CrossGroupPrincipalCovariance.java

  1. package org.drip.sample.simmvariance;

  3. import org.drip.numerical.common.FormatUtil;
  4. import org.drip.numerical.common.NumberUtil;
  5. import org.drip.numerical.eigen.EigenComponent;
  6. import org.drip.numerical.eigen.PowerIterationComponentExtractor;
  7. import org.drip.numerical.linearalgebra.Matrix;
  8. import org.drip.service.env.EnvManager;

  10. /*
  11.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  12.  */

  14. /*!
  15.  * Copyright (C) 2018 Lakshmi Krishnamurthy
  16.  * 
  17.  *  This file is part of DRIP, a free-software/open-source library for buy/side financial/trading model
  18.  *      libraries targeting analysts and developers
  19.  *      https://lakshmidrip.github.io/DRIP/
  20.  *  
  21.  *  DRIP is composed of four main libraries:
  22.  *  
  23.  *  - DRIP Fixed Income - https://lakshmidrip.github.io/DRIP-Fixed-Income/
  24.  *  - DRIP Asset Allocation - https://lakshmidrip.github.io/DRIP-Asset-Allocation/
  25.  *  - DRIP Numerical Optimizer - https://lakshmidrip.github.io/DRIP-Numerical-Optimizer/
  26.  *  - DRIP Statistical Learning - https://lakshmidrip.github.io/DRIP-Statistical-Learning/
  27.  * 
  28.  *  - DRIP Fixed Income: Library for Instrument/Trading Conventions, Treasury Futures/Options,
  29.  *      Funding/Forward/Overnight Curves, Multi-Curve Construction/Valuation, Collateral Valuation and XVA
  30.  *      Metric Generation, Calibration and Hedge Attributions, Statistical Curve Construction, Bond RV
  31.  *      Metrics, Stochastic Evolution and Option Pricing, Interest Rate Dynamics and Option Pricing, LMM
  32.  *      Extensions/Calibrations/Greeks, Algorithmic Differentiation, and Asset Backed Models and Analytics.
  33.  * 
  34.  *  - DRIP Asset Allocation: Library for model libraries for MPT framework, Black Litterman Strategy
  35.  *      Incorporator, Holdings Constraint, and Transaction Costs.
  36.  * 
  37.  *  - DRIP Numerical Optimizer: Library for Numerical Optimization and Spline Functionality.
  38.  * 
  39.  *  - DRIP Statistical Learning: Library for Statistical Evaluation and Machine Learning.
  40.  * 
  41.  *  Licensed under the Apache License, Version 2.0 (the "License");
  42.  *      you may not use this file except in compliance with the License.
  43.  *   
  44.  *  You may obtain a copy of the License at
  45.  *      http://www.apache.org/licenses/LICENSE-2.0
  46.  *  
  47.  *  Unless required by applicable law or agreed to in writing, software
  48.  *      distributed under the License is distributed on an "AS IS" BASIS,
  49.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  50.  *  
  51.  *  See the License for the specific language governing permissions and
  52.  *      limitations under the License.
  53.  */

  55. /**
  56.  * CrossGroupPrincipalCovariance demonstrates the Computation of the Cross Risk Group Principal Component
  57.  *  Co-variance using the Actual Risk Group Principal Component. The References are:
  58.  *  
  59.  *  - Andersen, L. B. G., M. Pykhtin, and A. Sokol (2017): Credit Exposure in the Presence of Initial Margin,
  60.  *      https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2806156, eSSRN.
  61.  *  
  62.  *  - Albanese, C., S. Caenazzo, and O. Frankel (2017): Regression Sensitivities for Initial Margin
  63.  *      Calculations, https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2763488, eSSRN.
  64.  *  
  65.  *  - Anfuso, F., D. Aziz, P. Giltinan, and K. Loukopoulus (2017): A Sound Modeling and Back-testing
  66.  *      Framework for Forecasting Initial Margin Requirements,
  67.  *      https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2716279, eSSRN.
  68.  *  
  69.  *  - Caspers, P., P. Giltinan, R. Lichters, and N. Nowaczyk (2017): Forecasting Initial Margin Requirements
  70.  *      - A Model Evaluation https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2911167, eSSRN.
  71.  *  
  72.  *  - International Swaps and Derivatives Association (2017): SIMM v2.0 Methodology,
  73.  *      https://www.isda.org/a/oFiDE/isda-simm-v2.pdf.
  74.  * 
  75.  * @author Lakshmi Krishnamurthy
  76.  */

  78. public class CrossGroupPrincipalCovariance
  79. {

  81.     public static final void main (
  82.         final String[] argumentArray)
  83.         throws Exception
  84.     {
  85.         EnvManager.InitEnv ("");

