FixFloatVABank.java

  1. package org.drip.sample.burgard2012;

  3. import org.drip.analytics.date.*;
  4. import org.drip.exposure.evolver.LatentStateVertexContainer;
  5. import org.drip.exposure.universe.*;
  6. import org.drip.measure.discrete.SequenceGenerator;
  7. import org.drip.measure.dynamics.DiffusionEvaluatorLinear;
  8. import org.drip.measure.process.DiffusionEvolver;
  9. import org.drip.measure.realization.*;
  10. import org.drip.numerical.common.FormatUtil;
  11. import org.drip.service.env.EnvManager;
  12. import org.drip.state.identifier.OTCFixFloatLabel;
  13. import org.drip.xva.gross.*;
  14. import org.drip.xva.netting.CollateralGroupPath;
  15. import org.drip.xva.strategy.*;
  16. import org.drip.xva.vertex.AlbaneseAndersen;

  18. /*
  19.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  20.  */

  22. /*!
  23.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  24.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  25.  * Copyright (C) 2018 Lakshmi Krishnamurthy
  26.  * Copyright (C) 2017 Lakshmi Krishnamurthy
  27.  * 
  28.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  29.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  30.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  31.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  32.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  33.  *      and computational support.
  34.  *  
  35.  *      https://lakshmidrip.github.io/DROP/
  36.  *  
  37.  *  DROP is composed of three modules:
  38.  *  
  39.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  40.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  41.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  42.  * 
  43.  *  DROP Product Core implements libraries for the following:
  44.  *  - Fixed Income Analytics
  45.  *  - Loan Analytics
  46.  *  - Transaction Cost Analytics
  47.  * 
  48.  *  DROP Portfolio Core implements libraries for the following:
  49.  *  - Asset Allocation Analytics
  50.  *  - Asset Liability Management Analytics
  51.  *  - Capital Estimation Analytics
  52.  *  - Exposure Analytics
  53.  *  - Margin Analytics
  54.  *  - XVA Analytics
  55.  * 
  56.  *  DROP Computational Core implements libraries for the following:
  57.  *  - Algorithm Support
  58.  *  - Computation Support
  59.  *  - Function Analysis
  60.  *  - Model Validation
  61.  *  - Numerical Analysis
  62.  *  - Numerical Optimizer
  63.  *  - Spline Builder
  64.  *  - Statistical Learning
  65.  * 
  66.  *  Documentation for DROP is Spread Over:
  67.  * 
  68.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  69.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  70.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  71.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  72.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  73.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  74.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  75.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  76.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  77.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  78.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  79.  * 
  80.  *  Licensed under the Apache License, Version 2.0 (the "License");
  81.  *      you may not use this file except in compliance with the License.
  82.  *   
  83.  *  You may obtain a copy of the License at
  84.  *      http://www.apache.org/licenses/LICENSE-2.0
  85.  *  
  86.  *  Unless required by applicable law or agreed to in writing, software
  87.  *      distributed under the License is distributed on an "AS IS" BASIS,
  88.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  89.  *  
  90.  *  See the License for the specific language governing permissions and
  91.  *      limitations under the License.
  92.  */

  94. /**
  95.  * <i>FixFloatVABank</i> illustrates the Fix-Float Swap Valuation Adjustment Metrics Dependence on the Bank
  96.  * Spread using the Set of Netting Group Exposure Simulations. The References are:
  97.  *  
  98.  * <br><br>
  99.  *  <ul>
  100.  *      <li>
  101.  *          Burgard, C., and M. Kjaer (2014): PDE Representations of Derivatives with Bilateral Counter-party
  102.  *              Risk and Funding Costs <i>Journal of Credit Risk</i> <b>7 (3)</b> 1-19
  103.  *      </li>
  104.  *      <li>
  105.  *          Burgard, C., and M. Kjaer (2014): In the Balance <i>Risk</i> <b>24 (11)</b> 72-75
  106.  *      </li>
  107.  *      <li>
  108.  *          Gregory, J. (2009): Being Two-faced over Counter-party Credit Risk <i>Risk</i> <b>20 (2)</b>
  109.  *              86-90
  110.  *      </li>
  111.  *      <li>
  112.  *          Li, B., and Y. Tang (2007): <i>Quantitative Analysis, Derivatives Modeling, and Trading
  113.  *              Strategies in the Presence of Counter-party Credit Risk for the Fixed Income Market</i>
  114.  *              <b>World Scientific Publishing</b> Singapore
  115.  *      </li>
  116.  *      <li>
  117.  *          Piterbarg, V. (2010): Funding Beyond Discounting: Collateral Agreements and Derivatives Pricing
  118.  *              <i>Risk</i> <b>21 (2)</b> 97-102
  119.  *      </li>
  120.  *  </ul>
  121.  *  
  122.  * <br><br>
  123.  *  <ul>
  124.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/PortfolioCore.md">Portfolio Core Module</a></li>
  125.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/XVAAnalyticsLibrary.md">XVA Analytics Library</a></li>
  126.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">DROP API Construction and Usage</a></li>
  127.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/burgard2012/README.md">Burgard Kjaer (2012) Valuation Adjustments</a></li>
  128.  *  </ul>
  129.  * <br><br>
  130.  * 
  131.  * @author Lakshmi Krishnamurthy
  132.  */

