RdStochasticEvolver.java

  1. package org.drip.dynamics.process;

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

  115. public class RdStochasticEvolver
  116. {
  117.     private org.drip.dynamics.ito.RdToR1Drift[] _driftFunctionArray = null;
  118.     private org.drip.dynamics.ito.RdStochasticDriver _stochasticDriver = null;
  119.     private org.drip.dynamics.ito.RdToR1Volatility[][] _volatilityFunctionGrid = null;

  121.     private double[] pointDriftArray (
  122.         final org.drip.dynamics.ito.TimeRdVertex currentVertex)
  123.     {
  124.         int dimension = _driftFunctionArray.length;
  125.         double[] pointDriftArray = new double[dimension];

  127.         for (int dimensionIndex = 0;
  128.             dimensionIndex < dimension;
  129.             ++dimensionIndex)
  130.         {
  131.             try
  132.             {
  133.                 pointDriftArray[dimensionIndex] = _driftFunctionArray[dimensionIndex].drift (
  134.                     currentVertex
  135.                 );
  136.             }
  137.             catch (java.lang.Exception e)
  138.             {
  139.                 e.printStackTrace();

  141.                 return null;
  142.             }
  143.         }

  145.         return pointDriftArray;
  146.     }

  148.     private double[][] pointVolatilityGrid (
  149.         final org.drip.dynamics.ito.TimeRdVertex currentVertex)
  150.     {
  151.         int dimension = _volatilityFunctionGrid.length;
  152.         double[][] pointVolatilityGrid = new double[dimension][dimension];

  154.         for (int dimensionIndexI = 0;
  155.             dimensionIndexI < dimension;
  156.             ++dimensionIndexI)
  157.         {
  158.             for (int dimensionIndexJ = 0;
  159.                 dimensionIndexJ < dimension;
  160.                 ++dimensionIndexJ)
  161.             {
  162.                 try
  163.                 {
  164.                     pointVolatilityGrid[dimensionIndexI][dimensionIndexJ] =
  165.                         _volatilityFunctionGrid[dimensionIndexI][dimensionIndexJ].volatility (
  166.                             currentVertex
  167.                         );
  168.                 }
  169.                 catch (java.lang.Exception e)
  170.                 {
  171.                     e.printStackTrace();

  173.                     return null;
  174.                 }
  175.             }
  176.         }

  178.         return pointVolatilityGrid;
  179.     }

  181.     /**
  182.      * RdStochasticEvolver Constructor
  183.      * 
  184.      * @param driftFunctionArray The Drift Function Array
  185.      * @param volatilityFunctionGrid The Volatility Function Grid
  186.      * @param stochasticDriver The Stochastic Driver
  187.      * 
  188.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  189.      */

  191.     public RdStochasticEvolver (
  192.         final org.drip.dynamics.ito.RdToR1Drift[] driftFunctionArray,
  193.         final org.drip.dynamics.ito.RdToR1Volatility[][] volatilityFunctionGrid,
  194.         final org.drip.dynamics.ito.RdStochasticDriver stochasticDriver)
  195.         throws java.lang.Exception
  196.     {
  197.         if (null == (_driftFunctionArray = driftFunctionArray) ||
  198.             null == (_volatilityFunctionGrid = volatilityFunctionGrid) ||
  199.             null == (_stochasticDriver = stochasticDriver))
  200.         {
  201.             throw new java.lang.Exception (
  202.                 "RdStochasticEvolver Constructor => Invalid Inputs"
  203.             );
  204.         }

  206.         int dimension = _driftFunctionArray.length;

  208.         if (0 == dimension ||
  209.             dimension != _volatilityFunctionGrid.length ||
  210.             null == _volatilityFunctionGrid[0] ||
  211.             dimension != _volatilityFunctionGrid[0].length)
  212.         {
  213.             throw new java.lang.Exception (
  214.                 "RdStochasticEvolver Constructor => Invalid Inputs"
  215.             );
  216.         }

  218.         for (int dimensionIndexI = 0;
  219.             dimensionIndexI < dimension;
  220.             ++dimensionIndexI)
  221.         {
  222.             if (null == _driftFunctionArray[dimensionIndexI])
  223.             {
  224.                 throw new java.lang.Exception (
  225.                     "RdStochasticEvolver Constructor => Invalid Inputs"
  226.                 );
  227.             }

