R1JointDiffusion.java

  1. package org.drip.sample.numeraire;

  3. import org.drip.measure.discrete.SequenceGenerator;
  4. import org.drip.measure.dynamics.DiffusionEvaluatorLogarithmic;
  5. import org.drip.measure.process.DiffusionEvolver;
  6. import org.drip.measure.realization.*;
  7. import org.drip.numerical.common.FormatUtil;
  8. import org.drip.numerical.linearalgebra.Matrix;
  9. import org.drip.service.env.EnvManager;

  11. /*
  12.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  13.  */

  15. /*!
  16.  * Copyright (C) 2018 Lakshmi Krishnamurthy
  17.  * Copyright (C) 2017 Lakshmi Krishnamurthy
  18.  * 
  19.  *  This file is part of DRIP, a free-software/open-source library for buy/side financial/trading model
  20.  *      libraries targeting analysts and developers
  21.  *      https://lakshmidrip.github.io/DRIP/
  22.  *  
  23.  *  DRIP is composed of four main libraries:
  24.  *  
  25.  *  - DRIP Fixed Income - https://lakshmidrip.github.io/DRIP-Fixed-Income/
  26.  *  - DRIP Asset Allocation - https://lakshmidrip.github.io/DRIP-Asset-Allocation/
  27.  *  - DRIP Numerical Optimizer - https://lakshmidrip.github.io/DRIP-Numerical-Optimizer/
  28.  *  - DRIP Statistical Learning - https://lakshmidrip.github.io/DRIP-Statistical-Learning/
  29.  * 
  30.  *  - DRIP Fixed Income: Library for Instrument/Trading Conventions, Treasury Futures/Options,
  31.  *      Funding/Forward/Overnight Curves, Multi-Curve Construction/Valuation, Collateral Valuation and XVA
  32.  *      Metric Generation, Calibration and Hedge Attributions, Statistical Curve Construction, Bond RV
  33.  *      Metrics, Stochastic Evolution and Option Pricing, Interest Rate Dynamics and Option Pricing, LMM
  34.  *      Extensions/Calibrations/Greeks, Algorithmic Differentiation, and Asset Backed Models and Analytics.
  35.  * 
  36.  *  - DRIP Asset Allocation: Library for model libraries for MPT framework, Black Litterman Strategy
  37.  *      Incorporator, Holdings Constraint, and Transaction Costs.
  38.  * 
  39.  *  - DRIP Numerical Optimizer: Library for Numerical Optimization and Spline Functionality.
  40.  * 
  41.  *  - DRIP Statistical Learning: Library for Statistical Evaluation and Machine Learning.
  42.  * 
  43.  *  Licensed under the Apache License, Version 2.0 (the "License");
  44.  *      you may not use this file except in compliance with the License.
  45.  *   
  46.  *  You may obtain a copy of the License at
  47.  *      http://www.apache.org/licenses/LICENSE-2.0
  48.  *  
  49.  *  Unless required by applicable law or agreed to in writing, software
  50.  *      distributed under the License is distributed on an "AS IS" BASIS,
  51.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  52.  *  
  53.  *  See the License for the specific language governing permissions and
  54.  *      limitations under the License.
  55.  */

  57. /**
  58.  * R1JointDiffusion demonstrates the Joint Evolution of R^1 Diffusion Variates - the Continuous Asset, the
  59.  *  Collateral, the Bank, and the Counter-Party Numeraires involved in the Dynamic XVA Replication Portfolio
  60.  *  of the Burgard and Kjaer (2011) Methodology. The References are:
  61.  *  
  62.  *  - Burgard, C., and M. Kjaer (2014): PDE Representations of Derivatives with Bilateral Counter-party Risk
  63.  *      and Funding Costs, Journal of Credit Risk, 7 (3) 1-19.
  64.  *  
  65.  *  - Cesari, G., J. Aquilina, N. Charpillon, X. Filipovic, G. Lee, and L. Manda (2009): Modeling, Pricing,
  66.  *      and Hedging Counter-party Credit Exposure - A Technical Guide, Springer Finance, New York.
  67.  *  
  68.  *  - Gregory, J. (2009): Being Two-faced over Counter-party Credit Risk, Risk 20 (2) 86-90.
  69.  *  
  70.  *  - Li, B., and Y. Tang (2007): Quantitative Analysis, Derivatives Modeling, and Trading Strategies in the
  71.  *      Presence of Counter-party Credit Risk for the Fixed Income Market, World Scientific Publishing,
  72.  *      Singapore.
  73.  * 
  74.  *  - Piterbarg, V. (2010): Funding Beyond Discounting: Collateral Agreements and Derivatives Pricing, Risk
  75.  *      21 (2) 97-102.
  76.  * 
  77.  * @author Lakshmi Krishnamurthy
  78.  */

