FundingBasisEvolver.java

  1. package org.drip.exposure.csadynamics;

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

  79. /**
  80.  * <i>FundingBasisEvolver</i> implements a Two Factor Stochastic Funding Model Evolver with a Log Normal
  81.  * Forward Process and a Mean Reverting Diffusion Process for the Funding Spread. The References are:
  82.  *  
  83.  * <br><br>
  84.  *      <ul>
  85.  *          <li>
  86.  *              Antonov, A., and M. Arneguy (2009): Analytical Formulas for Pricing CMS Products in the LIBOR
  87.  *                  Market Model with Stochastic Volatility 
  88.  *                  https://papers.ssrn.com/sol3/Papers.cfm?abstract_id=1352606 <b>eSSRN</b>
  89.  *          </li>
  90.  *          <li>
  91.  *              Burgard, C., and M. Kjaer (2009): Modeling and successful Management of Credit Counter-party
  92.  *                  Risk of Derivative Portfolios <i>ICBI Conference</i> <b>Rome</b>
  93.  *          </li>
  94.  *          <li>
  95.  *              Gregory, J. (2009): Being Two-faced over Counter-party Credit Risk <i>Risk</i> <b>20 (2)</b>
  96.  *                  86-90
  97.  *          </li>
  98.  *          <li>
  99.  *              Johannes, M., and S. Sundaresan (2007): Pricing Collateralized Swaps <i>Journal of
  100.  *                  Finance</i> <b>62</b> 383-410
  101.  *          </li>
  102.  *          <li>
  103.  *              Piterbarg, V. (2010): Funding Beyond Discounting: Collateral Agreements and Derivatives
  104.  *                  Pricing <i>Risk</i> <b>21 (2)</b> 97-102
  105.  *          </li>
  106.  *      </ul>
  107.  *
  108.  *  <br><br>
  109.  *  <ul>
  110.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/PortfolioCore.md">Portfolio Core Module</a></li>
  111.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ExposureAnalyticsLibrary.md">Exposure Analytics</a></li>
  112.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/exposure/README.md">Exposure Group Level Collateralized/Uncollateralized Exposure</a></li>
  113.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/exposure/csadynamics/README.md">CSA Numeraire Basis/Measure Dynamics</a></li>
  114.  *  </ul>
  115.  * 
  116.  * @author Lakshmi Krishnamurthy
  117.  */

  119. public class FundingBasisEvolver
  120. {
  121.     private double _correlation = java.lang.Double.NaN;
  122.     private org.drip.measure.dynamics.DiffusionEvaluatorLogarithmic _underlyingEvolver = null;
  123.     private org.drip.measure.dynamics.DiffusionEvaluatorMeanReversion _fundingSpreadEvolver = null;

  125.     /**
  126.      * FundingBasisEvolver Constructor
  127.      * 
  128.      * @param underlyingEvolver The Underlying Diffusion Evolver
  129.      * @param fundingSpreadEvolver The Funding Spread Diffusion Evolver
  130.      * @param correlation Correlation between the Underlying and the Funding Spread Processes
  131.      * 
  132.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  133.      */

  135.     public FundingBasisEvolver (
  136.         final org.drip.measure.dynamics.DiffusionEvaluatorLogarithmic underlyingEvolver,
  137.         final org.drip.measure.dynamics.DiffusionEvaluatorMeanReversion fundingSpreadEvolver,
  138.         final double correlation)
  139.         throws java.lang.Exception
  140.     {
  141.         if (null == (_underlyingEvolver = underlyingEvolver) ||
  142.             null == (_fundingSpreadEvolver = fundingSpreadEvolver) ||
  143.             !org.drip.numerical.common.NumberUtil.IsValid (_correlation = correlation) ||
  144.             1. < _correlation || -1. > _correlation)
  145.         {
  146.             throw new java.lang.Exception ("FundingBasisEvolver Constructor => Invalid Inputs");
  147.         }
  148.     }

  150.     /**
  151.      * Retrieve the Underlying Diffusion Evolver
  152.      * 
  153.      * @return The Underlying Diffusion Evolver
  154.      */

  156.     public org.drip.measure.dynamics.DiffusionEvaluatorLogarithmic underlyingEvolver()
  157.     {
  158.         return _underlyingEvolver;
  159.     }

  161.     /**
  162.      * Retrieve the Funding Spread Diffusion Evolver
  163.      * 
  164.      * @return The Funding Spread Diffusion Evolver
  165.      */

