RiskMeasureSensitivity.java

package org.drip.simm.product;

/*
 * -*- 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>RiskMeasureSensitivity</i> holds the Risk Class Bucket Sensitivities for a single Risk Measure. 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/product/README.md">ISDA SIMM Risk Factor Sensitivities</a></li>
 *  </ul>
 * <br><br>
 * 
 * @author Lakshmi Krishnamurthy
 */

public class RiskMeasureSensitivity
{
	private java.util.Map<java.lang.String, org.drip.simm.product.BucketSensitivity> _bucketSensitivityMap =
		null;

	private static final double PositionPrincipalComponentCovariance (
		final org.drip.simm.margin.BucketAggregate bucketAggregate,
		final org.drip.simm.foundation.MarginEstimationSettings marginEstimationSettings)
		throws java.lang.Exception
	{
		java.lang.String positionPrincipalComponentScheme =
			marginEstimationSettings.positionPrincipalComponentScheme();

		if (positionPrincipalComponentScheme.equalsIgnoreCase
			(org.drip.simm.foundation.MarginEstimationSettings.POSITION_PRINCIPAL_COMPONENT_COVARIANCE_ESTIMATOR_FRTB))
		{
			return bucketAggregate.positionPrincipalComponentCovarianceFRTB();
		}

		if (positionPrincipalComponentScheme.equalsIgnoreCase
			(org.drip.simm.foundation.MarginEstimationSettings.POSITION_PRINCIPAL_COMPONENT_COVARIANCE_ESTIMATOR_ISDA))
		{
			return bucketAggregate.positionPrincipalComponentCovarianceISDA();
		}

		throw new java.lang.Exception
			("RiskMeasureSensitivity::PositionPrincipalComponentCovariance => Invalid Inputs");
	}

	/**
	 * RiskMeasureSensitivity Constructor
	 * 
	 * @param bucketSensitivityMap The Risk Class Bucket Sensitivity Map
	 * 
	 * @throws java.lang.Exception Thrown if the Inputs are Invalid
	 */

	public RiskMeasureSensitivity (
		final java.util.Map<java.lang.String, org.drip.simm.product.BucketSensitivity>
			bucketSensitivityMap)
		throws java.lang.Exception
	{
		if (null == (_bucketSensitivityMap = bucketSensitivityMap) || 0 == _bucketSensitivityMap.size())
		{
			throw new java.lang.Exception ("RiskMeasureSensitivity Constructor => Invalid Inputs");
		}
	}

	/**
	 * Retrieve the Risk Class Bucket Sensitivity Map
	 * 
	 * @return The Risk Class Bucket Sensitivity Map
	 */

	public java.util.Map<java.lang.String, org.drip.simm.product.BucketSensitivity> bucketSensitivityMap()
	{
		return _bucketSensitivityMap;
	}

	/**
	 * Generate the Linear Risk Measure Aggregate
	 * 
	 * @param riskMeasureSensitivitySettings The Risk Measure Sensitivity Settings
	 * @param marginEstimationSettings Margin Estimation Settings
	 * 
	 * @return The Linear Risk Measure Aggregate
	 */

	public org.drip.simm.margin.RiskMeasureAggregate linearAggregate (
		final org.drip.simm.parameters.RiskMeasureSensitivitySettings riskMeasureSensitivitySettings,
		final org.drip.simm.foundation.MarginEstimationSettings marginEstimationSettings)
	{
		if (null == _bucketSensitivityMap ||
			null == riskMeasureSensitivitySettings ||
			null == marginEstimationSettings)
		{
			return null;
		}

		double coreSBAVariance = 0.;

		java.util.Map<java.lang.String, org.drip.simm.margin.BucketAggregate> bucketAggregateMap = new
			java.util.TreeMap<java.lang.String, org.drip.simm.margin.BucketAggregate>();

		java.util.Map<java.lang.String, org.drip.simm.parameters.BucketSensitivitySettings>
			bucketSensitivitySettingsMap = riskMeasureSensitivitySettings.bucketSettingsMap();

		org.drip.measure.stochastic.LabelCorrelation crossBucketCorrelation =
			riskMeasureSensitivitySettings.crossBucketCorrelation();

		for (java.util.Map.Entry<java.lang.String, org.drip.simm.product.BucketSensitivity>
			bucketSensitivityEntry : _bucketSensitivityMap.entrySet())
		{
			java.lang.String bucketIndex = bucketSensitivityEntry.getKey();

			org.drip.simm.product.BucketSensitivity bucketSensitivity = bucketSensitivityEntry.getValue();

