ContinuousForwardRateVolatility.java

  1. package org.drip.sample.lmm;

  3. import org.drip.analytics.date.JulianDate;
  4. import org.drip.analytics.definition.MarketSurface;
  5. import org.drip.dynamics.lmm.LognormalLIBORVolatility;
  6. import org.drip.numerical.common.FormatUtil;
  7. import org.drip.sequence.random.*;
  8. import org.drip.service.env.EnvManager;
  9. import org.drip.spline.basis.PolynomialFunctionSetParams;
  10. import org.drip.spline.params.*;
  11. import org.drip.spline.stretch.MultiSegmentSequenceBuilder;
  12. import org.drip.state.creator.*;
  13. import org.drip.state.forward.ForwardCurve;
  14. import org.drip.state.identifier.ForwardLabel;

  16. /*
  17.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  18.  */

  20. /*!
  21.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  22.  * Copyright (C) 2018 Lakshmi Krishnamurthy
  23.  * Copyright (C) 2017 Lakshmi Krishnamurthy
  24.  * Copyright (C) 2016 Lakshmi Krishnamurthy
  25.  * Copyright (C) 2015 Lakshmi Krishnamurthy
  26.  * 
  27.  *  This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
  28.  *      calculations, valuation adjustment, and portfolio construction within and across fixed income,
  29.  *      credit, commodity, equity, FX, and structured products.
  30.  *  
  31.  *      https://lakshmidrip.github.io/DROP/
  32.  *  
  33.  *  DROP is composed of three modules:
  34.  *  
  35.  *  - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
  36.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  37.  *  - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
  38.  * 
  39.  *  DROP Analytics Core implements libraries for the following:
  40.  *  - Fixed Income Analytics
  41.  *  - Asset Backed Analytics
  42.  *  - XVA Analytics
  43.  *  - Exposure and Margin Analytics
  44.  * 
  45.  *  DROP Portfolio Core implements libraries for the following:
  46.  *  - Asset Allocation Analytics
  47.  *  - Transaction Cost Analytics
  48.  * 
  49.  *  DROP Numerical Core implements libraries for the following:
  50.  *  - Statistical Learning
  51.  *  - Numerical Optimizer
  52.  *  - Spline Builder
  53.  *  - Algorithm Support
  54.  * 
  55.  *  Documentation for DROP is Spread Over:
  56.  * 
  57.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  58.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  59.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  60.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  61.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  62.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  63.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  64.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  65.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  66.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  67.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  68.  * 
  69.  *  Licensed under the Apache License, Version 2.0 (the "License");
  70.  *      you may not use this file except in compliance with the License.
  71.  *   
  72.  *  You may obtain a copy of the License at
  73.  *      http://www.apache.org/licenses/LICENSE-2.0
  74.  *  
  75.  *  Unless required by applicable law or agreed to in writing, software
  76.  *      distributed under the License is distributed on an "AS IS" BASIS,
  77.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  78.  *  
  79.  *  See the License for the specific language governing permissions and
  80.  *      limitations under the License.
  81.  */

  83. /**
  84.  * <i>ContinuousForwardRateVolatility</i> demonstrates the Implying of the Volatility of the Continuously
  85.  * Compounded Forward Rate from the Corresponding LIBOR Forward Rate Volatility. The References are:
  86.  *  
  87.  * <br><br>
  88.  *  <ul>
  89.  *      <li>
  90.  *          Goldys, B., M. Musiela, and D. Sondermann (1994): Log-normality of Rates and Term Structure
  91.  *              Models, The University of New South Wales.
  92.  *      </li>
  93.  *      <li>
  94.  *          Musiela, M. (1994): Nominal Annual Rates and Log-normal Volatility Structure, The University of
  95.  *              New South Wales.
  96.  *      </li>
  97.  *      <li>
  98.  *          Brace, A., D. Gatarek, and M. Musiela (1997): The Market Model of Interest Rate Dynamics,
  99.  *              Mathematical Finance 7 (2), 127-155.
  100.  *      </li>
  101.  *  </ul>
  102.  *  
  103.  * <br><br>
  104.  *  <ul>
  105.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/AnalyticsCore.md">Analytics Core Module</a></li>
  106.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FixedIncomeAnalyticsLibrary.md">Fixed Income Analytics Library</a></li>
  107.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">Sample</a></li>
  108.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/lmm/README.md">LIBOR Market (LMM-BGM Variant) Evolution</a></li>
  109.  *  </ul>
  110.  * <br><br>
  111.  *
  112.  * @author Lakshmi Krishnamurthy
  113.  */

