVAValue,
  240.                 -1. * dealerSeniorDefaultIntensity * gainOnDealerDefault,
  241.                 -1. * gainOnClientDefault,
  242.                 0.
  243.             );
  244.         }
  245.         catch (java.lang.Exception e)
  246.         {
  247.             e.printStackTrace();
  248.         }

  250.         return null;
  251.     }

  253.     /**
  254.      * Generate the Time Increment Run Attribution using the Burgard Kjaer Scheme
  255.      * 
  256.      * @param marketEdge The Market Edge
  257.      * @param initialTrajectoryVertex The Starting Evolution Trajectory Vertex
  258.      * @param collateral The Off-setting Collateral
  259.      * 
  260.      * @return The Time Increment Run Attribution using the Burgard Kjaer Scheme
  261.      */

  263.     public org.drip.xva.pde.BurgardKjaerEdgeAttribution edgeRunAttribution (
  264.         final org.drip.exposure.universe.MarketEdge marketEdge,
  265.         final org.drip.xva.derivative.EvolutionTrajectoryVertex initialTrajectoryVertex,
  266.         final double collateral)
  267.     {
  268.         if (null == marketEdge ||
  269.             null == initialTrajectoryVertex)
  270.         {
  271.             return null;
  272.         }

  274.         org.drip.exposure.universe.MarketVertex finalMarketVertex = marketEdge.finish();

  276.         double derivativeXVAValue = initialTrajectoryVertex.positionGreekVertex().derivativeXVAValue();

  278.         org.drip.exposure.universe.MarketVertexEntity finalDealerMarketVertex = finalMarketVertex.dealer();

  280.         org.drip.exposure.universe.MarketVertexEntity finalClientMarketVertex = finalMarketVertex.client();

  282.         double clientRecoveryRate = finalClientMarketVertex.seniorRecoveryRate();

  284.         double dealerDefaultIntensity = finalDealerMarketVertex.hazardRate();

  286.         double clientDefaultIntensity = finalClientMarketVertex.hazardRate();

  288.         double closeOutMTM = org.drip.xva.definition.PDEEvolutionControl.CLOSEOUT_GREGORY_LI_TANG ==
  289.             _pdeEvolutionControl.closeOutScheme() ? derivativeXVAValue : derivativeXVAValue;

  291.         double dealerExposure = closeOutMTM > 0. ? closeOutMTM : finalDealerMarketVertex.seniorRecoveryRate()
  292.             * closeOutMTM;

  294.         double derivativeXVAClientDefaultGrowth = -1. * clientDefaultIntensity *
  295.             (closeOutMTM < 0. ? closeOutMTM : clientRecoveryRate * closeOutMTM);

  297.         double dealerSeniorFundingSpread = finalDealerMarketVertex.seniorFundingSpread() /
  298.             marketEdge.vertexIncrement();

  300.         try
  301.         {
  302.             double initialPortfolioValue = finalMarketVertex.latentStateValue
  303.                 (_tradeablesContainer.assetList().get (0).label());

  305.             double portfolioValueBump = _pdeEvolutionControl.sensitivityShiftFactor() *
  306.                 initialPortfolioValue;

  308.             double[] bumpedThetaArray = new org.drip.xva.pde.ParabolicDifferentialOperator
  309.                 (_tradeablesContainer.assetList().get (0)).thetaUpDown (
  310.                     initialTrajectoryVertex,
  311.                     initialPortfolioValue,
  312.                     portfolioValueBump
  313.                 );

  315.             if (null == bumpedThetaArray || 3 != bumpedThetaArray.length)
  316.             {
  317.                 return null;
  318.             }

  320.             return new org.drip.xva.pde.BurgardKjaerEdgeAttribution (
  321.                 portfolioValueBump,
  322.                 -1. * bumpedThetaArray[0],
  323.                 -1. * bumpedThetaArray[1],
  324.                 -1. * bumpedThetaArray[2],
  325.                 finalMarketVertex.csaReplicator() * collateral,
  326.                 (dealerDefaultIntensity + clientDefaultIntensity) * derivativeXVAValue,
  327.                 dealerSeniorFundingSpread * dealerExposure,
  328.                 -1. * dealerDefaultIntensity * dealerExposure,
  329.                 derivativeXVAClientDefaultGrowth
  330.             );
  331.         }
  332.         catch (java.lang.Exception e)
  333.         {
  334.             e.printStackTrace();
  335.         }

  337.         return null;
  338.     }
  339. }
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