LognormalLIBORVolatility.java

  1. package org.drip.dynamics.lmm;

  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
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  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
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  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>LognormalLIBORVolatility</i> implements the Multi-Factor Log-normal LIBOR Volatility as formulated in:
  83.  *
  84.  *  <br><br>
  85.  *  <ul>
  86.  *      <li>
  87.  *          Goldys, B., M. Musiela, and D. Sondermann (1994): <i>Log-normality of Rates and Term Structure
  88.  *              Models</i> <b>The University of New South Wales</b>
  89.  *      </li>
  90.  *      <li>
  91.  *          Musiela, M. (1994): <i>Nominal Annual Rates and Log-normal Volatility Structure</i> <b>The
  92.  *              University of New South Wales</b>
  93.  *      </li>
  94.  *      <li>
  95.  *          Brace, A., D. Gatarek, and M. Musiela (1997): The Market Model of Interest Rate Dynamics
  96.  *              <i>Mathematical Finance</i> <b>7 (2)</b> 127-155
  97.  *      </li>
  98.  *  </ul>
  99.  *
  100.  *  <br><br>
  101.  *  <ul>
  102.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ProductCore.md">Product Core Module</a></li>
  103.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FixedIncomeAnalyticsLibrary.md">Fixed Income Analytics</a></li>
  104.  *      <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>
  105.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/dynamics/lmm/README.md">LMM Based Latent State Evolution</a></li>
  106.  *  </ul>
  107.  *
  108.  * @author Lakshmi Krishnamurthy
  109.  */

  111. public class LognormalLIBORVolatility extends org.drip.dynamics.hjm.MultiFactorVolatility {
  112.     private int _iSpotDate = java.lang.Integer.MIN_VALUE;
  113.     private org.drip.state.identifier.ForwardLabel _lslForward = null;

  115.     /**
  116.      * LognormalLIBORVolatility Constructor
  117.      * 
  118.      * @param iSpotDate The Spot Date
  119.      * @param lslForward The Forward Label
  120.      * @param aMSVolatility Array of the Multi-Factor Volatility Surfaces
  121.      * @param pfsg Principal Factor Sequence Generator
  122.      * 
  123.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  124.      */

  126.     public LognormalLIBORVolatility (
  127.         final int iSpotDate,
  128.         final org.drip.state.identifier.ForwardLabel lslForward,
  129.         final org.drip.analytics.definition.MarketSurface[] aMSVolatility,
  130.         final org.drip.sequence.random.PrincipalFactorSequenceGenerator pfsg)
  131.         throws java.lang.Exception
  132.     {
  133.         super (aMSVolatility, pfsg);

  135.         if (null == (_lslForward = lslForward))
  136.             throw new java.lang.Exception ("LognormalLIBORVolatility ctr: Invalid Inputs");

  138.         _iSpotDate = iSpotDate;
  139.     }

  141.     /**
  142.      * Retrieve the Spot Date
  143.      * 
  144.      * @return The Spot Date
  145.      */

  147.     public int spotDate()
  148.     {
  149.         return _iSpotDate;
  150.     }

  152.     /**
  153.      * Retrieve the Forward Label
  154.      * 
  155.      * @return The Forward Label
  156.      */

  158.     public org.drip.state.identifier.ForwardLabel forwardLabel()
  159.     {
  160.         return _lslForward;
  161.     }

  163.     /**
  164.      * Compute the Constraint in the Difference in the Volatility of the Continuously Compounded Forward Rate
  165.      *  between the Target Date and the Target Date + Forward Tenor
  166.      * 
  167.      * @param fc The Forward Curve Instance
  168.      * @param iTargetDate The Target Date
  169.      * 
  170.      * @return The Constraint in the Difference in the Volatility of the Continuously Compounded Forward Rate
  171.      */

  173.     public double[] continuousForwardVolatilityConstraint (
  174.         final org.drip.state.forward.ForwardCurve fc,
  175.         final int iTargetDate)
  176.     {
  177.         if (null == fc || iTargetDate <= _iSpotDate) return null;