  80. public class R1JointDiffusion {

  82.     private static final double[][] NumeraireSequence (
  83.         final int iCount,
  84.         final double[][] aadblCorrelation,
  85.         final String strHeader)
  86.         throws Exception
  87.     {
  88.         double[][] aadblGaussianJoint = SequenceGenerator.GaussianJoint (
  89.             iCount,
  90.             aadblCorrelation
  91.         );

  93.         System.out.println();

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

  97.         System.out.println (strHeader);

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

  101.         for (int i = 0; i < iCount; ++i) {
  102.             String strDump = "\t||" + FormatUtil.FormatDouble (i, 2, 0, 1.) + " |";

  104.             for (int j = 0; j < aadblCorrelation.length; ++j)
  105.                 strDump = strDump + " " + FormatUtil.FormatDouble (aadblGaussianJoint[i][j], 1, 6, 1.) + " |";

  107.             System.out.println (strDump + "|");
  108.         }

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

  112.         System.out.println();

  114.         return Matrix.Transpose (aadblGaussianJoint);
  115.     }

  117.     public static final void main (
  118.         final String[] astrArgs)
  119.         throws Exception
  120.     {
  121.         EnvManager.InitEnv ("");

  123.         double dblTimeWidth = 1. / 24.;
  124.         double dblTime = 1.;
  125.         double[][] aadblCorrelation = new double[][] {
  126.             {1.00, 0.20, 0.15, 0.05}, // #0 ASSET
  127.             {0.20, 1.00, 0.13, 0.25}, // #1 COLLATERAL
  128.             {0.15, 0.13, 1.00, 0.00}, // #2 BANK
  129.             {0.05, 0.25, 0.00, 1.00}  // #3 COUNTER PARTY
  130.         };
  131.         double dblAssetDrift = 0.06;
  132.         double dblAssetVolatility = 0.15;
  133.         double dblTerminalBankNumeraire = 1.;
  134.         double dblTerminalAssetNumeraire = 1.;
  135.         double dblTerminalCollateralNumeraire = 1.;

  137.         int iNumTimeStep = (int) (dblTime / dblTimeWidth);
  138.         double[] adblTimeWidth = new double[iNumTimeStep];

  140.         for (int i = 0; i < iNumTimeStep; ++i)
  141.             adblTimeWidth[i] = dblTimeWidth;

  143.         DiffusionEvolver meAsset = new DiffusionEvolver (
  144.             DiffusionEvaluatorLogarithmic.Standard (
  145.                 dblAssetDrift,
  146.                 dblAssetVolatility
  147.             )
  148.         );

  150.         double[][] aadblNumeraireTimeSeries = NumeraireSequence (
  151.             iNumTimeStep,
  152.             aadblCorrelation,
  153.             "\t|| ASSET, COLLATERAL, BANK, COUNTER PARTY REALIZATION ||"
  154.         );

  156.         JumpDiffusionEdge[] aR1AssetLR = meAsset.incrementSequence (
  157.             new JumpDiffusionVertex (
  158.                 dblTime,
  159.                 dblTerminalAssetNumeraire,
  160.                 0.,
  161.                 false
  162.             ),
  163.             JumpDiffusionEdgeUnit.Diffusion (
  164.                 adblTimeWidth,
  165.                 aadblNumeraireTimeSeries[0]
  166.             ),
  167.             -1. * dblTimeWidth
  168.         );

  170.         JumpDiffusionEdge[] aR1CollateralLR = meAsset.incrementSequence (
  171.             new JumpDiffusionVertex (
  172.                 dblTime,
  173.                 dblTerminalCollateralNumeraire,
  174.                 0.,
  175.                 false
  176.             ),
  177.             JumpDiffusionEdgeUnit.Diffusion (
  178.                 adblTimeWidth,
  179.                 aadblNumeraireTimeSeries[1]
  180.             ),
  181.             -1. * dblTimeWidth
  182.         );