  87.         double[][] correlationMatrix =
  88.         {
  89.             {1.00, 0.99, 0.79, 0.67, 0.53, 0.42, 0.37, 0.30, 0.22, 0.18, 0.16, 0.12},
  90.             {0.99, 1.00, 0.79, 0.67, 0.53, 0.42, 0.37, 0.30, 0.22, 0.18, 0.16, 0.12},
  91.             {0.79, 0.79, 1.00, 0.85, 0.69, 0.57, 0.50, 0.42, 0.32, 0.25, 0.23, 0.20},
  92.             {0.67, 0.67, 0.85, 1.00, 0.86, 0.76, 0.69, 0.59, 0.47, 0.40, 0.37, 0.32},
  93.             {0.53, 0.53, 0.69, 0.86, 1.00, 0.93, 0.87, 0.77, 0.63, 0.57, 0.54, 0.50},
  94.             {0.42, 0.42, 0.57, 0.76, 0.93, 1.00, 0.98, 0.90, 0.77, 0.70, 0.67, 0.63},
  95.             {0.37, 0.37, 0.50, 0.69, 0.87, 0.98, 1.00, 0.96, 0.84, 0.78, 0.75, 0.71},
  96.             {0.30, 0.30, 0.42, 0.59, 0.77, 0.90, 0.96, 1.00, 0.93, 0.89, 0.86, 0.82},
  97.             {0.22, 0.22, 0.32, 0.47, 0.63, 0.77, 0.84, 0.93, 1.00, 0.98, 0.96, 0.94},
  98.             {0.18, 0.18, 0.25, 0.40, 0.57, 0.70, 0.78, 0.89, 0.98, 1.00, 0.99, 0.98},
  99.             {0.16, 0.16, 0.23, 0.37, 0.54, 0.67, 0.75, 0.86, 0.96, 0.99, 1.00, 0.99},
  100.             {0.12, 0.12, 0.20, 0.32, 0.50, 0.63, 0.71, 0.82, 0.94, 0.98, 0.99, 1.00}
  101.         };
  102.         double crossBucketCorrelation = 0.27;

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

  107.         System.out.println
  108.             ("\t||                                                       TENOR CORRELATION MATRIX FOR GIRR                                                       |");

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

  113.         NumberUtil.PrintMatrix (
  114.             "\t|| GIRR2.0",
  115.             correlationMatrix
  116.         );

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

  121.         System.out.println();

  123.         PowerIterationComponentExtractor pice = new PowerIterationComponentExtractor (
  124.             30,
  125.             0.000001,
  126.             false
  127.         );

  129.         EigenComponent principalComponent = pice.principalComponent (correlationMatrix);

  131.         double[] rawEigenvector = principalComponent.eigenVector();

  133.         double rawEigenvalue = principalComponent.eigenValue();

  135.         double scaledEigenvalue = Math.sqrt (rawEigenvalue);

  137.         double[] scaledEigenvector = new double[rawEigenvector.length];

  139.         String rawEigenDump    = "\t||   RAW    || " +
  140.             "[" + FormatUtil.FormatDouble (rawEigenvalue, 1, 4, 1.) + "] => ";

  142.         String scaledEigenDump = "\t||  SCALED  || " +
  143.             "[" + FormatUtil.FormatDouble (scaledEigenvalue, 1, 4, 1.) + "] => ";

  145.         for (int i = 0; i < rawEigenvector.length; ++i)
  146.         {
  147.             rawEigenDump += FormatUtil.FormatDouble (rawEigenvector[i], 1, 4, 1.) + " | ";

  149.             scaledEigenDump += FormatUtil.FormatDouble (
  150.                 scaledEigenvector[i] = scaledEigenvalue * rawEigenvector[i], 1, 4, 1.
  151.             ) + " | ";
  152.         }

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

  157.         System.out.println (rawEigenDump);

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

  162.         System.out.println (scaledEigenDump);

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

  167.         System.out.println();

  169.         double[][] unadjustedOffDiagonalBlockMatrix = Matrix.CrossProduct (
  170.             scaledEigenvector,
  171.             scaledEigenvector
  172.         );

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

  177.         System.out.println
  178.             ("\t||                                                   GIRR 2.0 UNADJUSTED OFF-DIAGONAL COVARIANCE ENTRIES                                                    |");

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

  183.         NumberUtil.PrintMatrix (
  184.             "\t|| OFF-DIAGONAL UNADJ",
  185.             unadjustedOffDiagonalBlockMatrix
  186.         );

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

  191.         System.out.println();

  193.         double[][] adjustedOffDiagonalBlockMatrix = Matrix.Scale2D (
  194.             unadjustedOffDiagonalBlockMatrix,
  195.             crossBucketCorrelation
  196.         );

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

  201.         System.out.println
  202.             ("\t||                                                   GIRR 2.0 ADJUSTED OFF-DIAGONAL COVARIANCE ENTRIES                                                    |");

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

  207.         NumberUtil.PrintMatrix (
  208.             "\t|| OFF-DIAGONAL ADJ",
  209.             adjustedOffDiagonalBlockMatrix
  210.         );

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

  215.         EnvManager.TerminateEnv();
  216.     }
  217. }
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