PortfolioPathAggregationCorrelated.java

package org.drip.sample.netting;

import org.drip.analytics.date.*;
import org.drip.exposure.evolver.LatentStateVertexContainer;
import org.drip.exposure.universe.*;
import org.drip.measure.discrete.SequenceGenerator;
import org.drip.measure.dynamics.*;
import org.drip.measure.process.DiffusionEvolver;
import org.drip.measure.realization.*;
import org.drip.numerical.common.FormatUtil;
import org.drip.numerical.linearalgebra.Matrix;
import org.drip.service.env.EnvManager;
import org.drip.state.identifier.OTCFixFloatLabel;
import org.drip.xva.gross.*;
import org.drip.xva.netting.CollateralGroupPath;
import org.drip.xva.strategy.*;
import org.drip.xva.vertex.AlbaneseAndersen;

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

/*!
 * Copyright (C) 2018 Lakshmi Krishnamurthy
 * Copyright (C) 2017 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.
 */

/**
 * PortfolioPathAggregationCorrelated generates the Aggregation of the Portfolio Paths evolved using
 *  Correlated Market Parameters. The References are:
 *  
 *  - Burgard, C., and M. Kjaer (2014): PDE Representations of Derivatives with Bilateral Counter-party Risk
 *      and Funding Costs, Journal of Credit Risk, 7 (3) 1-19.
 *  
 *  - Burgard, C., and M. Kjaer (2014): In the Balance, Risk, 24 (11) 72-75.
 *  
 *  - Gregory, J. (2009): Being Two-faced over Counter-party Credit Risk, Risk 20 (2) 86-90.
 *  
 *  - Li, B., and Y. Tang (2007): Quantitative Analysis, Derivatives Modeling, and Trading Strategies in the
 *      Presence of Counter-party Credit Risk for the Fixed Income Market, World Scientific Publishing,
 *      Singapore.
 * 
 *  - Piterbarg, V. (2010): Funding Beyond Discounting: Collateral Agreements and Derivatives Pricing, Risk
 *      21 (2) 97-102.
 * 
 * @author Lakshmi Krishnamurthy
 */

public class PortfolioPathAggregationCorrelated {

    private static final double[] NumeraireValueRealization (
        final DiffusionEvolver deNumeraireValue,
        final double dblNumeraireValueInitial,
        final double dblTime,
        final double dblTimeWidth,
        final double[] adblRandom,
        final int iNumStep)
        throws Exception
    {
        double[] adblNumeraireValue = new double[iNumStep + 1];
        adblNumeraireValue[0] = dblNumeraireValueInitial;
        double[] adblTimeWidth = new double[iNumStep];

        for (int i = 0; i < iNumStep; ++i)
            adblTimeWidth[i] = dblTimeWidth;

        JumpDiffusionEdge[] aJDE = deNumeraireValue.incrementSequence (
            new JumpDiffusionVertex (
                dblTime,
                dblNumeraireValueInitial,
                0.,
                false
            ),
            JumpDiffusionEdgeUnit.Diffusion (
                adblTimeWidth,
                adblRandom
            ),
            dblTimeWidth
        );

        for (int j = 1; j <= iNumStep; ++j)
            adblNumeraireValue[j] = aJDE[j - 1].finish();

        return adblNumeraireValue;
    }

    private static final double[] VertexNumeraireRealization (
        final DiffusionEvolver deNumeraireValue,
        final double dblNumeraireValueInitial,
        final double dblTime,
        final double dblTimeWidth,
        final double[] adblRandom,
        final int iNumStep)
        throws Exception
    {
        double[] adblNumeraireValue = new double[iNumStep + 1];
        double[] adblTimeWidth = new double[iNumStep];

        for (int i = 0; i < iNumStep; ++i)
            adblTimeWidth[i] = dblTimeWidth;

