DiffusionTensor.java

  1. package org.drip.dynamics.ito;

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

  77. /**
  78.  * <i>DiffusionTensor</i> Diffusion Tensor generates Cross-Product from the Multivariate Volatility
  79.  *  Functions. The References are:
  80.  *  
  81.  *  <br><br>
  82.  *  <ul>
  83.  *      <li>
  84.  *          Doob, J. L. (1942): The Brownian Movement and Stochastic Equations <i>Annals of Mathematics</i>
  85.  *              <b>43 (2)</b> 351-369
  86.  *      </li>
  87.  *      <li>
  88.  *          Gardiner, C. W. (2009): <i>Stochastic Methods: A Handbook for the Natural and Social Sciences
  89.  *              4<sup>th</sup> Edition</i> <b>Springer-Verlag</b>
  90.  *      </li>
  91.  *      <li>
  92.  *          Kadanoff, L. P. (2000): <i>Statistical Physics: Statics, Dynamics, and Re-normalization</i>
  93.  *              <b>World Scientific</b>
  94.  *      </li>
  95.  *      <li>
  96.  *          Karatzas, I., and S. E. Shreve (1991): <i>Brownian Motion and Stochastic Calculus 2<sup>nd</sup>
  97.  *              Edition</i> <b>Springer-Verlag</b>
  98.  *      </li>
  99.  *      <li>
  100.  *          Risken, H., and F. Till (1996): <i>The Fokker-Planck Equation – Methods of Solution and
  101.  *              Applications</i> <b>Springer</b>
  102.  *      </li>
  103.  *  </ul>
  104.  *
  105.  *  <br><br>
  106.  *  <ul>
  107.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ProductCore.md">Product Core Module</a></li>
  108.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FixedIncomeAnalyticsLibrary.md">Fixed Income Analytics</a></li>
  109.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/dynamics/README.md">HJM, Hull White, LMM, and SABR Dynamic Evolution Models</a></li>
  110.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/dynamics/ito/README.md">Ito Stochastic Process Dynamics Foundation</a></li>
  111.  *  </ul>
  112.  *
  113.  * @author Lakshmi Krishnamurthy
  114.  */

  116. public class DiffusionTensor
  117. {
  118.     private org.drip.dynamics.ito.RdToR1Volatility[][] _volatilityFunctionGrid = null;

  120.     /**
  121.      * DiffusionTensor Constructor
  122.      * 
  123.      * @param volatilityFunctionGrid  Square Volatility Grid
  124.      * 
  125.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  126.      */

  128.     public DiffusionTensor (
  129.         final org.drip.dynamics.ito.RdToR1Volatility[][] volatilityFunctionGrid)
  130.         throws java.lang.Exception
  131.     {
  132.         if (null == (_volatilityFunctionGrid = volatilityFunctionGrid))
  133.         {
  134.             throw new java.lang.Exception (
  135.                 "DiffusionTensor Constructor => Invalid Inputs"
  136.             );
  137.         }

  139.         int factorCount = 0;
  140.         int dimension = _volatilityFunctionGrid.length;

  142.         if (0 == dimension)
  143.         {
  144.             throw new java.lang.Exception (
  145.                 "DiffusionTensor Constructor => Invalid Inputs"
  146.             );
  147.         }

  149.         for (int dimensionIndex = 0;
  150.             dimensionIndex < dimension;
  151.             ++dimensionIndex)
  152.         {
  153.             if (null == _volatilityFunctionGrid[dimensionIndex])
  154.             {
  155.                 throw new java.lang.Exception (
  156.                     "DiffusionTensor Constructor => Invalid Inputs"
  157.                 );
  158.             }

  160.             if (0 == dimensionIndex)
  161.             {
  162.                 if (0 == (factorCount = _volatilityFunctionGrid[dimensionIndex].length))
  163.                 {
  164.                     throw new java.lang.Exception (
  165.                         "DiffusionTensor Constructor => Invalid Inputs"
  166.                     );
  167.                 }
  168.             }

  170.             if (null == _volatilityFunctionGrid[dimensionIndex] ||
  171.                     factorCount != _volatilityFunctionGrid[dimensionIndex].length)
  172.             {
  173.                 throw new java.lang.Exception (
  174.                     "DiffusionTensor Constructor => Invalid Inputs"
  175.                 );
  176.             }
  177.         }
  178.     }

  180.     /**
  181.      * Retrieve the Square Volatility Grid
  182.      * 
  183.      * @return The Square Volatility Grid
  184.      */

  186.     public org.drip.dynamics.ito.RdToR1Volatility[][] volatilityFunctionGrid()
  187.     {
  188.         return _volatilityFunctionGrid;
  189.     }

  191.     /**
  192.      * Retrieve the Dimension Count
  193.      * 
  194.      * @return The Dimension Count
  195.      */

  197.     public int dimension()
  198.     {
  199.         return _volatilityFunctionGrid.length;
  200.     }

  202.     /**
  203.      * Retrieve the Factor Count
  204.      * 
  205.      * @return The Factor Count
  206.      */

  208.     public int factorCount()
  209.     {
  210.         return _volatilityFunctionGrid[0].length;
  211.     }

  213.     /**
  214.      * Estimate the Diffusion Coefficient
  215.      * 
  216.      * @param timeRdVertex  R<sup>d</sup> Property Variate/Time Coordinate Vertex
  217.      * @param variateIndexI Variate Index I
  218.      * @param variateIndexJ Variate Index J
  219.      * 
  220.      * @return The Diffusion Coefficient
  221.      * 
  222.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  223.      */

  225.     public double diffusionCoefficient (
  226.         final org.drip.dynamics.ito.TimeRdVertex timeRdVertex,
  227.         final int variateIndexI,
  228.         final int variateIndexJ)
  229.         throws java.lang.Exception
  230.     {
  231.         if (null == timeRdVertex)
  232.         {
  233.             throw new java.lang.Exception (
  234.                 "DiffusionTensor::diffusionCoefficient => Invalid Inputs"
  235.             );
  236.         }

  238.         double diffusionCoefficient = 0.;
  239.         int dimension = _volatilityFunctionGrid.length;
  240.         int factorCount = _volatilityFunctionGrid[0].length;

  242.         if (dimension >= variateIndexI || dimension >= variateIndexJ)
  243.         {
  244.             throw new java.lang.Exception (
  245.                 "DiffusionTensor::diffusionCoefficient => Invalid Inputs"
  246.             );
  247.         }

  249.         for (int factorIndex = 0;
  250.             factorIndex < factorCount;
  251.             ++factorIndex)
  252.         {
  253.             diffusionCoefficient = diffusionCoefficient +
  254.                 _volatilityFunctionGrid[variateIndexI][factorIndex].volatility (
  255.                     timeRdVertex
  256.                 ) * _volatilityFunctionGrid[variateIndexJ][factorIndex].volatility (
  257.                     timeRdVertex
  258.                 );
  259.         }

  261.         return 0.5 * diffusionCoefficient;
  262.     }
  263. }
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