  167.     public org.drip.measure.dynamics.DiffusionEvaluatorMeanReversion fundingSpreadEvolver()
  168.     {
  169.         return _fundingSpreadEvolver;
  170.     }

  172.     /**
  173.      * Retrieve the Correlation between the Underlying and the Funding Spread Processes
  174.      * 
  175.      * @return The Correlation between the Underlying and the Funding Spread Processes
  176.      */

  178.     public double underlyingFundingSpreadCorrelation()
  179.     {
  180.         return _correlation;
  181.     }

  183.     /**
  184.      * Generate the CSA Forward Diffusion Process
  185.      * 
  186.      * @return The CSA Forward Diffusion Process
  187.      */

  189.     public org.drip.measure.process.DiffusionEvolver csaForwardProcess()
  190.     {
  191.         try
  192.         {
  193.             org.drip.measure.dynamics.LocalEvaluator driftEvolver = new
  194.                 org.drip.measure.dynamics.LocalEvaluator()
  195.             {
  196.                 @Override public double value (
  197.                     final org.drip.measure.realization.JumpDiffusionVertex vertex)
  198.                     throws java.lang.Exception
  199.                 {
  200.                     return 0.;
  201.                 }
  202.             };

  204.             org.drip.measure.dynamics.LocalEvaluator volatilityEvolver = new
  205.                 org.drip.measure.dynamics.LocalEvaluator()
  206.             {
  207.                 @Override public double value (
  208.                     final org.drip.measure.realization.JumpDiffusionVertex vertex)
  209.                     throws java.lang.Exception
  210.                 {
  211.                     if (null == vertex)
  212.                         throw new java.lang.Exception
  213.                             ("FundingBasisEvolver::CSAForwardVolatility::Evaluator::value => Invalid Inputs");

  215.                     return vertex.value() * _underlyingEvolver.volatilityValue();
  216.                 }
  217.             };

  219.             return new org.drip.measure.process.DiffusionEvolver (
  220.                 new org.drip.measure.dynamics.DiffusionEvaluator (
  221.                     driftEvolver,
  222.                     volatilityEvolver
  223.                 )
  224.             );
  225.         }
  226.         catch (java.lang.Exception e)
  227.         {
  228.             e.printStackTrace();
  229.         }

  231.         return null;
  232.     }

  234.     /**
  235.      * Generate the Funding Numeraire Diffusion Process
  236.      * 
  237.      * @param tenor The Tenor of the Underlying Forward
  238.      * 
  239.      * @return The Funding Numeraire Diffusion Process
  240.      */

  242.     public org.drip.measure.process.DiffusionEvolver fundingNumeraireProcess (
  243.         final java.lang.String tenor)
  244.     {
  245.         try {
  246.             double meanReversionSpeed = _fundingSpreadEvolver.meanReversionRate();

  248.             double b = org.drip.analytics.support.Helper.TenorToYearFraction (tenor);

  250.             if (0. != meanReversionSpeed)
  251.             {
  252.                 b = (1. - java.lang.Math.exp (-1. * meanReversionSpeed * b)) / meanReversionSpeed;
  253.             }

  255.             final double piterbarg2010BFactor = b;

  257.             org.drip.measure.dynamics.LocalEvaluator driftEvaluator = new
  258.                 org.drip.measure.dynamics.LocalEvaluator()
  259.             {
  260.                 @Override public double value (
  261.                     final org.drip.measure.realization.JumpDiffusionVertex jumpDiffusionVertex)
  262.                     throws java.lang.Exception
  263.                 {
  264.                     return 0.;
  265.                 }
  266.             };

  268.             org.drip.measure.dynamics.LocalEvaluator volatilityEvaluator = new
  269.                 org.drip.measure.dynamics.LocalEvaluator()
  270.             {
  271.                 @Override public double value (
  272.                     final org.drip.measure.realization.JumpDiffusionVertex jumpDiffusionVertex)
  273.                     throws java.lang.Exception
  274.                 {
  275.                     if (null == jumpDiffusionVertex)
  276.                     {
  277.                         throw new java.lang.Exception
  278.                             ("FundingBasisEvolver::CSAFundingNumeraireVolatility::Evaluator::value => Invalid Inputs");
  279.                     }

  281.                     return -1. * jumpDiffusionVertex.value() * piterbarg2010BFactor *
  282.                         _fundingSpreadEvolver.volatilityValue();
  283.                 }
  284.             };