        JumpDiffusionVertex[] aJDV = deNumeraireValue.vertexSequenceReverse (
            new JumpDiffusionVertex (
                dblTime,
                dblNumeraireValueInitial,
                0.,
                false
            ),
            JumpDiffusionEdgeUnit.Diffusion (
                adblTimeWidth,
                adblRandom
            ),
            adblTimeWidth
        );

        for (int j = 0; j <= iNumStep; ++j)
            adblNumeraireValue[j] = aJDV[j].value();

        return adblNumeraireValue;
    }

    public static final void main (
        final String[] astrArgs)
        throws Exception
    {
        EnvManager.InitEnv ("");

        int iNumStep = 10;
        double dblTime = 5.;
        int iNumPath = 10000;
        double dblCollateralPortfolioDrift = 0.06;
        double dblCollateralPortfolioVolatility = 0.15;
        double dblCollateralPortfolioInitial = 1.;
        double dblOvernightDrift = 0.004;
        double dblOvernightVolatility = 0.02;
        double dblOvernightInitial = 1.;
        double dblCSADrift = 0.01;
        double dblCSAVolatility = 0.05;
        double dblCSAInitial = 1.;
        double dblBankHazardRateDrift = 0.002;
        double dblBankHazardRateVolatility = 0.20;
        double dblBankHazardRateInitial = 0.015;
        double dblBankRecoveryRateDrift = 0.002;
        double dblBankRecoveryRateVolatility = 0.02;
        double dblBankRecoveryRateInitial = 0.40;
        double dblCounterPartyHazardRateDrift = 0.002;
        double dblCounterPartyHazardRateVolatility = 0.30;
        double dblCounterPartyHazardRateInitial = 0.030;
        double dblCounterPartyRecoveryRateDrift = 0.002;
        double dblCounterPartyRecoveryRateVolatility = 0.02;
        double dblCounterPartyRecoveryRateInitial = 0.30;
        double dblBankFundingSpreadDrift = 0.00002;
        double dblBankFundingSpreadVolatility = 0.002;
        double dblCounterPartyFundingSpreadDrift = 0.000022;
        double dblCounterPartyFundingSpreadVolatility = 0.0022;

        double[][] aadblCorrelation = new double[][] {
            {1.00,  0.00,  0.03,  0.07,  0.04,  0.05,  0.08,  0.00,  0.00},  // PORTFOLIO
            {0.00,  1.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  1.00},  // OVERNIGHT
            {0.03,  0.00,  1.00,  0.26,  0.33,  0.21,  0.35,  0.13,  0.00},  // CSA
            {0.07,  0.00,  0.26,  1.00,  0.45, -0.17,  0.07,  0.77,  0.00},  // BANK HAZARD
            {0.04,  0.00,  0.33,  0.45,  1.00, -0.22, -0.54,  0.58,  0.00},  // COUNTER PARTY HAZARD
            {0.05,  0.00,  0.21, -0.17, -0.22,  1.00,  0.47, -0.23,  0.00},  // BANK RECOVERY
            {0.08,  0.00,  0.35,  0.07, -0.54,  0.47,  1.00,  0.01,  0.00},  // COUNTER PARTY RECOVERY
            {0.00,  0.00,  0.13,  0.77,  0.58, -0.23,  0.01,  1.00,  0.00},  // BANK FUNDING SPREAD
            {0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  1.00}   // COUNTER PARTY FUNDING SPREAD
        };

        double dblTimeWidth = dblTime / iNumStep;
        JulianDate[] adtVertex = new JulianDate[iNumStep + 1];
        double[][] aadblCollateralBalance = new double[iNumPath][iNumStep + 1];
        double[][] aadblCollateralPortfolio = new double[iNumPath][iNumStep + 1];
        MonoPathExposureAdjustment[] aMPEA = new MonoPathExposureAdjustment[iNumPath];
        double dblBankFundingSpreadInitial = dblBankHazardRateInitial / (1. - dblBankRecoveryRateInitial);
        double dblCounterPartyFundingSpreadInitial = dblCounterPartyHazardRateInitial / (1. - dblCounterPartyRecoveryRateInitial);

