R1CIRStochasticEvolver.java

  1. package org.drip.dynamics.meanreverting;

  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>R1CIRStochasticEvolver</i> implements the R<sup>1</sup> Cos-Ingersoll-Ross Stochastic Evolver. The
  79.  *  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/meanreverting/README.md">Mean Reverting Stochastic Process Dynamics</a></li>
  111.  *  </ul>
  112.  *
  113.  * @author Lakshmi Krishnamurthy
  114.  */

  116. public class R1CIRStochasticEvolver
  117.     extends org.drip.dynamics.meanreverting.R1CKLSStochasticEvolver
  118. {

  120.     /**
  121.      * Construct a Weiner Instance of R1CIRStochasticEvolver Process
  122.      * 
  123.      * @param meanReversionSpeed The Mean Reversion Speed
  124.      * @param meanReversionLevel The Mean Reversion Level
  125.      * @param volatility The Volatility
  126.      * @param timeWidth Wiener Time Width
  127.      * 
  128.      * @return Weiner Instance of R1CIRStochasticEvolver Process
  129.      */

  131.     public static R1CIRStochasticEvolver Wiener (
  132.         final double meanReversionSpeed,
  133.         final double meanReversionLevel,
  134.         final double volatility,
  135.         final double timeWidth)
  136.     {
  137.         try
  138.         {
  139.             return new R1CIRStochasticEvolver (
  140.                 meanReversionSpeed,
  141.                 meanReversionLevel,
  142.                 volatility,
  143.                 new org.drip.dynamics.ito.R1WienerDriver (
  144.                     timeWidth
  145.                 )
  146.             );
  147.         }
  148.         catch (java.lang.Exception e)
  149.         {
  150.             e.printStackTrace();
  151.         }

  153.         return null;
  154.     }

  156.     /**
  157.      * R1CIRStochasticEvolver Constructor
  158.      * 
  159.      * @param meanReversionSpeed The Mean Reversion Speed
  160.      * @param meanReversionLevel The Mean Reversion Level
  161.      * @param volatilityCoefficient The Volatility Coefficient
  162.      * @param r1StochasticDriver The Stochastic Driver
  163.      * 
  164.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  165.      */

  167.     public R1CIRStochasticEvolver (
  168.         final double meanReversionSpeed,
  169.         final double meanReversionLevel,
  170.         final double volatilityCoefficient,
  171.         final org.drip.dynamics.ito.R1StochasticDriver r1StochasticDriver)
  172.         throws java.lang.Exception
  173.     {
  174.         super (
  175.             org.drip.dynamics.meanreverting.CKLSParameters.CoxIngersollRoss (
  176.                 meanReversionSpeed,
  177.                 meanReversionLevel,
  178.                 volatilityCoefficient
  179.             ),
  180.             r1StochasticDriver
  181.         );
  182.     }

  184.     /**
  185.      * Indicate it the Evolution includes Zero, or is strictly Positive
  186.      * 
  187.      * @return TRUE - Evoltuion is Strictly Positive
  188.      */

  190.     public boolean evolutionStrictlyPositive()
  191.     {
  192.         org.drip.dynamics.meanreverting.CKLSParameters cklsParameters = cklsParameters();

  194.         double volatilityCoefficient = cklsParameters.volatilityCoefficient();

  196.         return 2. * cklsParameters.meanReversionSpeed() * cklsParameters.meanReversionLevel() >=
  197.             volatilityCoefficient * volatilityCoefficient;
  198.     }

  200.     /**
  201.      * Compute the Expected Value of x at a time t from a Starting Value x0
  202.      * 
  203.      * @param x0 Starting Variate
  204.      * @param t Time
  205.      * 
  206.      * @return Expected Value of x
  207.      * 
  208.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  209.      */

  211.     public double mean (
  212.         final double x0,
  213.         final double t)
  214.         throws java.lang.Exception
  215.     {
  216.         if (!org.drip.numerical.common.NumberUtil.IsValid (
  217.                 x0
  218.             ) || !org.drip.numerical.common.NumberUtil.IsValid (
  219.                 t
  220.             ) || 0. > t
  221.         )
  222.         {
  223.             throw new java.lang.Exception (
  224.                 "R1CIRStochasticEvolver::mean => Invalid Inputs"
  225.             );
  226.         }

  228.         double timeDecayFactor = java.lang.Math.exp (
  229.             -1. * cklsParameters().meanReversionSpeed() * t
  230.         );

  232.         return x0 * timeDecayFactor + cklsParameters().meanReversionLevel() * (1. - timeDecayFactor);
  233.     }

  235.     /**
  236.      * Compute the Time Variance of x across at a Time Value t
  237.      * 
  238.      * @param x0 Starting Variate
  239.      * @param t Time t
  240.      * 
  241.      * @return Time Variance of x
  242.      * 
  243.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  244.      */

  246.     public double timeVariance (
  247.         final double x0,
  248.         final double t)
  249.         throws java.lang.Exception
  250.     {
  251.         if (!org.drip.numerical.common.NumberUtil.IsValid (
  252.                 t
  253.             ) || 0. > t
  254.         )
  255.         {
  256.             throw new java.lang.Exception (
  257.                 "R1VasicekStochasticEvolver::timeCovariance => Invalid Inputs"
  258.             );
  259.         }

