R1VasicekStochasticEvolver.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>R1VasicekStochasticEvolver</i> implements the R<sup>1</sup> Vasicek Stochastic Evolver. The References
  79.  *  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 R1VasicekStochasticEvolver
  117.     extends org.drip.dynamics.meanreverting.R1CKLSStochasticEvolver
  118. {

  120.     /**
  121.      * Construct a Weiner Instance of R1VasicekStochasticEvolver 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 R1VasicekStochasticEvolver Process
  129.      */

  131.     public static R1VasicekStochasticEvolver Wiener (
  132.         final double meanReversionSpeed,
  133.         final double meanReversionLevel,
  134.         final double volatility,
  135.         final double timeWidth)
  136.     {
  137.         try
  138.         {
  139.             return new R1VasicekStochasticEvolver (
  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.      * R1VasicekStochasticEvolver Constructor
  158.      * 
  159.      * @param meanReversionSpeed The Mean Reversion Speed
  160.      * @param meanReversionLevel The Mean Reversion Level
  161.      * @param volatility The Volatility
  162.      * @param r1StochasticDriver The Stochastic Driver
  163.      * 
  164.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  165.      */

  167.     public R1VasicekStochasticEvolver (
  168.         final double meanReversionSpeed,
  169.         final double meanReversionLevel,
  170.         final double volatility,
  171.         final org.drip.dynamics.ito.R1StochasticDriver r1StochasticDriver)
  172.         throws java.lang.Exception
  173.     {
  174.         super (
  175.             org.drip.dynamics.meanreverting.CKLSParameters.Vasicek (
  176.                 meanReversionSpeed,
  177.                 meanReversionLevel,
  178.                 volatility
  179.             ),
  180.             r1StochasticDriver
  181.         );
  182.     }

  184.     /**
  185.      * Compute the Expected Value of x at a time t from a Starting Value x0
  186.      * 
  187.      * @param x0 Starting Variate
  188.      * @param t Time
  189.      * 
  190.      * @return Expected Value of x
  191.      * 
  192.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  193.      */

  195.     public double mean (
  196.         final double x0,
  197.         final double t)
  198.         throws java.lang.Exception
  199.     {
  200.         if (!org.drip.numerical.common.NumberUtil.IsValid (
  201.                 x0
  202.             ) || !org.drip.numerical.common.NumberUtil.IsValid (
  203.                 t
  204.             ) || 0. > t
  205.         )
  206.         {
  207.             throw new java.lang.Exception (
  208.                 "R1VasicekStochasticEvolver::mean => Invalid Inputs"
  209.             );
  210.         }

  212.         double timeDecayFactor = java.lang.Math.exp (
  213.             -1. * cklsParameters().meanReversionSpeed() * t
  214.         );

  216.         return x0 * timeDecayFactor + cklsParameters().meanReversionLevel() * (1. - timeDecayFactor);
  217.     }

  219.     /**
  220.      * Compute the Time Co-variance of x across Time Values t and s
  221.      * 
  222.      * @param x0 Starting Variate
  223.      * @param s Time s
  224.      * @param t Time t
  225.      * 
  226.      * @return Time Co-variance of x
  227.      * 
  228.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  229.      */

  231.     public double timeCovariance (
  232.         final double x0,
  233.         final double s,
  234.         final double t)
  235.         throws java.lang.Exception
  236.     {
  237.         if (!org.drip.numerical.common.NumberUtil.IsValid (
  238.                 s
  239.             ) || 0. > s || !org.drip.numerical.common.NumberUtil.IsValid (
  240.                 t
  241.             ) || 0. > t
  242.         )
  243.         {
  244.             throw new java.lang.Exception (
  245.                 "R1VasicekStochasticEvolver::timeCovariance => Invalid Inputs"
  246.             );
  247.         }

  249.         double volatility = cklsParameters().volatilityCoefficient();

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

  253.         return 0.5 * volatility * volatility / meanReversionSpeed *
  254.         (
  255.             (
  256.                 java.lang.Math.exp (
  257.                     -1. * meanReversionSpeed * java.lang.Math.abs (
  258.                         s - t
  259.                     )
  260.                 ) - java.lang.Math.exp (
  261.                     -1. * meanReversionSpeed * (s + t)
  262.                 )
  263.             )
  264.         );
  265.     }

