R1ProbabilityDensityFunctionCIR.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>R1ProbabilityDensityFunctionCIR</i> exposes the R<sup>1</sup> Probability Density Function Evaluation
  79.  *  Equation for an Underlying CIR Process. 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/process/README.md">Ito-Dynamics Based Stochastic Process</a></li>
  111.  *  </ul>
  112.  *
  113.  * @author Lakshmi Krishnamurthy
  114.  */

  116. public class R1ProbabilityDensityFunctionCIR
  117.     extends org.drip.dynamics.process.R1ProbabilityDensityFunction
  118. {
  119.     private double _q = java.lang.Double.NaN;
  120.     private double _r0 = java.lang.Double.NaN;
  121.     private double _twoAOverSigmaSquared = java.lang.Double.NaN;
  122.     private org.drip.dynamics.meanreverting.CKLSParameters _cklsParameters = null;
  123.     private org.drip.specialfunction.definition.ModifiedBesselFirstKindEstimator
  124.         _modifiedBesselFirstKindEstimator = null;

  126.     /**
  127.      * R1ProbabilityDensityFunctionCIR Constructor
  128.      * 
  129.      * @param r0 Starting Value for r
  130.      * @param cklsParameters The CKLS Parameters
  131.      * @param modifiedBesselFirstKindEstimator Modified Bessel Estimator of the First Kind
  132.      * 
  133.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  134.      */

  136.     public R1ProbabilityDensityFunctionCIR (
  137.         final double r0,
  138.         final org.drip.dynamics.meanreverting.CKLSParameters cklsParameters,
  139.         final org.drip.specialfunction.definition.ModifiedBesselFirstKindEstimator
  140.             modifiedBesselFirstKindEstimator)
  141.         throws java.lang.Exception
  142.     {
  143.         if (!org.drip.numerical.common.NumberUtil.IsValid (
  144.                 _r0 = r0
  145.             ) ||
  146.             null == (_cklsParameters = cklsParameters) ||
  147.             null == (_modifiedBesselFirstKindEstimator = modifiedBesselFirstKindEstimator)
  148.         )
  149.         {
  150.             throw new java.lang.Exception (
  151.                 "R1ProbabilityDensityFunctionCIR Constructor => Invalid Inputs"
  152.             );
  153.         }

  155.         double volatilityCoefficient = _cklsParameters.volatilityCoefficient();

  157.         _q = _cklsParameters.meanReversionLevel() * (
  158.             _twoAOverSigmaSquared = 2. * _cklsParameters.meanReversionSpeed() / volatilityCoefficient /
  159.                 volatilityCoefficient
  160.         ) - 1.;
  161.     }

  163.     /**
  164.      * Retrieve "q"
  165.      * 
  166.      * @return "q"
  167.      */

  169.     public double q()
  170.     {
  171.         return _q;
  172.     }

  174.     /**
  175.      * Retrieve the Starting Value for r
  176.      * 
  177.      * @return Starting Value for r
  178.      */

  180.     public double r0()
  181.     {
  182.         return _r0;
  183.     }

  185.     /**
  186.      * Retrieve the CKLS Parameters
  187.      * 
  188.      * @return The CKLS Parameters
  189.      */

  191.     public org.drip.dynamics.meanreverting.CKLSParameters cklsParameters()
  192.     {
  193.         return _cklsParameters;
  194.     }

  196.     /**
  197.      * Retrieve the Modified Bessel Estimator of the First Kind
  198.      * 
  199.      * @return The Modified Bessel Estimator of the First Kind
  200.      */

  202.     public org.drip.specialfunction.definition.ModifiedBesselFirstKindEstimator
  203.         modifiedBesselFirstKindEstimator()
  204.     {
  205.         return _modifiedBesselFirstKindEstimator;
  206.     }

  208.     @Override public double density (
  209.         final org.drip.dynamics.ito.TimeR1Vertex r1TimeVertex)
  210.         throws java.lang.Exception
  211.     {
  212.         if (null == r1TimeVertex)
  213.         {
  214.             throw new java.lang.Exception (
  215.                 "R1ProbabilityDensityFunctionCIR::density => Invalid Inputs"
  216.             );
  217.         }

  219.         double ePowerMinusAT = java.lang.Math.exp (
  220.             -1. * _cklsParameters.meanReversionSpeed() * r1TimeVertex.t()
  221.         );

  223.         double c = _twoAOverSigmaSquared / (1. - ePowerMinusAT);
  224.         double u = c * _r0 * ePowerMinusAT;

  226.         double v = c * r1TimeVertex.x();

  228.         return c * java.lang.Math.exp (
  229.             -1. * (u + v)
  230.         ) * java.lang.Math.pow (
  231.             u / v,
  232.             0.5 * _q
  233.         ) * _modifiedBesselFirstKindEstimator.bigI (
  234.             _q,
  235.             2. * java.lang.Math.sqrt (
  236.                 u * v
  237.             )
  238.         );
  239.     }
  240. }
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