RiskGroupPrincipalCovariance.java
package org.drip.simm.foundation;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2020 Lakshmi Krishnamurthy
* Copyright (C) 2019 Lakshmi Krishnamurthy
* Copyright (C) 2018 Lakshmi Krishnamurthy
*
* This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
* asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
* analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
* equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
* numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
* and computational support.
*
* https://lakshmidrip.github.io/DROP/
*
* DROP is composed of three modules:
*
* - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
* - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
* - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
*
* DROP Product Core implements libraries for the following:
* - Fixed Income Analytics
* - Loan Analytics
* - Transaction Cost Analytics
*
* DROP Portfolio Core implements libraries for the following:
* - Asset Allocation Analytics
* - Asset Liability Management Analytics
* - Capital Estimation Analytics
* - Exposure Analytics
* - Margin Analytics
* - XVA Analytics
*
* DROP Computational Core implements libraries for the following:
* - Algorithm Support
* - Computation Support
* - Function Analysis
* - Model Validation
* - Numerical Analysis
* - Numerical Optimizer
* - Spline Builder
* - Statistical Learning
*
* Documentation for DROP is Spread Over:
*
* - Main => https://lakshmidrip.github.io/DROP/
* - Wiki => https://github.com/lakshmiDRIP/DROP/wiki
* - GitHub => https://github.com/lakshmiDRIP/DROP
* - Repo Layout Taxonomy => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
* - Javadoc => https://lakshmidrip.github.io/DROP/Javadoc/index.html
* - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
* - Release Versions => https://lakshmidrip.github.io/DROP/version.html
* - Community Credits => https://lakshmidrip.github.io/DROP/credits.html
* - Issues Catalog => https://github.com/lakshmiDRIP/DROP/issues
* - JUnit => https://lakshmidrip.github.io/DROP/junit/index.html
* - Jacoco => https://lakshmidrip.github.io/DROP/jacoco/index.html
*
* 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.
*/
/**
* <i>RiskGroupPrincipalCovariance</i> contains the Cross Risk-Group Principal Component Based Co-variance.
* The References are:
*
* <br><br>
* <ul>
* <li>
* 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 <b>eSSRN</b>
* </li>
* <li>
* Albanese, C., S. Caenazzo, and O. Frankel (2017): Regression Sensitivities for Initial Margin
* Calculations https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2763488 <b>eSSRN</b>
* </li>
* <li>
* 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 <b>eSSRN</b>
* </li>
* <li>
* 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
* <b>eSSRN</b>
* </li>
* <li>
* International Swaps and Derivatives Association (2017): SIMM v2.0 Methodology
* https://www.isda.org/a/oFiDE/isda-simm-v2.pdf
* </li>
* </ul>
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/PortfolioCore.md">Portfolio Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/MarginAnalyticsLibrary.md">Initial and Variation Margin Analytics</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/simm/README.md">Initial Margin Analytics based on ISDA SIMM and its Variants</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/simm/foundation/README.md">Foundation Utilities for ISDA SIMM</a></li>
* </ul>
* <br><br>
*
* @author Lakshmi Krishnamurthy
*/
public class RiskGroupPrincipalCovariance
{
private double _extraGroupCorrelation = java.lang.Double.NaN;
private org.drip.numerical.eigen.EigenComponent _principalEigenComponent = null;
/**
* Construct the Standard RiskGroupPrincipalCovariance Instance from the Bucket Correlation Matrix and
* the Cross Correlation Entry
*
* @param intraGroupCorrelationMatrix The Intra-Group Correlation Matrix
* @param extraGroupCorrelation Cross Group Correlation
*
* @return The Standard RiskGroupPrincipalCovariance Instance
*/
public static final RiskGroupPrincipalCovariance Standard (
final double[][] intraGroupCorrelationMatrix,
final double extraGroupCorrelation)
{
try
{
return new RiskGroupPrincipalCovariance (
new org.drip.numerical.eigen.PowerIterationComponentExtractor (
30,
0.000001,
false
).principalComponent (intraGroupCorrelationMatrix),
extraGroupCorrelation
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* RiskGroupPrincipalCovariance Constructor
*
* @param principalEigenComponent Intra-Group Principal Eigen-Component
* @param extraGroupCorrelation Cross Group Correlation
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public RiskGroupPrincipalCovariance (
final org.drip.numerical.eigen.EigenComponent principalEigenComponent,
final double extraGroupCorrelation)
throws java.lang.Exception
{
if (null == (_principalEigenComponent = principalEigenComponent) ||
!org.drip.numerical.common.NumberUtil.IsValid (_extraGroupCorrelation = extraGroupCorrelation) ||
-1. > _extraGroupCorrelation || 1. < _extraGroupCorrelation)
{
throw new java.lang.Exception ("RiskGroupPrincipalCovariance Constructor => Invalid Inputs");
}
}
/**
* Retrieve the Intra-Group Principal Eigen-Component
*
* @return The Intra-Group Principal Eigen-Component
*/
public org.drip.numerical.eigen.EigenComponent principalEigenComponent()
{
return _principalEigenComponent;
}
/**
* Retrieve the Cross Group Correlation
*
* @return The Cross Group Correlation
*/
public double extraGroupCorrelation()
{
return _extraGroupCorrelation;
}
/**
* Retrieve the Scaled Principal Eigen-vector
*
* @return The Scaled Principal Eigen-vector
*/
public double[] scaledPrincipalEigenvector()
{
double scaleFactor = java.lang.Math.sqrt (_principalEigenComponent.eigenValue());
double[] principalEigenvector = _principalEigenComponent.eigenVector();
int componentCount = principalEigenvector.length;
double[] scaledPrincipalEigenvector = new double[componentCount];
for (int componentIndex = 0; componentIndex < componentCount; ++componentIndex)
{
scaledPrincipalEigenvector[componentIndex] = principalEigenvector[componentIndex] * scaleFactor;
}
return scaledPrincipalEigenvector;
}
/**
* Retrieve the Unadjusted Cross-Group Co-variance
*
* @return The Unadjusted Cross-Group Co-variance
*/
public double[][] unadjustedCovariance()
{
double[] scaledPrincipalEigenvector = scaledPrincipalEigenvector();
return org.drip.numerical.linearalgebra.Matrix.CrossProduct (
scaledPrincipalEigenvector,
scaledPrincipalEigenvector
);
}
/**
* Retrieve the Adjusted Cross-Group Co-variance
*
* @return The Adjusted Cross-Group Co-variance
*/
public double[][] adjustedCovariance()
{
return org.drip.numerical.linearalgebra.Matrix.Scale2D (
unadjustedCovariance(),
_extraGroupCorrelation
);
}
}