CrossGroupPrincipalCovariance.java
package org.drip.sample.simmvariance;
import org.drip.numerical.common.FormatUtil;
import org.drip.numerical.common.NumberUtil;
import org.drip.numerical.eigen.EigenComponent;
import org.drip.numerical.eigen.PowerIterationComponentExtractor;
import org.drip.numerical.linearalgebra.Matrix;
import org.drip.service.env.EnvManager;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2018 Lakshmi Krishnamurthy
*
* This file is part of DRIP, a free-software/open-source library for buy/side financial/trading model
* libraries targeting analysts and developers
* https://lakshmidrip.github.io/DRIP/
*
* DRIP is composed of four main libraries:
*
* - DRIP Fixed Income - https://lakshmidrip.github.io/DRIP-Fixed-Income/
* - DRIP Asset Allocation - https://lakshmidrip.github.io/DRIP-Asset-Allocation/
* - DRIP Numerical Optimizer - https://lakshmidrip.github.io/DRIP-Numerical-Optimizer/
* - DRIP Statistical Learning - https://lakshmidrip.github.io/DRIP-Statistical-Learning/
*
* - DRIP Fixed Income: Library for Instrument/Trading Conventions, Treasury Futures/Options,
* Funding/Forward/Overnight Curves, Multi-Curve Construction/Valuation, Collateral Valuation and XVA
* Metric Generation, Calibration and Hedge Attributions, Statistical Curve Construction, Bond RV
* Metrics, Stochastic Evolution and Option Pricing, Interest Rate Dynamics and Option Pricing, LMM
* Extensions/Calibrations/Greeks, Algorithmic Differentiation, and Asset Backed Models and Analytics.
*
* - DRIP Asset Allocation: Library for model libraries for MPT framework, Black Litterman Strategy
* Incorporator, Holdings Constraint, and Transaction Costs.
*
* - DRIP Numerical Optimizer: Library for Numerical Optimization and Spline Functionality.
*
* - DRIP Statistical Learning: Library for Statistical Evaluation and Machine Learning.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
*
* You may obtain a copy of the License at
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
*
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/**
* CrossGroupPrincipalCovariance demonstrates the Computation of the Cross Risk Group Principal Component
* Co-variance using the Actual Risk Group Principal Component. The References are:
*
* - Andersen, L. B. G., M. Pykhtin, and A. Sokol (2017): Credit Exposure in the Presence of Initial Margin,
* https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2806156, eSSRN.
*
* - Albanese, C., S. Caenazzo, and O. Frankel (2017): Regression Sensitivities for Initial Margin
* Calculations, https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2763488, eSSRN.
*
* - Anfuso, F., D. Aziz, P. Giltinan, and K. Loukopoulus (2017): A Sound Modeling and Back-testing
* Framework for Forecasting Initial Margin Requirements,
* https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2716279, eSSRN.
*
* - Caspers, P., P. Giltinan, R. Lichters, and N. Nowaczyk (2017): Forecasting Initial Margin Requirements
* - A Model Evaluation https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2911167, eSSRN.
*
* - International Swaps and Derivatives Association (2017): SIMM v2.0 Methodology,
* https://www.isda.org/a/oFiDE/isda-simm-v2.pdf.