  261.         double volatilityCoefficient = cklsParameters().volatilityCoefficient();

  263.         double meanReversionSpeed = cklsParameters().meanReversionSpeed();

  265.         double timeDecayFactor = java.lang.Math.exp (
  266.             -1. * meanReversionSpeed * t
  267.         );

  269.         double oneMinusTimeDecayFactor = 1. - timeDecayFactor;

  271.         return volatilityCoefficient * volatilityCoefficient / meanReversionSpeed * oneMinusTimeDecayFactor *
  272.         (
  273.             x0 * timeDecayFactor + 0.5 * cklsParameters().meanReversionLevel() * oneMinusTimeDecayFactor
  274.         );
  275.     }

  277.     @Override public org.drip.measure.statistics.PopulationCentralMeasures
  278.         temporalPopulationCentralMeasures (
  279.             final double x0,
  280.             final double t)
  281.     {
  282.         try
  283.         {
  284.             return new org.drip.measure.statistics.PopulationCentralMeasures (
  285.                 mean (
  286.                     x0,
  287.                     t
  288.                 ),
  289.                 timeVariance (
  290.                     x0,
  291.                     t
  292.                 )
  293.             );
  294.         }
  295.         catch (java.lang.Exception e)
  296.         {
  297.             e.printStackTrace();
  298.         }

  300.         return null;
  301.     }

  303.     @Override public org.drip.measure.statistics.PopulationCentralMeasures
  304.         steadyStatePopulationCentralMeasures (
  305.             final double x0)
  306.     {
  307.         double volatility = cklsParameters().volatilityCoefficient();

  309.         try
  310.         {
  311.             return new org.drip.measure.statistics.PopulationCentralMeasures (
  312.                 cklsParameters().meanReversionLevel(),
  313.                 0.5 * volatility * volatility / cklsParameters().meanReversionSpeed()
  314.             );
  315.         }
  316.         catch (java.lang.Exception e)
  317.         {
  318.             e.printStackTrace();
  319.         }

  321.         return null;
  322.     }

  324.     @Override public org.drip.measure.chisquare.R1NonCentral futureValueDistribution (
  325.         final double r0,
  326.         final double t)
  327.     {
  328.         if (!org.drip.numerical.common.NumberUtil.IsValid (
  329.                 r0
  330.             ) || !org.drip.numerical.common.NumberUtil.IsValid (
  331.                 t
  332.             ) || 0. > t
  333.         )
  334.         {
  335.             return null;
  336.         }

  338.         int digammaTermCount = 1000;
  339.         int besselFirstTermCount = 20;

  341.         org.drip.dynamics.meanreverting.CKLSParameters cklsParameters = cklsParameters();

  343.         double ePowerMinusAT = java.lang.Math.exp (
  344.             -1. * cklsParameters.meanReversionSpeed() * t
  345.         );

  347.         org.drip.function.definition.R1ToR1 gammaEstimator =
  348.             new org.drip.specialfunction.gamma.EulerIntegralSecondKind (
  349.                 null
  350.             );

  352.         try
  353.         {
  354.             return new org.drip.measure.chisquare.R1NonCentral (
  355.                 new org.drip.measure.chisquare.R1NonCentralParameters (
  356.                     cklsParameters.meanReversionLevel() * (1. - ePowerMinusAT),
  357.                     r0 * ePowerMinusAT
  358.                 ),
  359.                 gammaEstimator,
  360.                 org.drip.specialfunction.digamma.CumulativeSeriesEstimator.AbramowitzStegun2007 (
  361.                     digammaTermCount
  362.                 ),
  363.                 new org.drip.function.definition.R2ToR1()
  364.                 {
  365.                     @Override public double evaluate (
  366.                         final double s,
  367.                         final double t)
  368.                         throws Exception
  369.                     {
  370.                         return new org.drip.specialfunction.incompletegamma.LowerEulerIntegral (
  371.                             null,
  372.                             t
  373.                         ).evaluate (
  374.                             s
  375.                         );
  376.                     }
  377.                 },
  378.                 org.drip.specialfunction.bessel.ModifiedFirstFrobeniusSeriesEstimator.Standard (
  379.                     gammaEstimator,
  380.                     besselFirstTermCount
  381.                 )
  382.             );
  383.         }
  384.         catch (java.lang.Exception e)
  385.         {
  386.             e.printStackTrace();
  387.         }

  389.         return null;
  390.     }

  392.     @Override public org.drip.dynamics.kolmogorov.R1FokkerPlanckCIR fokkerPlanckGenerator()
  393.     {
  394.         try
  395.         {
  396.             return new org.drip.dynamics.kolmogorov.R1FokkerPlanckCIR (
  397.                 cklsParameters()
  398.             );
  399.         }
  400.         catch (java.lang.Exception e)
  401.         {
  402.             e.printStackTrace();
  403.         }

  405.         return null;
  406.     }
  407. }
Created with JaCoCo 0.7.9.201702052155