        JulianDate dtSpot = DateUtil.Today();

        for (int j = 0; j <= iNumStep; ++j)
            adtVertex[j] = dtSpot.addMonths (6 * j + 6);

        DiffusionEvolver deCollateralPortfolio = new DiffusionEvolver (
            DiffusionEvaluatorLogarithmic.Standard (
                dblCollateralPortfolioDrift,
                dblCollateralPortfolioVolatility
            )
        );

        DiffusionEvolver deOvernight = new DiffusionEvolver (
            DiffusionEvaluatorLogarithmic.Standard (
                dblOvernightDrift,
                dblOvernightVolatility
            )
        );

        DiffusionEvolver deCSA = new DiffusionEvolver (
            DiffusionEvaluatorLogarithmic.Standard (
                dblCSADrift,
                dblCSAVolatility
            )
        );

        DiffusionEvolver deBankHazardRate = new DiffusionEvolver (
            DiffusionEvaluatorLogarithmic.Standard (
                dblBankHazardRateDrift,
                dblBankHazardRateVolatility
            )
        );

        DiffusionEvolver deCounterPartyHazardRate = new DiffusionEvolver (
            DiffusionEvaluatorLogarithmic.Standard (
                dblCounterPartyHazardRateDrift,
                dblCounterPartyHazardRateVolatility
            )
        );

        DiffusionEvolver deBankRecoveryRate = new DiffusionEvolver (
            DiffusionEvaluatorLogarithmic.Standard (
                dblBankRecoveryRateDrift,
                dblBankRecoveryRateVolatility
            )
        );

        DiffusionEvolver deCounterPartyRecoveryRate = new DiffusionEvolver (
            DiffusionEvaluatorLogarithmic.Standard (
                dblCounterPartyRecoveryRateDrift,
                dblCounterPartyRecoveryRateVolatility
            )
        );

        DiffusionEvolver deBankFundingSpread = new DiffusionEvolver (
            DiffusionEvaluatorLinear.Standard (
                dblBankFundingSpreadDrift,
                dblBankFundingSpreadVolatility
            )
        );

        DiffusionEvolver deCounterPartyFundingSpread = new DiffusionEvolver (
            DiffusionEvaluatorLinear.Standard (
                dblCounterPartyFundingSpreadDrift,
                dblCounterPartyFundingSpreadVolatility
            )
        );

        for (int i = 0; i < iNumPath; ++i) {
            double[][] aadblNumeraire = Matrix.Transpose (
                SequenceGenerator.GaussianJoint (
                    iNumStep,
                    aadblCorrelation
                )
            );

            aadblCollateralPortfolio[i] = NumeraireValueRealization (
                deCollateralPortfolio,
                dblCollateralPortfolioInitial,
                dblTime,
                dblTimeWidth,
                aadblNumeraire[0],
                iNumStep
            );

            double[] adblOvernightNumeraire = VertexNumeraireRealization (
                deOvernight,
                dblOvernightInitial,
                dblTime,
                dblTimeWidth,
                aadblNumeraire[1],
                iNumStep
            );

            double[] adblCSA = VertexNumeraireRealization (
                deCSA,
                dblCSAInitial,
                dblTime,
                dblTimeWidth,
                aadblNumeraire[2],
                iNumStep
            );

            double[] adblBankHazardRate = NumeraireValueRealization (
                deBankHazardRate,
                dblBankHazardRateInitial,
                dblTime,
                dblTimeWidth,
                aadblNumeraire[3],
                iNumStep
            );

            double[] adblCounterPartyHazardRate = NumeraireValueRealization (
                deCounterPartyHazardRate,
                dblCounterPartyHazardRateInitial,
                dblTime,
                dblTimeWidth,
                aadblNumeraire[4],
                iNumStep
            );

            double[] adblBankRecoveryRate = NumeraireValueRealization (
                deBankRecoveryRate,
                dblBankRecoveryRateInitial,
                dblTime,
                dblTimeWidth,
                aadblNumeraire[5],
                iNumStep
            );

