StochasticVolatilityStateEvolver.java

  1. package org.drip.dynamics.sabr;

  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.  * Copyright (C) 2018 Lakshmi Krishnamurthy
  11.  * Copyright (C) 2017 Lakshmi Krishnamurthy
  12.  * Copyright (C) 2016 Lakshmi Krishnamurthy
  13.  * Copyright (C) 2015 Lakshmi Krishnamurthy
  14.  * 
  15.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  16.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  17.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  18.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  19.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  20.  *      and computational support.
  21.  *  
  22.  *      https://lakshmidrip.github.io/DROP/
  23.  *  
  24.  *  DROP is composed of three modules:
  25.  *  
  26.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  27.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  28.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  29.  * 
  30.  *  DROP Product Core implements libraries for the following:
  31.  *  - Fixed Income Analytics
  32.  *  - Loan Analytics
  33.  *  - Transaction Cost Analytics
  34.  * 
  35.  *  DROP Portfolio Core implements libraries for the following:
  36.  *  - Asset Allocation Analytics
  37.  *  - Asset Liability Management Analytics
  38.  *  - Capital Estimation Analytics
  39.  *  - Exposure Analytics
  40.  *  - Margin Analytics
  41.  *  - XVA Analytics
  42.  * 
  43.  *  DROP Computational Core implements libraries for the following:
  44.  *  - Algorithm Support
  45.  *  - Computation Support
  46.  *  - Function Analysis
  47.  *  - Model Validation
  48.  *  - Numerical Analysis
  49.  *  - Numerical Optimizer
  50.  *  - Spline Builder
  51.  *  - Statistical Learning
  52.  * 
  53.  *  Documentation for DROP is Spread Over:
  54.  * 
  55.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  56.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  57.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  58.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  59.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  60.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  61.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  62.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  63.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  64.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  65.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  66.  * 
  67.  *  Licensed under the Apache License, Version 2.0 (the "License");
  68.  *      you may not use this file except in compliance with the License.
  69.  *   
  70.  *  You may obtain a copy of the License at
  71.  *      http://www.apache.org/licenses/LICENSE-2.0
  72.  *  
  73.  *  Unless required by applicable law or agreed to in writing, software
  74.  *      distributed under the License is distributed on an "AS IS" BASIS,
  75.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  76.  *  
  77.  *  See the License for the specific language governing permissions and
  78.  *      limitations under the License.
  79.  */

  81. /**
  82.  * <i>StochasticVolatilityStateEvolver</i> provides the SABR Stochastic Volatility Evolution Dynamics.
  83.  *
  84.  *  <br><br>
  85.  *  <ul>
  86.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ProductCore.md">Product Core Module</a></li>
  87.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FixedIncomeAnalyticsLibrary.md">Fixed Income Analytics</a></li>
  88.  *      <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>
  89.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/dynamics/sabr/README.md">SABR Based Latent State Evolution</a></li>
  90.  *  </ul>
  91.  *
  92.  * @author Lakshmi Krishnamurthy
  93.  */

  95. public class StochasticVolatilityStateEvolver implements org.drip.dynamics.evolution.PointStateEvolver {
  96.     private double _dblRho = java.lang.Double.NaN;
  97.     private double _dblBeta = java.lang.Double.NaN;
  98.     private double _dblIdiosyncraticRho = java.lang.Double.NaN;
  99.     private double _dblVolatilityOfVolatility = java.lang.Double.NaN;
  100.     private org.drip.state.identifier.ForwardLabel _lslForward = null;
  101.     private org.drip.sequence.random.UnivariateSequenceGenerator _usgForwardRate = null;
  102.     private org.drip.sequence.random.UnivariateSequenceGenerator _usgForwardRateVolatilityIdiosyncratic =
  103.         null;