*
* @author Lakshmi Krishnamurthy
*/
public class CrossGroupPrincipalCovariance
{
public static final void main (
final String[] argumentArray)
throws Exception
{
EnvManager.InitEnv ("");
double[][] correlationMatrix =
{
{1.00, 0.99, 0.79, 0.67, 0.53, 0.42, 0.37, 0.30, 0.22, 0.18, 0.16, 0.12},
{0.99, 1.00, 0.79, 0.67, 0.53, 0.42, 0.37, 0.30, 0.22, 0.18, 0.16, 0.12},
{0.79, 0.79, 1.00, 0.85, 0.69, 0.57, 0.50, 0.42, 0.32, 0.25, 0.23, 0.20},
{0.67, 0.67, 0.85, 1.00, 0.86, 0.76, 0.69, 0.59, 0.47, 0.40, 0.37, 0.32},
{0.53, 0.53, 0.69, 0.86, 1.00, 0.93, 0.87, 0.77, 0.63, 0.57, 0.54, 0.50},
{0.42, 0.42, 0.57, 0.76, 0.93, 1.00, 0.98, 0.90, 0.77, 0.70, 0.67, 0.63},
{0.37, 0.37, 0.50, 0.69, 0.87, 0.98, 1.00, 0.96, 0.84, 0.78, 0.75, 0.71},
{0.30, 0.30, 0.42, 0.59, 0.77, 0.90, 0.96, 1.00, 0.93, 0.89, 0.86, 0.82},
{0.22, 0.22, 0.32, 0.47, 0.63, 0.77, 0.84, 0.93, 1.00, 0.98, 0.96, 0.94},
{0.18, 0.18, 0.25, 0.40, 0.57, 0.70, 0.78, 0.89, 0.98, 1.00, 0.99, 0.98},
{0.16, 0.16, 0.23, 0.37, 0.54, 0.67, 0.75, 0.86, 0.96, 0.99, 1.00, 0.99},
{0.12, 0.12, 0.20, 0.32, 0.50, 0.63, 0.71, 0.82, 0.94, 0.98, 0.99, 1.00}
};
double crossBucketCorrelation = 0.27;
System.out.println
("\t||-----------------------------------------------------------------------------------------------------------------------------------------------|");
System.out.println
("\t|| TENOR CORRELATION MATRIX FOR GIRR |");
System.out.println
("\t||-----------------------------------------------------------------------------------------------------------------------------------------------|");
NumberUtil.PrintMatrix (
"\t|| GIRR2.0",
correlationMatrix
);
System.out.println
("\t||-----------------------------------------------------------------------------------------------------------------------------------------------|");
System.out.println();
PowerIterationComponentExtractor pice = new PowerIterationComponentExtractor (
30,
0.000001,
false
);
EigenComponent principalComponent = pice.principalComponent (correlationMatrix);
double[] rawEigenvector = principalComponent.eigenVector();
double rawEigenvalue = principalComponent.eigenValue();
double scaledEigenvalue = Math.sqrt (rawEigenvalue);
double[] scaledEigenvector = new double[rawEigenvector.length];
String rawEigenDump = "\t|| RAW || " +
"[" + FormatUtil.FormatDouble (rawEigenvalue, 1, 4, 1.) + "] => ";
String scaledEigenDump = "\t|| SCALED || " +
"[" + FormatUtil.FormatDouble (scaledEigenvalue, 1, 4, 1.) + "] => ";
for (int i = 0; i < rawEigenvector.length; ++i)
{
rawEigenDump += FormatUtil.FormatDouble (rawEigenvector[i], 1, 4, 1.) + " | ";
scaledEigenDump += FormatUtil.FormatDouble (
scaledEigenvector[i] = scaledEigenvalue * rawEigenvector[i], 1, 4, 1.
) + " | ";
}
System.out.println
("\t||------------------------------------------------------------------------------------------------------------------------------------------------|");
System.out.println (rawEigenDump);
System.out.println
("\t||------------------------------------------------------------------------------------------------------------------------------------------------|");
System.out.println (scaledEigenDump);
System.out.println
("\t||------------------------------------------------------------------------------------------------------------------------------------------------|");
System.out.println();
double[][] unadjustedOffDiagonalBlockMatrix = Matrix.CrossProduct (
scaledEigenvector,
scaledEigenvector
);
System.out.println
("\t||----------------------------------------------------------------------------------------------------------------------------------------------------------|");
System.out.println
("\t|| GIRR 2.0 UNADJUSTED OFF-DIAGONAL COVARIANCE ENTRIES |");
System.out.println
("\t||----------------------------------------------------------------------------------------------------------------------------------------------------------|");
NumberUtil.PrintMatrix (
"\t|| OFF-DIAGONAL UNADJ",
unadjustedOffDiagonalBlockMatrix
);
System.out.println
("\t||----------------------------------------------------------------------------------------------------------------------------------------------------------|");
System.out.println();
double[][] adjustedOffDiagonalBlockMatrix = Matrix.Scale2D (
unadjustedOffDiagonalBlockMatrix,
crossBucketCorrelation
);
System.out.println
("\t||--------------------------------------------------------------------------------------------------------------------------------------------------------|");
System.out.println
("\t|| GIRR 2.0 ADJUSTED OFF-DIAGONAL COVARIANCE ENTRIES |");
System.out.println
("\t||--------------------------------------------------------------------------------------------------------------------------------------------------------|");
NumberUtil.PrintMatrix (
"\t|| OFF-DIAGONAL ADJ",
adjustedOffDiagonalBlockMatrix
);
System.out.println
("\t||--------------------------------------------------------------------------------------------------------------------------------------------------------|");
EnvManager.TerminateEnv();
}
}