  229.             for (int dimensionIndexJ = 0;
  230.                 dimensionIndexJ < dimension;
  231.                 ++dimensionIndexJ)
  232.             {
  233.                 if (null == _volatilityFunctionGrid[dimensionIndexI][dimensionIndexJ])
  234.                 {
  235.                     throw new java.lang.Exception (
  236.                         "RdStochasticEvolver Constructor => Invalid Inputs"
  237.                     );
  238.                 }
  239.             }
  240.         }
  241.     }

  243.     /**
  244.      * Retrieve the Drift Function Array
  245.      * 
  246.      * @return The Drift Function Array
  247.      */

  249.     public org.drip.dynamics.ito.RdToR1Drift[] driftFunctionArray()
  250.     {
  251.         return _driftFunctionArray;
  252.     }

  254.     /**
  255.      * Retrieve the Volatility Function Grid
  256.      * 
  257.      * @return The Volatility Function Grid
  258.      */

  260.     public org.drip.dynamics.ito.RdToR1Volatility[][] volatilityFunctionGrid()
  261.     {
  262.         return _volatilityFunctionGrid;
  263.     }

  265.     /**
  266.      * Retrieve the Stochastic Driver
  267.      * 
  268.      * @return The Stochastic Driver
  269.      */

  271.     public org.drip.dynamics.ito.RdStochasticDriver stochasticDriver()
  272.     {
  273.         return _stochasticDriver;
  274.     }

  276.     /**
  277.      * Generate the Next Vertex in the Iteration
  278.      * 
  279.      * @param currentVertex The Current Vertex
  280.      * @param timeIncrement The Time Increment
  281.      * 
  282.      * @return The Next Vertex
  283.      */

  285.     public org.drip.dynamics.ito.TimeRdVertex evolve (
  286.         final org.drip.dynamics.ito.TimeRdVertex currentVertex,
  287.         final double timeIncrement)
  288.     {
  289.         if (null == currentVertex ||
  290.             !org.drip.numerical.common.NumberUtil.IsValid (
  291.                 timeIncrement
  292.             )
  293.         )
  294.         {
  295.             return null;
  296.         }

  298.         double[] pointDriftArray = pointDriftArray (
  299.             currentVertex
  300.         );

  302.         if (null == pointDriftArray)
  303.         {
  304.             return null;
  305.         }

  307.         double[] volatilityShiftArray = org.drip.numerical.linearalgebra.Matrix.Product (
  308.             pointVolatilityGrid (
  309.                 currentVertex
  310.             ),
  311.             _stochasticDriver.emitSingle()
  312.         );

  314.         if (null == volatilityShiftArray)
  315.         {
  316.             return null;
  317.         }

  319.         int dimension = _driftFunctionArray.length;
  320.         double[] xNextArray = new double[dimension];

  322.         double[] xCurrentArray = currentVertex.xArray();

  324.         for (int dimensionIndex = 0;
  325.             dimensionIndex < dimension;
  326.             ++dimensionIndex)
  327.         {
  328.             xNextArray[dimensionIndex] = xCurrentArray[dimensionIndex] +
  329.                 pointDriftArray[dimensionIndex] * timeIncrement +
  330.                 volatilityShiftArray[dimensionIndex];
  331.         }

  333.         try
  334.         {
  335.             return new org.drip.dynamics.ito.TimeRdVertex (
  336.                 currentVertex.t() + timeIncrement,
  337.                 xNextArray
  338.             );
  339.         }
  340.         catch (java.lang.Exception e)
  341.         {
  342.             e.printStackTrace();
  343.         }

  345.         return null;
  346.     }

  348.     /**
  349.      * Construct the Fokker Planck PDF Generator corresponding to R<sup>d</sup> Stochastic Evolver
  350.      * 
  351.      * @return The Fokker Planck PDF Generator corresponding to R<sup>d</sup> Stochastic Evolver
  352.      */

  354.     public org.drip.dynamics.kolmogorov.RdFokkerPlanck fokkerPlanckGenerator()
  355.     {
  356.         try
  357.         {
  358.             return new org.drip.dynamics.kolmogorov.RdFokkerPlanck (
  359.                 _driftFunctionArray,
  360.                 new org.drip.dynamics.ito.DiffusionTensor (
  361.                     _volatilityFunctionGrid
  362.                 ),
  363.                 null
  364.             );
  365.         }
  366.         catch (java.lang.Exception e)
  367.         {
  368.             e.printStackTrace();
  369.         }

  371.         return null;
  372.     }
  373. }
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