  105.     /**
  106.      * Create a Gaussian SABR Instance
  107.      * 
  108.      * @param lslForward The Forward Rate Latent State Label
  109.      * @param dblRho SABR Rho
  110.      * @param dblVolatilityOfVolatility SABR Volatility Of Volatility
  111.      * @param usgForwardRate The Forward Rate Univariate Sequence Generator
  112.      * @param usgForwardRateVolatilityIdiosyncratic The Idiosyncratic Component Forward Rate Volatility
  113.      *  Univariate Sequence Generator
  114.      * 
  115.      * @return The Gaussian SABR Instance
  116.      */

  118.     public static final StochasticVolatilityStateEvolver Gaussian (
  119.         final org.drip.state.identifier.ForwardLabel lslForward,
  120.         final double dblRho,
  121.         final double dblVolatilityOfVolatility,
  122.         final org.drip.sequence.random.UnivariateSequenceGenerator usgForwardRate,
  123.         final org.drip.sequence.random.UnivariateSequenceGenerator usgForwardRateVolatilityIdiosyncratic)
  124.     {
  125.         try {
  126.             return new StochasticVolatilityStateEvolver (lslForward, 0., dblRho, dblVolatilityOfVolatility,
  127.                 usgForwardRate, usgForwardRateVolatilityIdiosyncratic);
  128.         } catch (java.lang.Exception e) {
  129.             e.printStackTrace();
  130.         }

  132.         return null;
  133.     }

  135.     /**
  136.      * Create a Log-normal SABR Instance
  137.      * 
  138.      * @param lslForward The Forward Rate Latent State Label
  139.      * @param dblRho SABR Rho
  140.      * @param dblVolatilityOfVolatility SABR Volatility Of Volatility
  141.      * @param usgForwardRate The Forward Rate Univariate Sequence Generator
  142.      * @param usgForwardRateVolatilityIdiosyncratic The Idiosyncratic Component Forward Rate Volatility
  143.      *  Univariate Sequence Generator
  144.      * 
  145.      * @return The Log-normal SABR Instance
  146.      */

  148.     public static final StochasticVolatilityStateEvolver Lognormal (
  149.         final org.drip.state.identifier.ForwardLabel lslForward,
  150.         final double dblRho,
  151.         final double dblVolatilityOfVolatility,
  152.         final org.drip.sequence.random.UnivariateSequenceGenerator usgForwardRate,
  153.         final org.drip.sequence.random.UnivariateSequenceGenerator usgForwardRateVolatilityIdiosyncratic)
  154.     {
  155.         try {
  156.             return new StochasticVolatilityStateEvolver (lslForward, 1., dblRho, dblVolatilityOfVolatility,
  157.                 usgForwardRate, usgForwardRateVolatilityIdiosyncratic);
  158.         } catch (java.lang.Exception e) {
  159.             e.printStackTrace();
  160.         }

  162.         return null;
  163.     }

  165.     /**
  166.      * Create a Constant Elasticity of Variance SABR Instance
  167.      * 
  168.      * @param lslForward The Forward Rate Latent State Label
  169.      * @param dblBeta SABR Beta
  170.      * @param dblRho SABR Rho
  171.      * @param usgForwardRate The Forward Rate Univariate Sequence Generator
  172.      * @param usgForwardRateVolatilityIdiosyncratic The Idiosyncratic Component Forward Rate Volatility
  173.      *  Univariate Sequence Generator
  174.      * 
  175.      * @return The Constant Elasticity of Variance SABR Instance
  176.      */

  178.     public static final StochasticVolatilityStateEvolver CEV (
  179.         final org.drip.state.identifier.ForwardLabel lslForward,
  180.         final double dblBeta,
  181.         final double dblRho,
  182.         final org.drip.sequence.random.UnivariateSequenceGenerator usgForwardRate,
  183.         final org.drip.sequence.random.UnivariateSequenceGenerator usgForwardRateVolatilityIdiosyncratic)
  184.     {
  185.         try {
  186.             return new StochasticVolatilityStateEvolver (lslForward, dblBeta, dblRho, 0., usgForwardRate,
  187.                 usgForwardRateVolatilityIdiosyncratic);
  188.         } catch (java.lang.Exception e) {
  189.             e.printStackTrace();
  190.         }

