ParabolicDifferentialOperator.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>ParabolicDifferentialOperator</i> sets up the Parabolic Differential Equation based on the Ito
  81.  * Evolution Differential for the Reference Underlier Asset, as laid out in Burgard and Kjaer (2014). The
  82.  * References 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 ParabolicDifferentialOperator
  123. {
  124.     private org.drip.exposure.evolver.PrimarySecurity _tradeable = null;

  126.     /**
  127.      * ParabolicDifferentialOperator Constructor
  128.      * 
  129.      * @param tradeable The Tradeable Position
  130.      * 
  131.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  132.      */

  134.     public ParabolicDifferentialOperator (
  135.         final org.drip.exposure.evolver.PrimarySecurity tradeable)
  136.         throws java.lang.Exception
  137.     {
  138.         if (null == (_tradeable = tradeable))
  139.         {
  140.             throw new java.lang.Exception ("ParabolicDifferentialOperator Constructor => Invalid Inputs");
  141.         }
  142.     }

  144.     /**
  145.      * Retrieve the Tradeable Position
  146.      * 
  147.      * @return The Tradeable Position
  148.      */

  150.     public org.drip.exposure.evolver.PrimarySecurity asset()
  151.     {
  152.         return _tradeable;
  153.     }

  155.     /**
  156.      * Compute the Theta for the Derivative from the Asset Edge Value
  157.      * 
  158.      * @param evolutionTrajectoryVertex The Derivative's Evolution Trajectory Vertex
  159.      * @param positionValueVertex The Position Value Vertex
  160.      * 
  161.      * @return The Theta
  162.      * 
  163.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  164.      */

  166.     public double theta (
  167.         final org.drip.xva.derivative.EvolutionTrajectoryVertex evolutionTrajectoryVertex,
  168.         final double positionValueVertex)
  169.         throws java.lang.Exception
  170.     {
  171.         if (null == evolutionTrajectoryVertex ||
  172.             !org.drip.numerical.common.NumberUtil.IsValid (positionValueVertex))
  173.         {
  174.             throw new java.lang.Exception ("ParabolicDifferentialOperator::theta => Invalid Inputs");
  175.         }

  177.         org.drip.xva.derivative.PositionGreekVertex positionGreekVertex =
  178.             evolutionTrajectoryVertex.positionGreekVertex();

  180.         double volatility = _tradeable.evolver().evaluator().volatility().value (
  181.             new org.drip.measure.realization.JumpDiffusionVertex (
  182.                 evolutionTrajectoryVertex.time(),
  183.                 positionValueVertex,
  184.                 0.,
  185.                 false
  186.             )
  187.         );

  189.         return
  190.             0.5 * volatility * volatility * positionValueVertex * positionValueVertex *
  191.                 positionGreekVertex.derivativeXVAValueGamma() -
  192.             _tradeable.cashAccumulationRate() * positionValueVertex *
  193.                 positionGreekVertex.derivativeXVAValueDelta();
  194.     }

  196.     /**
  197.      * Compute the Up/Down Thetas
  198.      *  
  199.      * @param evolutionTrajectoryVertex The Derivative's Evolution Trajectory Vertex
  200.      * @param positionValueVertex The Asset Numeraire Vertex Value
  201.      * @param shift The Amount to Shift the Reference Underlier Numeraire By
  202.      * 
  203.      * @return The Array of the Up/Down Thetas
  204.      */

  206.     public double[] thetaUpDown (
  207.         final org.drip.xva.derivative.EvolutionTrajectoryVertex evolutionTrajectoryVertex,
  208.         final double positionValueVertex,
  209.         final double shift)
  210.     {
  211.         if (null == evolutionTrajectoryVertex ||
  212.             !org.drip.numerical.common.NumberUtil.IsValid (positionValueVertex) ||
  213.             !org.drip.numerical.common.NumberUtil.IsValid (shift))
  214.         {
  215.             return null;
  216.         }

  218.         org.drip.xva.derivative.PositionGreekVertex positionGreekVertex =
  219.             evolutionTrajectoryVertex.positionGreekVertex();

  221.         double positionValueVertexDown = positionValueVertex - shift;
  222.         double positionValueVertexUp = positionValueVertex + shift;
  223.         double volatility = java.lang.Double.NaN;

  225.         try
  226.         {
  227.             volatility = _tradeable.evolver().evaluator().volatility().value (
  228.                 new org.drip.measure.realization.JumpDiffusionVertex (
  229.                     evolutionTrajectoryVertex.time(),
  230.                     positionValueVertex,
  231.                     0.,
  232.                     false
  233.                 )
  234.             );
  235.         }
  236.         catch (java.lang.Exception e)
  237.         {
  238.             e.printStackTrace();

  240.             return null;
  241.         }

  243.         double gammaCoefficient = 0.5 * volatility * volatility *
  244.             positionGreekVertex.derivativeXVAValueGamma();

  246.         double deltaCoefficient = -1. * _tradeable.cashAccumulationRate() *
  247.             positionGreekVertex.derivativeXVAValueDelta();

  249.         return new double[]
  250.         {
  251.             gammaCoefficient * positionValueVertexDown * positionValueVertexDown + deltaCoefficient *
  252.                 positionValueVertexDown,
  253.             gammaCoefficient * positionValueVertex * positionValueVertex + deltaCoefficient *
  254.                 positionValueVertex,
  255.             gammaCoefficient * positionValueVertexUp * positionValueVertexUp + deltaCoefficient *
  256.                 positionValueVertexUp
  257.         };
  258.     }
  259. }
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