ExponentialAffineZeroCoefficients.java

  1. package org.drip.dynamics.physical;

  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>ExponentialAffineZeroCoefficients</i> contains the Exponential Affine Coefficients for a Zero-coupon
  79.  *  Bond priced using the CIR Process. The 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/physical/README.md">Implementation of Physical Process Dynamics</a></li>
  111.  *  </ul>
  112.  *
  113.  * @author Lakshmi Krishnamurthy
  114.  */

  116. public class ExponentialAffineZeroCoefficients
  117. {
  118.     private double _A = java.lang.Double.NaN;
  119.     private double _B = java.lang.Double.NaN;

  121.     /**
  122.      * Construct an Instance of ExponentialAffineZeroCoefficients using the CIR Stochastic Evolver
  123.      * 
  124.      * @param r1CIRStochasticEvolver The CIR Stochastic Evolver
  125.      * @param ttm The Time to Maturity
  126.      * 
  127.      * @return The ExponentialAffineZeroCoefficients Instance
  128.      */

  130.     public static final ExponentialAffineZeroCoefficients FromCIR (
  131.         final org.drip.dynamics.meanreverting.R1CIRStochasticEvolver r1CIRStochasticEvolver,
  132.         final double ttm)
  133.     {
  134.         if (null == r1CIRStochasticEvolver ||
  135.             !org.drip.numerical.common.NumberUtil.IsValid (
  136.                 ttm
  137.             ) || 0. > ttm
  138.         )
  139.         {
  140.             return null;
  141.         }

  143.         org.drip.dynamics.meanreverting.CKLSParameters cklsParameters =
  144.             r1CIRStochasticEvolver.cklsParameters();

  146.         double meanReversionSpeed = cklsParameters.meanReversionSpeed();

  148.         double volatilityCoefficient = cklsParameters.volatilityCoefficient();

  150.         double sigmaSquared = volatilityCoefficient * volatilityCoefficient;

  152.         double h = java.lang.Math.sqrt (
  153.             meanReversionSpeed * meanReversionSpeed + 2. * sigmaSquared
  154.         );

  156.         double hT = h * ttm;
  157.         double twoH = 2 * h;
  158.         double aPlusH = meanReversionSpeed + h;

  160.         double exp_hT_MinusOne = java.lang.Math.exp (
  161.             hT
  162.         ) - 1.;

  164.         double inverseOfTwoHPlus_APlusHTimes__exp_hT_MinusOne__ = 1. / (
  165.             twoH + aPlusH * (
  166.                 java.lang.Math.exp (
  167.                     hT
  168.                 ) - 1.
  169.             )
  170.         );

  172.         try
  173.         {
  174.             return new ExponentialAffineZeroCoefficients (
  175.                 java.lang.Math.pow (
  176.                     twoH * java.lang.Math.exp (
  177.                         0.5 * aPlusH * ttm
  178.                     ) * inverseOfTwoHPlus_APlusHTimes__exp_hT_MinusOne__,
  179.                     2. * meanReversionSpeed * cklsParameters.meanReversionLevel() / sigmaSquared
  180.                 ),
  181.                 2. * exp_hT_MinusOne * inverseOfTwoHPlus_APlusHTimes__exp_hT_MinusOne__
  182.             );
  183.         }
  184.         catch (java.lang.Exception e)
  185.         {
  186.             e.printStackTrace();
  187.         }

  189.         return null;
  190.     }

  192.     /**
  193.      * ExponentialAffineZeroCoefficients Constructor
  194.      * 
  195.      * @param a Exponential Affine "A"
  196.      * @param b Exponential Affine "B"
  197.      * 
  198.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  199.      */

  201.     public ExponentialAffineZeroCoefficients (
  202.         final double a,
  203.         final double b)
  204.         throws java.lang.Exception
  205.     {
  206.         if (!org.drip.numerical.common.NumberUtil.IsValid (
  207.                 _A = a
  208.             ) || !org.drip.numerical.common.NumberUtil.IsValid (
  209.                 _B = b
  210.             )
  211.         )
  212.         {
  213.             throw new java.lang.Exception (
  214.                 "ExponentialAffineZeroCoefficients Constructor => Invalid Inputs"
  215.             );
  216.         }
  217.     }

  219.     /**
  220.      * Retrieve Exponential Affine "A"
  221.      * 
  222.      * @return The Exponential Affine "A"
  223.      */

  225.     public double a()
  226.     {
  227.         return _A;
  228.     }

  230.     /**
  231.      * Retrieve Exponential Affine "B"
  232.      * 
  233.      * @return The Exponential Affine "B"
  234.      */

  236.     public double b()
  237.     {
  238.         return _B;
  239.     }

  241.     /**
  242.      * Compute the Price given the Initial Rate
  243.      * 
  244.      * @param r0 The Initial Rate
  245.      * 
  246.      * @return Price given the Initial Rate
  247.      * 
  248.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  249.      */

  251.     public double price (
  252.         final double r0)
  253.         throws java.lang.Exception
  254.     {
  255.         if (!org.drip.numerical.common.NumberUtil.IsValid (
  256.             r0
  257.         ))
  258.         {
  259.             throw new java.lang.Exception (
  260.                 "ExponentialAffineZeroCoefficients::price => Invalid Inputs"
  261.             );
  262.         }

  264.         return _A * java.lang.Math.exp (
  265.             -1. * _B * r0
  266.         );
  267.     }
  268. }
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