  192.         return null;
  193.     }

  195.     /**
  196.      * StochasticVolatilityStateEvolver Constructor
  197.      * 
  198.      * @param lslForward The Forward Rate Latent State Label
  199.      * @param dblBeta SABR Beta
  200.      * @param dblRho SABR Rho
  201.      * @param dblVolatilityOfVolatility SABR Volatility Of Volatility
  202.      * @param usgForwardRate The Forward Rate Univariate Sequence Generator
  203.      * @param usgForwardRateVolatilityIdiosyncratic The Idiosyncratic Component Forward Rate Volatility
  204.      *  Univariate Sequence Generator
  205.      * 
  206.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  207.      */

  209.     public StochasticVolatilityStateEvolver (
  210.         final org.drip.state.identifier.ForwardLabel lslForward,
  211.         final double dblBeta,
  212.         final double dblRho,
  213.         final double dblVolatilityOfVolatility,
  214.         final org.drip.sequence.random.UnivariateSequenceGenerator usgForwardRate,
  215.         final org.drip.sequence.random.UnivariateSequenceGenerator usgForwardRateVolatilityIdiosyncratic)
  216.         throws java.lang.Exception
  217.     {
  218.         if (null == (_lslForward = lslForward) || !org.drip.numerical.common.NumberUtil.IsValid (_dblBeta =
  219.             dblBeta) || !org.drip.numerical.common.NumberUtil.IsValid (_dblRho = dblRho) || _dblRho < -1. ||
  220.                 _dblRho > 1. || !org.drip.numerical.common.NumberUtil.IsValid (_dblVolatilityOfVolatility =
  221.                     dblVolatilityOfVolatility) || null == (_usgForwardRate = usgForwardRate) || (0. !=
  222.                         _dblVolatilityOfVolatility && null == (_usgForwardRateVolatilityIdiosyncratic =
  223.                             usgForwardRateVolatilityIdiosyncratic)))
  224.             throw new java.lang.Exception ("StochasticVolatilityStateEvolver ctr => Invalid Inputs");

  226.         _dblIdiosyncraticRho = java.lang.Math.sqrt (1. - _dblRho * _dblRho);
  227.     }

  229.     /**
  230.      * Retrieve the Forward Label
  231.      * 
  232.      * @return The Forward Label
  233.      */

  235.     public org.drip.state.identifier.ForwardLabel forwardLabel()
  236.     {
  237.         return _lslForward;
  238.     }

  240.     /**
  241.      * Retrieve SABR Volatility of Volatility
  242.      * 
  243.      * @return SABR Volatility of Volatility
  244.      */

  246.     public double volatilityOfVolatility()
  247.     {
  248.         return _dblVolatilityOfVolatility;
  249.     }

  251.     /**
  252.      * Retrieve SABR Beta
  253.      * 
  254.      * @return SABR Beta
  255.      */

  257.     public double beta()
  258.     {
  259.         return _dblBeta;
  260.     }

  262.     /**
  263.      * Retrieve SABR Rho
  264.      * 
  265.      * @return SABR Rho
  266.      */

  268.     public double rho()
  269.     {
  270.         return _dblRho;
  271.     }

  273.     /**
  274.      * The Forward Rate Univariate Random Variable Generator Sequence
  275.      * 
  276.      * @return The Forward Rate Univariate Random Variable Generator Sequence
  277.      */

  279.     public org.drip.sequence.random.UnivariateSequenceGenerator usgForwardRate()
  280.     {
  281.         return _usgForwardRate;
  282.     }

  284.     /**
  285.      * The Idiosyncratic Component of Forward Rate Volatility Univariate Random Variable Generator Sequence
  286.      * 
  287.      * @return The Idiosyncratic Component of Forward Rate Volatility Univariate Random Variable Generator
  288.      *  Sequence
  289.      */

