R1UnivariateCIRPDF.java

  1. package org.drip.function.r1tor1;

  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>R1UnivariateCIRPDF</i> exposes the R<sup>1</sup> Univariate Cox-Ingersoll-Ross Probability Density
  79.  *  Function. The References are:
  80.  *  
  81.  *  <br><br>
  82.  *  <ul>
  83.  *      <li>
  84.  *          Bogoliubov, N. N., and D. P. Sankevich (1994): N. N. Bogoliubov and Statistical Mechanics
  85.  *              <i>Russian Mathematical Surveys</i> <b>49 (5)</b> 19-49
  86.  *      </li>
  87.  *      <li>
  88.  *          Holubec, V., K. Kroy, and S. Steffenoni (2019): Physically Consistent Numerical Solver for
  89.  *              Time-dependent Fokker-Planck Equations <i>Physical Review E</i> <b>99 (4)</b> 032117
  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.  *          Ottinger, H. C. (1996): <i>Stochastic Processes in Polymeric Fluids</i> <b>Springer-Verlag</b>
  97.  *              Berlin-Heidelberg
  98.  *      </li>
  99.  *      <li>
  100.  *          Wikipedia (2019): Fokker-Planck Equation
  101.  *              https://en.wikipedia.org/wiki/Fokker%E2%80%93Planck_equation
  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/kolmogorov/README.md">Fokker Planck Kolmogorov Forward/Backward</a></li>
  111.  *  </ul>
  112.  *
  113.  * @author Lakshmi Krishnamurthy
  114.  */

  116. public class R1UnivariateCIRPDF
  117.     extends org.drip.function.definition.R1ToR1
  118. {
  119.     private double _beta = java.lang.Double.NaN;
  120.     private double _alpha = java.lang.Double.NaN;
  121.     private org.drip.function.definition.R1ToR1 _gammaFunction = null;

  123.     /**
  124.      * Construct a Standard Instance of R1UnivariateCIRPDF
  125.      * 
  126.      * @param cklsParameters The CKLS Parameters
  127.      * 
  128.      * @return Standard Instance of R1UnivariateCIRPDF
  129.      */

  131.     public static final R1UnivariateCIRPDF Standard (
  132.         final org.drip.dynamics.meanreverting.CKLSParameters cklsParameters)
  133.     {
  134.         if (null == cklsParameters)
  135.         {
  136.             return null;
  137.         }

  139.         double volatility = cklsParameters.volatilityCoefficient();

  141.         double beta = 2. * cklsParameters.meanReversionSpeed() / volatility / volatility;

  143.         try
  144.         {
  145.             return new R1UnivariateCIRPDF (
  146.                 beta * cklsParameters.meanReversionLevel(),
  147.                 beta,
  148.                 new org.drip.specialfunction.gamma.NemesAnalytic (
  149.                     null
  150.                 )
  151.             );
  152.         }
  153.         catch (java.lang.Exception e)
  154.         {
  155.             e.printStackTrace();
  156.         }

  158.         return null;
  159.     }

  161.     /**
  162.      * R1UnivariateCIRPDF Constructor
  163.      * 
  164.      * @param alpha The Alpha
  165.      * @param beta The Beta
  166.      * @param gammaFunction The Gamma Function
  167.      * 
  168.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  169.      */

  171.     public R1UnivariateCIRPDF (
  172.         final double alpha,
  173.         final double beta,
  174.         final org.drip.function.definition.R1ToR1 gammaFunction)
  175.         throws java.lang.Exception
  176.     {
  177.         super (
  178.             null
  179.         );

  181.         if (!org.drip.numerical.common.NumberUtil.IsValid (
  182.                 _alpha = alpha
  183.             ) || !org.drip.numerical.common.NumberUtil.IsValid (
  184.                 _beta = beta
  185.             ) || null == (_gammaFunction = gammaFunction)
  186.         )
  187.         {
  188.             throw new java.lang.Exception (
  189.                 "R1UnivariateCIRPDF CVonstructor => IOnvalid Inputs"
  190.             );
  191.         }
  192.     }

  194.     /**
  195.      * Retrieve Alpha
  196.      * 
  197.      * @return The Alpha
  198.      */

  200.     public double alpha()
  201.     {
  202.         return _alpha;
  203.     }

  205.     /**
  206.      * Retrieve Beta
  207.      * 
  208.      * @return The Beta
  209.      */

  211.     public double beta()
  212.     {
  213.         return _beta;
  214.     }

  216.     /**
  217.      * Retrieve the Gamma Function
  218.      * 
  219.      * @return The Gamma Function
  220.      */

  222.     public org.drip.function.definition.R1ToR1 gammaFunction()
  223.     {
  224.         return _gammaFunction;
  225.     }

  227.     @Override public double evaluate (
  228.         final double r)
  229.         throws java.lang.Exception
  230.     {
  231.         if (!org.drip.numerical.common.NumberUtil.IsValid (
  232.             r
  233.         ))
  234.         {
  235.             throw new java.lang.Exception (
  236.                 "R1UnivariateCIRPDF::evaluate => Invalid Inputs"
  237.             );
  238.         }

  240.         return java.lang.Math.pow (
  241.             _beta,
  242.             _alpha
  243.         ) * java.lang.Math.pow (
  244.             r,
  245.             _alpha - 1.
  246.         ) * java.lang.Math.exp (
  247.             -1. * _beta * r
  248.         ) / _gammaFunction.evaluate (
  249.             _alpha
  250.         );
  251.     }
  252. }
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