  184.         JumpDiffusionEdge[] aR1BankLR = meAsset.incrementSequence (
  185.             new JumpDiffusionVertex (
  186.                 dblTime,
  187.                 dblTerminalBankNumeraire,
  188.                 0.,
  189.                 false
  190.             ),
  191.             JumpDiffusionEdgeUnit.Diffusion (
  192.                 adblTimeWidth,
  193.                 aadblNumeraireTimeSeries[2]
  194.             ),
  195.             -1. * dblTimeWidth
  196.         );

  198.         JumpDiffusionEdge[] aR1CounterPartyLR = meAsset.incrementSequence (
  199.             new JumpDiffusionVertex (
  200.                 dblTime,
  201.                 dblTerminalBankNumeraire,
  202.                 0.,
  203.                 false
  204.             ),
  205.             JumpDiffusionEdgeUnit.Diffusion (
  206.                 adblTimeWidth,
  207.                 aadblNumeraireTimeSeries[3]
  208.             ),
  209.             -1. * dblTimeWidth
  210.         );

  212.         System.out.println();

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

  216.         System.out.println("\t||                  BURGARD & KJAER (2011) CORRELATED JOINT ASSET/COLLATERAL/BANK/COUNTER-PARTY NUMERAIRE EVOLUTION                 ||");

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

  220.         System.out.println("\t||    L -> R:                                                                                                                       ||");

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

  224.         System.out.println("\t||          - Asset Numeraire Finish Value                                                                                          ||");

  226.         System.out.println("\t||          - Asset Numeraire Start Value                                                                                           ||");

  228.         System.out.println("\t||          - Asset Numeraire Continuous Wander Realization                                                                         ||");

  230.         System.out.println("\t||          - Collateral Numeraire Finish Value                                                                                     ||");

  232.         System.out.println("\t||          - Collateral Numeraire Start Value                                                                                      ||");

  234.         System.out.println("\t||          - Collateral Numeraire Continuous Wander Realization                                                                    ||");

  236.         System.out.println("\t||          - Bank Numeraire Finish Value                                                                                           ||");

  238.         System.out.println("\t||          - Bank Numeraire Start Value                                                                                            ||");

  240.         System.out.println("\t||          - Bank Numeraire Continuous Wander Realization                                                                          ||");

  242.         System.out.println("\t||          - Counter-Party Numeraire Finish Value                                                                                  ||");

  244.         System.out.println("\t||          - Counter-Party Numeraire Start Value                                                                                   ||");

  246.         System.out.println("\t||          - Counter-Party Numeraire Continuous Wander Realization                                                                 ||");

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

  250.         for (int i = 0; i < iNumTimeStep; ++i) {
  251.             dblTime = dblTime - dblTimeWidth;

  253.             System.out.println (
  254.                 "\t|| " +
  255.                 FormatUtil.FormatDouble (dblTime, 1, 4, 1.) + " => " +
  256.                 FormatUtil.FormatDouble (aR1AssetLR[i].start(), 1, 4, 1.) + " | " +
  257.                 FormatUtil.FormatDouble (aR1AssetLR[i].finish(), 1, 4, 1.) + " | " +
  258.                 FormatUtil.FormatDouble (aR1AssetLR[i].diffusionWander(), 1, 4, 1.) + " ||" +
  259.                 FormatUtil.FormatDouble (aR1CollateralLR[i].start(), 1, 4, 1.) + " | " +
  260.                 FormatUtil.FormatDouble (aR1CollateralLR[i].finish(), 1, 4, 1.) + " | " +
  261.                 FormatUtil.FormatDouble (aR1CollateralLR[i].diffusionWander(), 1, 4, 1.) + " ||" +
  262.                 FormatUtil.FormatDouble (aR1BankLR[i].start(), 1, 4, 1.) + " | " +
  263.                 FormatUtil.FormatDouble (aR1BankLR[i].finish(), 1, 4, 1.) + " | " +
  264.                 FormatUtil.FormatDouble (aR1BankLR[i].diffusionWander(), 1, 4, 1.) + " ||" +
  265.                 FormatUtil.FormatDouble (aR1CounterPartyLR[i].start(), 1, 4, 1.) + " | " +
  266.                 FormatUtil.FormatDouble (aR1CounterPartyLR[i].finish(), 1, 4, 1.) + " | " +
  267.                 FormatUtil.FormatDouble (aR1CounterPartyLR[i].diffusionWander(), 1, 4, 1.) + " ||"
  268.             );
  269.         }

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

  273.         System.out.println();
  274.     }
  275. }
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