  134. public class FixFloatVABank {

  136.     private static final double[][] ATMSwapRateOffsetRealization (
  137.         final DiffusionEvolver deATMSwapRateOffset,
  138.         final double dblATMSwapRateOffsetInitial,
  139.         final double dblTime,
  140.         final double dblTimeWidth,
  141.         final int iNumStep,
  142.         final int iNumSimulation)
  143.         throws Exception
  144.     {
  145.         double[][] aablATMSwapRateOffset = new double[iNumSimulation][iNumStep + 1];
  146.         double[] adblTimeWidth = new double[iNumStep];

  148.         for (int i = 0; i < iNumStep; ++i)
  149.             adblTimeWidth[i] = dblTimeWidth;

  151.         for (int i = 0; i < iNumSimulation; ++i) {
  152.             JumpDiffusionEdge[] aJDE = deATMSwapRateOffset.incrementSequence (
  153.                 new JumpDiffusionVertex (
  154.                     dblTime,
  155.                     dblATMSwapRateOffsetInitial,
  156.                     0.,
  157.                     false
  158.                 ),
  159.                 JumpDiffusionEdgeUnit.Diffusion (
  160.                     adblTimeWidth,
  161.                     SequenceGenerator.Gaussian (iNumStep)
  162.                 ),
  163.                 dblTimeWidth
  164.             );

  166.             aablATMSwapRateOffset[i][0] = dblATMSwapRateOffsetInitial;

  168.             for (int j = 1; j <= iNumStep; ++j)
  169.                 aablATMSwapRateOffset[i][j] = aJDE[j - 1].finish();
  170.         }

  172.         return aablATMSwapRateOffset;
  173.     }

  175.     public static final void VA (
  176.         final double dblBankHazardRate)
  177.         throws Exception
  178.     {
  179.         int iNumStep = 10;
  180.         double dblTime = 5.;
  181.         int iNumPath = 10000;
  182.         double dblATMSwapRateOffsetDrift = 0.0;
  183.         double dblATMSwapRateOffsetVolatility = 0.15;
  184.         double dblATMSwapRateOffsetInitial = 0.;
  185.         double dblCSADrift = 0.01;
  186.         double dblBankRecoveryRate = 0.40;
  187.         double dblCounterPartyHazardRate = 0.025;
  188.         double dblCounterPartyRecoveryRate = 0.30;

  190.         double dblTimeWidth = dblTime / iNumStep;
  191.         MarketVertex[] aMV = new MarketVertex[iNumStep + 1];
  192.         JulianDate[] adtVertex = new JulianDate[iNumStep + 1];
  193.         MonoPathExposureAdjustment[] aMPEA = new MonoPathExposureAdjustment[iNumPath];
  194.         double dblBankFundingSpread = dblBankHazardRate / (1. - dblBankRecoveryRate);
  195.         double dblCounterPartyFundingSpread = dblCounterPartyHazardRate / (1. - dblCounterPartyRecoveryRate);

  197.         JulianDate dtSpot = DateUtil.Today();

  199.         double[][] aablATMSwapRateOffset = ATMSwapRateOffsetRealization (
  200.             new DiffusionEvolver (
  201.                 DiffusionEvaluatorLinear.Standard (
  202.                     dblATMSwapRateOffsetDrift,
  203.                     dblATMSwapRateOffsetVolatility
  204.                 )
  205.             ),
  206.             dblATMSwapRateOffsetInitial,
  207.             dblTime,
  208.             dblTimeWidth,
  209.             iNumStep,
  210.             iNumPath
  211.         );

  213.         for (int i = 0; i <= iNumStep; ++i)
  214.         {
  215.             LatentStateVertexContainer latentStateVertexContainer = new LatentStateVertexContainer();

  217.             latentStateVertexContainer.add (
  218.                 OTCFixFloatLabel.Standard ("USD-3M-10Y"),
  219.                 Double.NaN
  220.             );