  179.         java.lang.String strTenor = _lslForward.tenor();

  181.         org.drip.analytics.definition.MarketSurface[] aMS = volatilitySurface();

  183.         try {
  184.             double dblLIBORDCF = fc.forward (new org.drip.analytics.date.JulianDate (iTargetDate).addTenor
  185.                 (strTenor)) * org.drip.analytics.support.Helper.TenorToYearFraction (strTenor);

  187.             int iNumSurface = aMS.length;
  188.             double dblConstraintWeight = dblLIBORDCF / (1. + dblLIBORDCF);
  189.             double[] adblContinuousForwardVolatilityConstraint = new double[iNumSurface];

  191.             for (int i = 0; i < iNumSurface; ++i)
  192.                 adblContinuousForwardVolatilityConstraint[i] = dblConstraintWeight * aMS[i].node (_iSpotDate,
  193.                     iTargetDate);

  195.             return adblContinuousForwardVolatilityConstraint;
  196.         } catch (java.lang.Exception e) {
  197.             e.printStackTrace();
  198.         }

  200.         return null;
  201.     }

  203.     /**
  204.      * Compute the Volatility of the Continuously Compounded Forward Rate Up to the Target Date
  205.      * 
  206.      * @param iTargetDate The Target Date
  207.      * @param fc The Forward Curve Instance
  208.      * 
  209.      * @return The Volatility of the Continuously Compounded Forward Rate Up to the Target Date
  210.      */

  212.     public double[] continuousForwardVolatility (
  213.         final int iTargetDate,
  214.         final org.drip.state.forward.ForwardCurve fc)
  215.     {
  216.         if (iTargetDate <= _iSpotDate || null == fc) return null;

  218.         org.drip.sequence.random.PrincipalFactorSequenceGenerator pfsg = msg();

  220.         int iNumFactor = pfsg.numFactor();

  222.         boolean bLoop = true;
  223.         int iEndDate = _iSpotDate;
  224.         double dblTenorDCF = java.lang.Double.NaN;
  225.         double[] adblContinuousForwardVolatility = new double[iNumFactor];

  227.         java.lang.String strTenor = _lslForward.tenor();

  229.         try {
  230.             dblTenorDCF = org.drip.analytics.support.Helper.TenorToYearFraction (strTenor);
  231.         } catch (java.lang.Exception e) {
  232.             e.printStackTrace();

  234.             return null;
  235.         }

  237.         for (int i = 0; i < iNumFactor; ++i)
  238.             adblContinuousForwardVolatility[i] = 0.;

  240.         double[] adblFactorPointVolatility = factorPointVolatility (_iSpotDate, iEndDate);

  242.         while (bLoop) {
  243.             try {
  244.                 if ((iEndDate = new org.drip.analytics.date.JulianDate (iEndDate).addTenor
  245.                     (strTenor).julian()) > iTargetDate)
  246.                     bLoop = false;

  248.                 double dblLIBORTenorDCF = fc.forward (iEndDate) * dblTenorDCF;

  250.                 double dblLIBORLognormalVolatilityScaler = dblLIBORTenorDCF / (1. + dblLIBORTenorDCF);

  252.                 for (int i = 0; i < iNumFactor; ++i)
  253.                     adblContinuousForwardVolatility[i] += dblLIBORLognormalVolatilityScaler *
  254.                         adblFactorPointVolatility[i];
  255.             } catch (java.lang.Exception e) {
  256.                 e.printStackTrace();

  258.                 return null;
  259.             }
  260.         }

  262.         return adblContinuousForwardVolatility;
  263.     }

  265.     /**
  266.      * Compute the Volatility of the Continuously Compounded Forward Rate Up to the Target Date
  267.      * 
  268.      * @param iTargetDate The Target Date
  269.      * @param dc The Discount Curve Instance
  270.      * 
  271.      * @return The Volatility of the Continuously Compounded Forward Rate Up to the Target Date
  272.      */