  291.     public org.drip.sequence.random.UnivariateSequenceGenerator usgForwardRateVolatilityIdiosyncratic()
  292.     {
  293.         return _usgForwardRateVolatilityIdiosyncratic;
  294.     }

  296.     @Override public org.drip.dynamics.evolution.LSQMPointUpdate evolve (
  297.         final int iSpotDate,
  298.         final int iViewDate,
  299.         final int iSpotTimeIncrement,
  300.         final org.drip.dynamics.evolution.LSQMPointUpdate lsqmPrev)
  301.     {
  302.         if (iViewDate < iSpotDate || null == lsqmPrev || !(lsqmPrev instanceof
  303.             org.drip.dynamics.sabr.ForwardRateUpdate))
  304.             return null;
  305.         double dblForwardRateZ = _usgForwardRate.random();


  308.         double dblAnnualizedIncrement = 1. * iSpotTimeIncrement / 365.25;
  309.         org.drip.dynamics.sabr.ForwardRateUpdate fruPrev = (org.drip.dynamics.sabr.ForwardRateUpdate)
  310.             lsqmPrev;

  312.         double dblAnnualizedIncrementSQRT = java.lang.Math.sqrt (dblAnnualizedIncrement);

  314.         try {
  315.             double dblForwardRate = fruPrev.forwardRate();

  317.             double dblForwardRateVolatility = fruPrev.forwardRateVolatility();

  319.             double dblForwardRateIncrement = dblForwardRateVolatility * java.lang.Math.pow (dblForwardRate,
  320.                 _dblBeta) * dblAnnualizedIncrementSQRT * dblForwardRateZ;

  322.             double dblForwardRateVolatilityIncrement = _dblVolatilityOfVolatility * dblForwardRateVolatility
  323.                 * dblAnnualizedIncrementSQRT * (_dblRho * dblForwardRateZ + _dblIdiosyncraticRho *
  324.                     _usgForwardRateVolatilityIdiosyncratic.random());

  326.             return org.drip.dynamics.sabr.ForwardRateUpdate.Create (_lslForward, iSpotDate, iSpotDate +
  327.                 iSpotTimeIncrement, iViewDate, dblForwardRate + dblForwardRateIncrement,
  328.                     dblForwardRateIncrement, dblForwardRateVolatility + dblForwardRateVolatilityIncrement,
  329.                         dblForwardRateVolatilityIncrement);
  330.         } catch (java.lang.Exception e) {
  331.             e.printStackTrace();
  332.         }

  334.         return null;
  335.     }

  337.     /**
  338.      * Compute the Implied ATM Black Volatility for the ATM Forward Rate and the TTE
  339.      * 
  340.      * @param dblATMForwardRate ATM Forward Rate
  341.      * @param dblTTE Time to Expiry
  342.      * @param dblSigma0 Initial Sigma
  343.      * 
  344.      * @return The Implied Black Volatility Instance
  345.      */

  347.     public org.drip.dynamics.sabr.ImpliedBlackVolatility computeATMBlackVolatility (
  348.         final double dblATMForwardRate,
  349.         final double dblTTE,
  350.         final double dblSigma0)
  351.     {
  352.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblATMForwardRate) ||
  353.             !org.drip.numerical.common.NumberUtil.IsValid (dblTTE) || !org.drip.numerical.common.NumberUtil.IsValid
  354.                 (dblSigma0))
  355.             return null;

  357.         double dblF0KExpSQRT = java.lang.Math.pow (dblATMForwardRate, 1. - _dblBeta);

  359.         double dblA = dblSigma0 / dblF0KExpSQRT;
  360.         double dblB = 1. + dblTTE * (((1. - _dblBeta) * (1. - _dblBeta) * dblSigma0 * dblSigma0 / (24. *
  361.             dblF0KExpSQRT * dblF0KExpSQRT)) + (_dblRho * _dblBeta * _dblVolatilityOfVolatility * dblSigma0 /
  362.                 (4. * dblF0KExpSQRT)) + ((2. - 3. * _dblRho * _dblRho) * _dblVolatilityOfVolatility *
  363.                     _dblVolatilityOfVolatility / 24.));