  222.             aMV[i] = MarketVertex.Nodal (
  223.                 adtVertex[i] = dtSpot.addMonths (6 * i),
  224.                 0.,
  225.                 1.,
  226.                 dblCSADrift,
  227.                 Math.exp (-0.5 * dblCSADrift * iNumStep),
  228.                 new MarketVertexEntity (
  229.                     Math.exp (-0.5 * dblBankHazardRate * i),
  230.                     dblBankHazardRate,
  231.                     dblBankRecoveryRate,
  232.                     dblBankFundingSpread,
  233.                     Math.exp (-0.5 * dblBankHazardRate * (1. - dblBankRecoveryRate) * iNumStep),
  234.                     Double.NaN,
  235.                     Double.NaN,
  236.                     Double.NaN
  237.                 ),
  238.                 new MarketVertexEntity (
  239.                     Math.exp (-0.5 * dblCounterPartyHazardRate * i),
  240.                     dblCounterPartyHazardRate,
  241.                     dblCounterPartyRecoveryRate,
  242.                     dblCounterPartyFundingSpread,
  243.                     Math.exp (-0.5 * dblCounterPartyHazardRate * (1. - dblCounterPartyRecoveryRate) * iNumStep),
  244.                     Double.NaN,
  245.                     Double.NaN,
  246.                     Double.NaN
  247.                 ),
  248.                 latentStateVertexContainer
  249.             );
  250.         }

  252.         MarketPath mp = MarketPath.FromMarketVertexArray (aMV);

  254.         for (int i = 0; i < iNumPath; ++i) {
  255.             AlbaneseAndersen[] aHGVR = new AlbaneseAndersen[iNumStep + 1];

  257.             for (int j = 0; j <= iNumStep; ++j)
  258.                 aHGVR[j] = new AlbaneseAndersen (
  259.                     adtVertex[j],
  260.                     dblTimeWidth * (iNumStep - j) * aablATMSwapRateOffset[i][j],
  261.                     0.,
  262.                     0.
  263.                 );

  265.             CollateralGroupPath[] aHGP = new CollateralGroupPath[] {
  266.                 new CollateralGroupPath (
  267.                     aHGVR,
  268.                     mp
  269.                 )
  270.             };

  272.             aMPEA[i] = new MonoPathExposureAdjustment (
  273.                 new AlbaneseAndersenFundingGroupPath[] {
  274.                     AlbaneseAndersenFundingGroupPath.Mono (
  275.                         new AlbaneseAndersenNettingGroupPath (
  276.                             aHGP,
  277.                             mp
  278.                         ),
  279.                         mp
  280.                     )
  281.                 }
  282.             );
  283.         }

  285.         ExposureAdjustmentAggregator eaa = new ExposureAdjustmentAggregator (aMPEA);

  287.         System.out.println ("\t|| " +
  288.             FormatUtil.FormatDouble (dblBankHazardRate, 3, 0, 10000.) + " bp => " +
  289.             FormatUtil.FormatDouble (eaa.ucva().amount(), 1, 2, 100.) + "% | " +
  290.             FormatUtil.FormatDouble (eaa.ftdcva().amount(), 1, 2, 100.) + "% | " +
  291.             FormatUtil.FormatDouble (eaa.cva().amount(), 1, 2, 100.) + "% | " +
  292.             FormatUtil.FormatDouble (eaa.cvacl().amount(), 1, 2, 100.) + "% | " +
  293.             FormatUtil.FormatDouble (eaa.dva().amount(), 1, 2, 100.) + "% | " +
  294.             FormatUtil.FormatDouble (eaa.fva().amount(), 1, 2, 100.) + "% | " +
  295.             FormatUtil.FormatDouble (eaa.fda().amount(), 1, 2, 100.) + "% | " +
  296.             FormatUtil.FormatDouble (eaa.fca().amount(), 1, 2, 100.) + "% | " +
  297.             FormatUtil.FormatDouble (eaa.fba().amount(), 1, 2, 100.) + "% | " +
  298.             FormatUtil.FormatDouble (eaa.sfva().amount(), 1, 2, 100.) + "% | " +
  299.             FormatUtil.FormatDouble (eaa.total(), 1, 2, 100.) + "% ||"
  300.         );
  301.     }

  303.     public static final void main (
  304.         final String[] astrArgs)
  305.         throws Exception
  306.     {
  307.         EnvManager.InitEnv ("");

  309.         double[] adblBankHazardRate = new double[] {
  310.             0.0025,
  311.             0.0050,
  312.             0.0075,
  313.             0.0100,
  314.             0.0125,
  315.             0.0150,
  316.             0.0175,
  317.             0.0200,
  318.             0.0225,
  319.             0.0250,
  320.             0.0275,
  321.             0.0300
  322.         };

  324.         System.out.println();

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

  328.         System.out.println ("\t||                                      VA DEPENDENCE ON BANK HAZARD RATE                                      ||");

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

  332.         System.out.println ("\t||  Hazard =>  UCVA  | FTDCVA |   CVA  |  CVACL |   DVA  |   FVA  |   FDA  |   FCA  |   FBA  |  SFVA  |  Total ||");

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

  336.         for (double dblBankHazardRate : adblBankHazardRate)
  337.             VA (dblBankHazardRate);

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

  341.         System.out.println();

  343.         EnvManager.TerminateEnv();
  344.     }
  345. }
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