			org.drip.simm.margin.BucketAggregate bucketAggregate = bucketSensitivity.aggregate
				(bucketSensitivitySettingsMap.get (bucketIndex));

			if (null == bucketAggregate)
			{
				return null;
			}

			bucketAggregateMap.put (
				"" + bucketIndex,
				bucketAggregate
			);
		}

		try
		{
			for (java.util.Map.Entry<java.lang.String, org.drip.simm.margin.BucketAggregate>
				bucketAggregateMapOuterEntry : bucketAggregateMap.entrySet())
			{
				java.lang.String outerKey = bucketAggregateMapOuterEntry.getKey();

				org.drip.simm.margin.BucketAggregate bucketAggregateOuter =
					bucketAggregateMapOuterEntry.getValue();

				double weightedSensitivityVarianceOuter = bucketAggregateOuter.sensitivityMarginVariance();

				double positionPrincipalComponentCovarianceOuter = PositionPrincipalComponentCovariance (
					bucketAggregateOuter,
					marginEstimationSettings
				);

				for (java.util.Map.Entry<java.lang.String, org.drip.simm.margin.BucketAggregate>
					bucketAggregateMapInnerEntry : bucketAggregateMap.entrySet())
				{
					java.lang.String innerKey = bucketAggregateMapInnerEntry.getKey();

					if (!"-1".equalsIgnoreCase (outerKey) && !"-1".equalsIgnoreCase (innerKey))
					{
						coreSBAVariance = coreSBAVariance + (outerKey.equalsIgnoreCase (innerKey) ?
							weightedSensitivityVarianceOuter : crossBucketCorrelation.entry (
								"" + outerKey,
								"" + innerKey
							) * positionPrincipalComponentCovarianceOuter *
							PositionPrincipalComponentCovariance (
								bucketAggregateMapInnerEntry.getValue(),
								marginEstimationSettings
							)
						);
					}
				}
			}

			return new org.drip.simm.margin.RiskMeasureAggregate (
				bucketAggregateMap,
				coreSBAVariance,
				bucketAggregateMap.containsKey ("-1") ?
					bucketAggregateMap.get ("-1").sensitivityMarginVariance() : 0.
			);
		}
		catch (java.lang.Exception e)
		{
			e.printStackTrace();
		}

		return null;
	}

	/**
	 * Generate the Curvature Risk Measure Aggregate
	 * 
	 * @param riskMeasureSensitivitySettings The Risk Measure Sensitivity Settings
	 * @param marginEstimationSettings Margin Estimation Settings
	 * 
	 * @return The Curvature Risk Measure Aggregate
	 */

	public org.drip.simm.margin.RiskMeasureAggregate curvatureAggregate (
		final org.drip.simm.parameters.RiskMeasureSensitivitySettings riskMeasureSensitivitySettings,
		final org.drip.simm.foundation.MarginEstimationSettings marginEstimationSettings)
	{
		if (null == _bucketSensitivityMap ||
			null == riskMeasureSensitivitySettings ||
			null == marginEstimationSettings)
		{
			return null;
		}

		double coreSBAVariance = 0.;
		double cumulativeRiskFactorSensitivityMarginCore = 0.;
		double cumulativeRiskFactorSensitivityMarginResidual = 0.;
		double cumulativeRiskFactorSensitivityMarginCorePositive = 0.;
		double cumulativeRiskFactorSensitivityMarginResidualPositive = 0.;

		java.util.Map<java.lang.String, org.drip.simm.margin.BucketAggregate> bucketAggregateMap = new
			java.util.TreeMap<java.lang.String, org.drip.simm.margin.BucketAggregate>();

		java.util.Map<java.lang.String, org.drip.simm.parameters.BucketSensitivitySettings>
			bucketSensitivitySettingsMap = riskMeasureSensitivitySettings.bucketSettingsMap();

		org.drip.measure.stochastic.LabelCorrelation crossBucketCorrelation =
			riskMeasureSensitivitySettings.crossBucketCorrelation();

		org.drip.simm.foundation.CurvatureEstimator curvatureEstimator =
			marginEstimationSettings.curvatureEstimator();

		boolean isCorrelatorQuadratric = curvatureEstimator.isCorrelatorQuadratric();

		for (java.util.Map.Entry<java.lang.String, org.drip.simm.product.BucketSensitivity>
			bucketSensitivityEntry : _bucketSensitivityMap.entrySet())
		{
			java.lang.String bucketIndex = bucketSensitivityEntry.getKey();