            double[] adblCounterPartyRecoveryRate = NumeraireValueRealization (
                deCounterPartyRecoveryRate,
                dblCounterPartyRecoveryRateInitial,
                dblTime,
                dblTimeWidth,
                aadblNumeraire[6],
                iNumStep
            );

            double[] adblBankFundingSpread = NumeraireValueRealization (
                deBankFundingSpread,
                dblBankFundingSpreadInitial,
                dblTime,
                dblTimeWidth,
                aadblNumeraire[7],
                iNumStep
            );

            double[] adblCounterPartyFundingSpread = NumeraireValueRealization (
                deCounterPartyFundingSpread,
                dblCounterPartyFundingSpreadInitial,
                dblTime,
                dblTimeWidth,
                aadblNumeraire[8],
                iNumStep
            );

            MarketVertex[] aMV = new MarketVertex [iNumStep + 1];
            AlbaneseAndersen[] aHGVR = new AlbaneseAndersen[iNumStep + 1];

            for (int j = 0; j <= iNumStep; ++j)
            {
                LatentStateVertexContainer latentStateVertexContainer = new LatentStateVertexContainer();

                latentStateVertexContainer.add (
                    OTCFixFloatLabel.Standard ("USD-3M-10Y"),
                    Double.NaN
                );

                aMV[j] = MarketVertex.Nodal (
                    adtVertex[j] = dtSpot.addMonths (6 * j),
                    dblOvernightDrift,
                    adblOvernightNumeraire[j],
                    dblCSADrift,
                    adblCSA[j],
                    new MarketVertexEntity (
                        Math.exp (-0.5 * adblBankHazardRate[j] * j),
                        adblBankHazardRate[j],
                        adblBankRecoveryRate[j],
                        adblBankFundingSpread[j],
                        Math.exp (-0.5 * adblBankHazardRate[j] * (1. - adblBankRecoveryRate[j]) * (iNumStep - j)),
                        Double.NaN,
                        Double.NaN,
                        Double.NaN
                    ),
                    new MarketVertexEntity (
                        Math.exp (-0.5 * adblCounterPartyHazardRate[j] * j),
                        adblCounterPartyHazardRate[j],
                        adblCounterPartyRecoveryRate[j],
                        adblCounterPartyFundingSpread[j],
                        Math.exp (-0.5 * adblCounterPartyHazardRate[j] * (1. - adblCounterPartyRecoveryRate[j]) * (iNumStep - j)),
                        Double.NaN,
                        Double.NaN,
                        Double.NaN
                    ),
                    latentStateVertexContainer
                );

                aadblCollateralBalance[i][j] = 0.;

                aHGVR[j] = new AlbaneseAndersen (
                    adtVertex[j],
                    aadblCollateralPortfolio[i][j],
                    0.,
                    0.
                );
            }

            MarketPath marketPath = MarketPath.FromMarketVertexArray (aMV);

            CollateralGroupPath[] aHGP = new CollateralGroupPath[] {
                new CollateralGroupPath (
                    aHGVR,
                    marketPath
                )
            };

            aMPEA[i] = new MonoPathExposureAdjustment (
                new AlbaneseAndersenFundingGroupPath[] {
                    new AlbaneseAndersenFundingGroupPath (
                        new AlbaneseAndersenNettingGroupPath[] {
                            new AlbaneseAndersenNettingGroupPath (
                                aHGP,
                                marketPath
                            )
                        },
                        marketPath
                    )
                }
            );
        }

        ExposureAdjustmentAggregator eaa = new ExposureAdjustmentAggregator (aMPEA);

        JulianDate[] adtVertexNode = eaa.vertexDates();

        System.out.println();

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

        String strDump = "\t|         DATE         =>" ;

        for (int i = 0; i < adtVertexNode.length; ++i)
            strDump = strDump + " " + adtVertexNode[i] + " |";

        System.out.println (strDump);