  267.     @Override public org.drip.measure.statistics.PopulationCentralMeasures
  268.         temporalPopulationCentralMeasures (
  269.             final double x0,
  270.             final double t)
  271.     {
  272.         try
  273.         {
  274.             return new org.drip.measure.statistics.PopulationCentralMeasures (
  275.                 mean (
  276.                     x0,
  277.                     t
  278.                 ),
  279.                 timeCovariance (
  280.                     x0,
  281.                     t,
  282.                     t
  283.                 )
  284.             );
  285.         }
  286.         catch (java.lang.Exception e)
  287.         {
  288.             e.printStackTrace();
  289.         }

  291.         return null;
  292.     }

  294.     @Override public org.drip.measure.statistics.PopulationCentralMeasures
  295.         steadyStatePopulationCentralMeasures (
  296.             final double x0)
  297.     {
  298.         double volatility = cklsParameters().volatilityCoefficient();

  300.         try
  301.         {
  302.             return new org.drip.measure.statistics.PopulationCentralMeasures (
  303.                 cklsParameters().meanReversionLevel(),
  304.                 0.5 * volatility * volatility / cklsParameters().meanReversionSpeed()
  305.             );
  306.         }
  307.         catch (java.lang.Exception e)
  308.         {
  309.             e.printStackTrace();
  310.         }

  312.         return null;
  313.     }

  315.     /**
  316.      * Construct the Ait-Sahalia Maximum Likelihood Estimation Sampling Interval Discreteness Error
  317.      * 
  318.      * @param intervalWidth Sampling Interval Width
  319.      * 
  320.      * @return The Ait-Sahalia Maximum Likelihood Estimation Sampling Interval Discreteness Error
  321.      */

  323.     public double[][] aitSahaliaMLEAsymptote (
  324.         final double intervalWidth)
  325.     {
  326.         if (!org.drip.numerical.common.NumberUtil.IsValid (
  327.                 intervalWidth
  328.             ) || 0. >= intervalWidth
  329.         )
  330.         {
  331.             return null;
  332.         }

  334.         double volatility = cklsParameters().volatilityCoefficient();

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

  338.         double tTheta = intervalWidth * meanReversionSpeed;
  339.         double tSquaredThetaSquared = tTheta * tTheta;

  341.         double ePower_TTheta_ = java.lang.Math.exp (
  342.             tTheta
  343.         );

  345.         double ePower_TwoTTheta_ = ePower_TTheta_ * ePower_TTheta_;
  346.         double ePower_TwoTTheta_MinusOne = ePower_TwoTTheta_ - 1.;
  347.         double sigmaSquared = volatility * volatility;
  348.         double[][] aitSahaliaMLEAsymptote = new double[3][3];
  349.         double tSquared = intervalWidth * intervalWidth;
  350.         aitSahaliaMLEAsymptote[0][0] = ePower_TwoTTheta_MinusOne / tSquared;
  351.         aitSahaliaMLEAsymptote[0][1] = 0.;
  352.         aitSahaliaMLEAsymptote[0][2] = sigmaSquared * ePower_TwoTTheta_MinusOne *
  353.             (ePower_TwoTTheta_MinusOne - 2. * intervalWidth) / tSquared / meanReversionSpeed;
  354.         aitSahaliaMLEAsymptote[1][0] = 0.;
  355.         aitSahaliaMLEAsymptote[1][1] = 0.5 * sigmaSquared * (ePower_TTheta_ + 1.) / (ePower_TTheta_ - 1.) /
  356.             meanReversionSpeed;
  357.         aitSahaliaMLEAsymptote[1][2] = 0.;
  358.         aitSahaliaMLEAsymptote[2][0] = aitSahaliaMLEAsymptote[0][2];
  359.         aitSahaliaMLEAsymptote[2][1] = 0.;
  360.         aitSahaliaMLEAsymptote[2][2] = sigmaSquared * sigmaSquared * (
  361.             ePower_TwoTTheta_MinusOne * ePower_TwoTTheta_MinusOne +
  362.             2. * tSquaredThetaSquared * (ePower_TwoTTheta_ + 1.) +
  363.             4. * tTheta * ePower_TwoTTheta_MinusOne
  364.         ) / (ePower_TwoTTheta_MinusOne * tSquaredThetaSquared);
  365.         return aitSahaliaMLEAsymptote;
  366.     }
  367. }
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