			org.drip.simm.product.BucketSensitivity bucketSensitivity = bucketSensitivityEntry.getValue();

			org.drip.simm.margin.BucketAggregate bucketAggregate = bucketSensitivity.aggregate
				(bucketSensitivitySettingsMap.get (bucketIndex));

			if (null == bucketAggregate)
			{
				return null;
			}

			double bucketCumulativeRiskFactorSensitivityMargin =
				bucketAggregate.cumulativeSensitivityMargin();

			if (!"-1".equalsIgnoreCase (bucketIndex))
			{
				cumulativeRiskFactorSensitivityMarginCore = cumulativeRiskFactorSensitivityMarginCore +
					bucketCumulativeRiskFactorSensitivityMargin;

				cumulativeRiskFactorSensitivityMarginCorePositive =
					cumulativeRiskFactorSensitivityMarginCorePositive +
					java.lang.Math.max (
						bucketCumulativeRiskFactorSensitivityMargin,
						0.
					);
			}
			else
			{
				cumulativeRiskFactorSensitivityMarginResidual = cumulativeRiskFactorSensitivityMarginResidual
					+ bucketCumulativeRiskFactorSensitivityMargin;

				cumulativeRiskFactorSensitivityMarginResidualPositive =
					cumulativeRiskFactorSensitivityMarginResidualPositive +
					java.lang.Math.max (
						bucketCumulativeRiskFactorSensitivityMargin,
						0.
					);
			}

			bucketAggregateMap.put (
				bucketIndex,
				bucketAggregate
			);
		}

		try
		{
			for (java.util.Map.Entry<java.lang.String, org.drip.simm.margin.BucketAggregate>
				bucketAggregateMapOuterEntry : bucketAggregateMap.entrySet())
			{
				java.lang.String outerKey = bucketAggregateMapOuterEntry.getKey();

				org.drip.simm.margin.BucketAggregate bucketAggregateOuter =
					bucketAggregateMapOuterEntry.getValue();

				double weightedSensitivityVarianceOuter = bucketAggregateOuter.sensitivityMarginVariance();

				double positionPrincipalComponentCovarianceOuter = PositionPrincipalComponentCovariance (
					bucketAggregateOuter,
					marginEstimationSettings
				);

				for (java.util.Map.Entry<java.lang.String, org.drip.simm.margin.BucketAggregate>
					bucketAggregateMapInnerEntry : bucketAggregateMap.entrySet())
				{
					java.lang.String innerKey = bucketAggregateMapInnerEntry.getKey();

					if (!"-1".equalsIgnoreCase (outerKey) && !"-1".equalsIgnoreCase (innerKey))
					{
						if (outerKey.equalsIgnoreCase (innerKey))
						{
							coreSBAVariance = coreSBAVariance + weightedSensitivityVarianceOuter;
						}
						else
						{
							double correlation = crossBucketCorrelation.entry (
								"" + outerKey,
								"" + innerKey
							);

							double curvatureCorrelation = isCorrelatorQuadratric ? correlation * correlation
								: correlation;

							org.drip.simm.margin.BucketAggregate bucketAggregateInner =
								bucketAggregateMapInnerEntry.getValue();

							coreSBAVariance = coreSBAVariance + curvatureCorrelation *
								positionPrincipalComponentCovarianceOuter *
								curvatureEstimator.varianceModulator (
									outerKey,
									weightedSensitivityVarianceOuter,
									innerKey,
									bucketAggregateInner.sensitivityMarginVariance()
								) * PositionPrincipalComponentCovariance (
									bucketAggregateInner,
									marginEstimationSettings
								);
						}
					}
				}
			}

			double coreSBAMargin = curvatureEstimator.margin (
				cumulativeRiskFactorSensitivityMarginCore,
				cumulativeRiskFactorSensitivityMarginCorePositive,
				coreSBAVariance
			);

			double residualSBAMargin = !bucketAggregateMap.containsKey ("-1") ? 0. :
				curvatureEstimator.margin (
					cumulativeRiskFactorSensitivityMarginResidual,
					cumulativeRiskFactorSensitivityMarginResidualPositive,
					bucketAggregateMap.get ("-1").sensitivityMarginVariance()
				);

			return new org.drip.simm.margin.RiskMeasureAggregate (
				bucketAggregateMap,
				coreSBAMargin * coreSBAMargin,
				residualSBAMargin * residualSBAMargin
			);
		}
		catch (java.lang.Exception e)
		{
			e.printStackTrace();
		}

		return null;
	}
}