  286.             return new org.drip.measure.process.DiffusionEvolver (
  287.                 new org.drip.measure.dynamics.DiffusionEvaluator (
  288.                     driftEvaluator,
  289.                     volatilityEvaluator
  290.                 )
  291.             );
  292.         }
  293.         catch (java.lang.Exception e)
  294.         {
  295.             e.printStackTrace();
  296.         }

  298.         return null;
  299.     }

  301.     /**
  302.      * Generate the Funding Spread Numeraire Diffusion Process
  303.      * 
  304.      * @param tenor The Tenor of the Underlying Forward
  305.      * 
  306.      * @return The Funding Spread Numeraire Diffusion Process
  307.      */

  309.     public org.drip.measure.process.DiffusionEvolver fundingSpreadNumeraireProcess (
  310.         final java.lang.String tenor)
  311.     {
  312.         try
  313.         {
  314.             double meanReversionSpeed = _fundingSpreadEvolver.meanReversionRate();

  316.             double b = org.drip.analytics.support.Helper.TenorToYearFraction (tenor);

  318.             if (0. != meanReversionSpeed)
  319.             {
  320.                 b = (1. - java.lang.Math.exp (-1. * meanReversionSpeed * b)) / meanReversionSpeed;
  321.             }

  323.             final double piterbarg2010BFactor = b;

  325.             org.drip.measure.dynamics.LocalEvaluator driftEvaluator = new
  326.                 org.drip.measure.dynamics.LocalEvaluator()
  327.             {
  328.                 @Override public double value (
  329.                     final org.drip.measure.realization.JumpDiffusionVertex jumpDiffusionVertex)
  330.                     throws java.lang.Exception
  331.                 {
  332.                     return 0.;
  333.                 }
  334.             };

  336.             org.drip.measure.dynamics.LocalEvaluator volatilityEvaluator = new
  337.                 org.drip.measure.dynamics.LocalEvaluator()
  338.             {
  339.                 @Override public double value (
  340.                     final org.drip.measure.realization.JumpDiffusionVertex jumpDiffusionVertex)
  341.                     throws java.lang.Exception
  342.                 {
  343.                     if (null == jumpDiffusionVertex)
  344.                     {
  345.                         throw new java.lang.Exception
  346.                             ("FundingBasisEvolver::CSAFundingSpreadNumeraireVolatility::Evaluator::value => Invalid Inputs");
  347.                     }

  349.                     return -1. * jumpDiffusionVertex.value() * piterbarg2010BFactor *
  350.                         _fundingSpreadEvolver.volatilityValue();
  351.                 }
  352.             };

  354.             return new org.drip.measure.process.DiffusionEvolver (
  355.                 new org.drip.measure.dynamics.DiffusionEvaluator (
  356.                     driftEvaluator,
  357.                     volatilityEvaluator
  358.                 )
  359.             );
  360.         }
  361.         catch (java.lang.Exception e)
  362.         {
  363.             e.printStackTrace();
  364.         }

  366.         return null;
  367.     }

  369.     /**
  370.      * Compute the CSA vs. No CSA Forward Ratio
  371.      * 
  372.      * @param tenor The Tenor of the Underlying Forward
  373.      * 
  374.      * @return The CSA vs. No CSA Forward Ratio
  375.      * 
  376.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  377.      */

  379.     public double CSANoCSARatio (
  380.         final java.lang.String tenor)
  381.         throws java.lang.Exception
  382.     {
  383.         double underlyingVolatility = _underlyingEvolver.volatilityValue();

  385.         double meanReversionSpeed = _fundingSpreadEvolver.meanReversionRate();

  387.         double fundingSpreadVolatility = _fundingSpreadEvolver.volatilityValue();

  389.         double maturity = org.drip.analytics.support.Helper.TenorToYearFraction (tenor);

  391.         if (0. == meanReversionSpeed)
  392.         {
  393.             return java.lang.Math.exp (-0.5 * _correlation * underlyingVolatility *
  394.                 fundingSpreadVolatility * maturity * maturity);
  395.         }

  397.         double b = (1. - java.lang.Math.exp (-1. * meanReversionSpeed * maturity)) /
  398.             meanReversionSpeed;

  400.         return java.lang.Math.exp (-1. * _correlation * underlyingVolatility *
  401.             fundingSpreadVolatility * (maturity - b) / meanReversionSpeed);
  402.     }
  403. }
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