  274.     public double[] continuousForwardVolatility (
  275.         final int iTargetDate,
  276.         final org.drip.state.discount.MergedDiscountForwardCurve dc)
  277.     {
  278.         if (iTargetDate <= _iSpotDate || null == dc) return null;

  280.         org.drip.sequence.random.PrincipalFactorSequenceGenerator pfsg = msg();

  282.         int iNumFactor = pfsg.numFactor();

  284.         boolean bLoop = true;
  285.         int iStartDate = _iSpotDate;
  286.         double dblTenorDCF = java.lang.Double.NaN;
  287.         double[] adblContinuousForwardVolatility = new double[iNumFactor];

  289.         java.lang.String strTenor = _lslForward.tenor();

  291.         try {
  292.             dblTenorDCF = org.drip.analytics.support.Helper.TenorToYearFraction (strTenor);
  293.         } catch (java.lang.Exception e) {
  294.             e.printStackTrace();

  296.             return null;
  297.         }

  299.         for (int i = 0; i < iNumFactor; ++i)
  300.             adblContinuousForwardVolatility[i] = 0.;

  302.         double[] adblFactorPointVolatility = factorPointVolatility (_iSpotDate, iStartDate);

  304.         while (bLoop) {
  305.             try {
  306.                 double dblLIBORTenorDCF = dc.libor (iStartDate, strTenor) * dblTenorDCF;

  308.                 double dblLIBORLognormalVolatilityScaler = dblLIBORTenorDCF / (1. + dblLIBORTenorDCF);

  310.                 for (int i = 0; i < iNumFactor; ++i)
  311.                     adblContinuousForwardVolatility[i] += dblLIBORLognormalVolatilityScaler *
  312.                         adblFactorPointVolatility[i];

  314.                 if ((iStartDate = new org.drip.analytics.date.JulianDate (iStartDate).addTenor
  315.                     (strTenor).julian()) > iTargetDate)
  316.                     bLoop = false;
  317.             } catch (java.lang.Exception e) {
  318.                 e.printStackTrace();

  320.                 return null;
  321.             }
  322.         }

  324.         return adblContinuousForwardVolatility;
  325.     }

  327.     /**
  328.      * Multi-Factor Cross Volatility Integral
  329.      * 
  330.      * @param iForwardDate1 Forward Date #1
  331.      * @param iForwardDate2 Forward Date #2
  332.      * @param iTerminalDate The Terminal Date
  333.      * 
  334.      * @return The Multi-Factor Cross Volatility Integral
  335.      * 
  336.      * @throws java.lang.Exception Thrown if the Multi-Factor Cross Volatility Integral cannot be computed
  337.      */

  339.     public double crossVolatilityIntegralProduct (
  340.         final int iForwardDate1,
  341.         final int iForwardDate2,
  342.         final int iTerminalDate)
  343.         throws java.lang.Exception
  344.     {
  345.         if (iForwardDate1 < iTerminalDate || iForwardDate2 < iTerminalDate)
  346.             throw new java.lang.Exception
  347.                 ("LognormalLIBORVolatility::crossVolatilityIntegralProduct => Invalid Inputs");

  349.         org.drip.function.definition.R1ToR1 crossVolR1ToR1 = new org.drip.function.definition.R1ToR1 (null) {
  350.             @Override public double evaluate (
  351.                 final double dblDate)
  352.                 throws java.lang.Exception
  353.             {
  354.                 double dblCrossVolProduct = 0.;

  356.                 int iNumFactor = msg().numFactor();

  358.                 for (int iFactorIndex = 0; iFactorIndex < iNumFactor; ++iFactorIndex)
  359.                     dblCrossVolProduct += factorPointVolatility (iFactorIndex, (int) dblDate, iForwardDate1)
  360.                         * factorPointVolatility (iFactorIndex, (int) dblDate, iForwardDate2);

  362.                 return dblCrossVolProduct;
  363.             }
  364.         };

  366.         return crossVolR1ToR1.integrate (_iSpotDate, iTerminalDate);
  367.     }
  368. }
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