  365.         try {
  366.             return new org.drip.dynamics.sabr.ImpliedBlackVolatility (dblATMForwardRate, dblATMForwardRate,
  367.                 dblTTE, dblA, 0., 0., dblB, dblA * dblB);
  368.         } catch (java.lang.Exception e) {
  369.             e.printStackTrace();
  370.         }

  372.         return null;
  373.     }

  375.     /**
  376.      * Compute the Implied Black Volatility for the Specified Strike, the ATM Forward Rate, and the TTE
  377.      * 
  378.      * @param dblStrike Strike
  379.      * @param dblATMForwardRate ATM Forward Rate
  380.      * @param dblTTE Time to Expiry
  381.      * @param dblSigma0 Initial Sigma
  382.      * 
  383.      * @return The Implied Black Volatility Instance
  384.      */

  386.     public org.drip.dynamics.sabr.ImpliedBlackVolatility computeBlackVolatility (
  387.         final double dblStrike,
  388.         final double dblATMForwardRate,
  389.         final double dblTTE,
  390.         final double dblSigma0)
  391.     {
  392.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblStrike) ||
  393.             !org.drip.numerical.common.NumberUtil.IsValid (dblATMForwardRate) ||
  394.                 !org.drip.numerical.common.NumberUtil.IsValid (dblTTE) ||
  395.                     !org.drip.numerical.common.NumberUtil.IsValid (dblSigma0))
  396.             return null;

  398.         if (dblStrike == dblATMForwardRate)
  399.             return computeATMBlackVolatility (dblATMForwardRate, dblTTE, dblSigma0);

  401.         double dblLogF0ByK = java.lang.Math.log (dblATMForwardRate / dblStrike);

  403.         double dblF0KExpSQRT = java.lang.Math.pow (dblATMForwardRate * dblStrike, 0.5 * (1. - _dblBeta));

  405.         double dblZ = _dblVolatilityOfVolatility * dblF0KExpSQRT * dblLogF0ByK / dblSigma0;
  406.         double dblOneMinusBetaLogF0ByK = (1. - _dblBeta) * (1. - _dblBeta) * dblLogF0ByK * dblLogF0ByK;
  407.         double dblA = dblSigma0 / (dblF0KExpSQRT * (1. + (dblOneMinusBetaLogF0ByK / 24.) +
  408.             (dblOneMinusBetaLogF0ByK * dblOneMinusBetaLogF0ByK / 1920.)));
  409.         double dblB = 1. + dblTTE * (((1. - _dblBeta) * (1. - _dblBeta) * dblSigma0 * dblSigma0 / (24. *
  410.             dblF0KExpSQRT * dblF0KExpSQRT)) + (_dblRho * _dblBeta * _dblVolatilityOfVolatility * dblSigma0 /
  411.                 (4. * dblF0KExpSQRT)) + ((2. - 3. * _dblRho * _dblRho) * _dblVolatilityOfVolatility *
  412.                     _dblVolatilityOfVolatility / 24.));

  414.         double dblChiZ = java.lang.Math.log ((java.lang.Math.sqrt (1. - 2. * _dblRho * dblZ + dblZ * dblZ) +
  415.             dblZ - _dblRho) / (1. - _dblRho));

  417.         try {
  418.             return new org.drip.dynamics.sabr.ImpliedBlackVolatility (dblStrike, dblATMForwardRate, dblTTE,
  419.                 dblA, dblZ, dblChiZ, dblB, dblA * dblZ * dblB / dblChiZ);
  420.         } catch (java.lang.Exception e) {
  421.             e.printStackTrace();
  422.         }

  424.         return null;
  425.     }
  426. }
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