  115. public class ContinuousForwardRateVolatility {

  117.     private static final MarketSurface FlatVolatilitySurface (
  118.         final JulianDate dtStart,
  119.         final String strCurrency,
  120.         final double dblFlatVol)
  121.         throws Exception
  122.     {
  123.         return ScenarioMarketSurfaceBuilder.CustomSplineWireSurface (
  124.             "VIEW_TARGET_VOLATILITY_SURFACE",
  125.             dtStart,
  126.             strCurrency,
  127.             new double[] {
  128.                 dtStart.julian(),
  129.                 dtStart.addYears (2).julian(),
  130.                 dtStart.addYears (4).julian(),
  131.                 dtStart.addYears (6).julian(),
  132.                 dtStart.addYears (8).julian(),
  133.                 dtStart.addYears (10).julian()
  134.             },
  135.             new double[] {
  136.                 dtStart.julian(),
  137.                 dtStart.addYears (2).julian(),
  138.                 dtStart.addYears (4).julian(),
  139.                 dtStart.addYears (6).julian(),
  140.                 dtStart.addYears (8).julian(),
  141.                 dtStart.addYears (10).julian()
  142.             },
  143.             new double[][] {
  144.                 {dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol},
  145.                 {dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol},
  146.                 {dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol},
  147.                 {dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol},
  148.                 {dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol},
  149.                 {dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol},
  150.             },
  151.             new SegmentCustomBuilderControl (
  152.                 MultiSegmentSequenceBuilder.BASIS_SPLINE_POLYNOMIAL,
  153.                 new PolynomialFunctionSetParams (4),
  154.                 SegmentInelasticDesignControl.Create (
  155.                     2,
  156.                     2
  157.                 ),
  158.                 null,
  159.                 null
  160.             ),
  161.             new SegmentCustomBuilderControl (
  162.                 MultiSegmentSequenceBuilder.BASIS_SPLINE_POLYNOMIAL,
  163.                 new PolynomialFunctionSetParams (4),
  164.                 SegmentInelasticDesignControl.Create (
  165.                     2,
  166.                     2
  167.                 ),
  168.                 null,
  169.                 null
  170.             )
  171.         );
  172.     }

  174.     private static final void DisplayVolArray (
  175.         final String strTenor,
  176.         final double[] adblVol)
  177.     {
  178.         String strDump = "\t | " + strTenor + " => ";

  180.         for (int i = 0; i < adblVol.length; ++i)
  181.             strDump += FormatUtil.FormatDouble (adblVol[i], 1, 2, 100.) + "% |";

  183.         System.out.println (strDump);
  184.     }

  186.     public static void main (
  187.         final String[] astrArgs)
  188.         throws Exception
  189.     {
  190.         EnvManager.InitEnv ("");

  192.         String strTenor = "3M";
  193.         String strCurrency = "USD";
  194.         double dblFlatVol1 = 0.35;
  195.         double dblFlatVol2 = 0.42;
  196.         double dblFlatVol3 = 0.27;
  197.         double dblFlatForwardRate = 0.02;

  199.         int[] aiNumFactor = {
  200.             1, 2, 3
  201.         };

  203.         String[] astrForwardTenor = {
  204.             "1Y", "2Y", "3Y", "4Y", "5Y", "6Y", "7Y", "8Y"
  205.         };

  207.         ForwardLabel forwardLabel = ForwardLabel.Create (
  208.             strCurrency,
  209.             strTenor
  210.         );

  212.         JulianDate dtSpot = org.drip.analytics.date.DateUtil.Today();

  214.         MarketSurface mktSurfFlatVol1 = FlatVolatilitySurface (
  215.             dtSpot,
  216.             strCurrency,
  217.             dblFlatVol1
  218.         );

  220.         MarketSurface mktSurfFlatVol2 = FlatVolatilitySurface (
  221.             dtSpot,
  222.             strCurrency,
  223.             dblFlatVol2
  224.         );

  226.         MarketSurface mktSurfFlatVol3 = FlatVolatilitySurface (
  227.             dtSpot,
  228.             strCurrency,
  229.             dblFlatVol3
  230.         );

  232.         ForwardCurve fc = ScenarioForwardCurveBuilder.FlatForwardForwardCurve (
  233.             dtSpot,
  234.             forwardLabel,
  235.             dblFlatForwardRate
  236.         );

  238.         for (int iNumFactor : aiNumFactor) {
  239.             LognormalLIBORVolatility llv = new LognormalLIBORVolatility (
  240.                 dtSpot.julian(),
  241.                 forwardLabel,
  242.                 new MarketSurface[] {
  243.                     mktSurfFlatVol1,
  244.                     mktSurfFlatVol2,
  245.                     mktSurfFlatVol3
  246.                 },
  247.                 new PrincipalFactorSequenceGenerator (
  248.                     new UnivariateSequenceGenerator[] {
  249.                         new BoxMullerGaussian (
  250.                             0.,
  251.                             1.
  252.                         ),
  253.                         new BoxMullerGaussian (
  254.                             0.,
  255.                             1.
  256.                         ),
  257.                         new BoxMullerGaussian (
  258.                             0.,
  259.                             1.
  260.                         )
  261.                     },
  262.                     new double[][] {
  263.                         {1.0, 0.1, 0.2},
  264.                         {0.1, 1.0, 0.2},
  265.                         {0.2, 0.1, 1.0}
  266.                     },
  267.                     iNumFactor
  268.                 )
  269.             );

  271.             System.out.println ("\n\t |------------------------------|");

  273.             System.out.println ("\t |  CONTINUOUS FORWARD RATE VOL |");

  275.             System.out.println ("\t |    Num Factors: " + iNumFactor + "            |");

  277.             System.out.println ("\t |------------------------------|");

  279.             for (String strForwardTenor : astrForwardTenor)
  280.                 DisplayVolArray (
  281.                     strForwardTenor,
  282.                     llv.continuousForwardVolatility (
  283.                         dtSpot.addTenor (strForwardTenor).julian(),
  284.                         fc
  285.                     )
  286.                 );

  288.             System.out.println ("\t |------------------------------|");
  289.         }

  291.         EnvManager.TerminateEnv();
  292.     }
  293. }
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