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

        double[] adblExposure = eaa.collateralizedExposure();

        strDump = "\t|       EXPOSURE       =>";

        for (int j = 0; j < adblExposure.length; ++j)
            strDump = strDump + "   " + FormatUtil.FormatDouble (adblExposure[j], 1, 4, 1.) + "   |";

        System.out.println (strDump);

        double[] adblPositiveExposure = eaa.collateralizedPositiveExposure();

        strDump = "\t|  POSITIVE EXPOSURE   =>";

        for (int j = 0; j < adblPositiveExposure.length; ++j)
            strDump = strDump + "   " + FormatUtil.FormatDouble (adblPositiveExposure[j], 1, 4, 1.) + "   |";

        System.out.println (strDump);

        double[] adblNegativeExposure = eaa.collateralizedNegativeExposure();

        strDump = "\t|  NEGATIVE EXPOSURE   =>";

        for (int j = 0; j < adblNegativeExposure.length; ++j)
            strDump = strDump + "   " + FormatUtil.FormatDouble (adblNegativeExposure[j], 1, 4, 1.) + "   |";

        System.out.println (strDump);

        double[] adblExposurePV = eaa.collateralizedExposurePV();

        strDump = "\t|      EXPOSURE PV     =>";

        for (int j = 0; j < adblExposurePV.length; ++j)
            strDump = strDump + "   " + FormatUtil.FormatDouble (adblExposurePV[j], 1, 4, 1.) + "   |";

        System.out.println (strDump);

        double[] adblPositiveExposurePV = eaa.collateralizedPositiveExposurePV();

        strDump = "\t| POSITIVE EXPOSURE PV =>";

        for (int j = 0; j < adblPositiveExposurePV.length; ++j)
            strDump = strDump + "   " + FormatUtil.FormatDouble (adblPositiveExposurePV[j], 1, 4, 1.) + "   |";

        System.out.println (strDump);

        double[] adblNegativeExposurePV = eaa.collateralizedNegativeExposurePV();

        strDump = "\t| NEGATIVE EXPOSURE PV =>";

        for (int j = 0; j < adblNegativeExposurePV.length; ++j)
            strDump = strDump + "   " + FormatUtil.FormatDouble (adblNegativeExposurePV[j], 1, 4, 1.) + "   |";

        System.out.println (strDump);

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

        System.out.println();

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

        System.out.println ("\t||  UCVA  => " + FormatUtil.FormatDouble (eaa.ucva().amount(), 2, 2, 100.) + "% ||");

        System.out.println ("\t|| FTDCVA => " + FormatUtil.FormatDouble (eaa.ftdcva().amount(), 2, 2, 100.) + "% ||");

        System.out.println ("\t||  CVA   => " + FormatUtil.FormatDouble (eaa.cva().amount(), 2, 2, 100.) + "% ||");

        System.out.println ("\t||  CVACL => " + FormatUtil.FormatDouble (eaa.cvacl().amount(), 2, 2, 100.) + "% ||");

        System.out.println ("\t||  DVA   => " + FormatUtil.FormatDouble (eaa.dva().amount(), 2, 2, 100.) + "% ||");

        System.out.println ("\t||  FVA   => " + FormatUtil.FormatDouble (eaa.fva().amount(), 2, 2, 100.) + "% ||");

        System.out.println ("\t||  FDA   => " + FormatUtil.FormatDouble (eaa.fda().amount(), 2, 2, 100.) + "% ||");

        System.out.println ("\t||  FCA   => " + FormatUtil.FormatDouble (eaa.fca().amount(), 2, 2, 100.) + "% ||");

        System.out.println ("\t||  FBA   => " + FormatUtil.FormatDouble (eaa.fba().amount(), 2, 2, 100.) + "% ||");

        System.out.println ("\t||  SFVA  => " + FormatUtil.FormatDouble (eaa.sfva().amount(), 2, 2, 100.) + "% ||");

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

        EnvManager.TerminateEnv();
    }
}