CPGACollateralized.java

package org.drip.sample.xvadigest;

import org.drip.analytics.date.*;
import org.drip.exposure.evolver.LatentStateVertexContainer;
import org.drip.exposure.mpor.CollateralAmountEstimator;
import org.drip.exposure.universe.*;
import org.drip.measure.bridge.BrokenDateInterpolatorLinearT;
import org.drip.measure.discrete.SequenceGenerator;
import org.drip.measure.dynamics.DiffusionEvaluatorLinear;
import org.drip.measure.process.DiffusionEvolver;
import org.drip.measure.realization.*;
import org.drip.measure.statistics.UnivariateDiscreteThin;
import org.drip.numerical.common.FormatUtil;
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.proto.*;
import org.drip.xva.settings.*;
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.
 */

/**
 * CPGACollateralized illustrates the Counter Party Aggregation over Netting Groups based Collateralized
 *  Collateral Groups with several Fix-Float Swaps. 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 CPGACollateralized {

    private static final double[] ATMSwapRateOffsetRealization (
        final DiffusionEvolver deATMSwapRateOffset,
        final double dblATMSwapRateOffsetInitial,
        final double dblTime,
        final double dblTimeWidth,
        final int iNumStep)
        throws Exception
    {
        double[] adblATMSwapRateOffset = new double[iNumStep + 1];
        adblATMSwapRateOffset[0] = dblATMSwapRateOffsetInitial;
        double[] adblTimeWidth = new double[iNumStep];

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

        JumpDiffusionEdge[] aJDE = deATMSwapRateOffset.incrementSequence (
            new JumpDiffusionVertex (
                dblTime,
                dblATMSwapRateOffsetInitial,
                0.,
                false
            ),
            JumpDiffusionEdgeUnit.Diffusion (
                adblTimeWidth,
                SequenceGenerator.Gaussian (iNumStep)
            ),
            dblTimeWidth
        );

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

        return adblATMSwapRateOffset;
    }

    private static final double[] SwapPortfolioValueRealization (
        final DiffusionEvolver deATMSwapRate,
        final double dblATMSwapRateStart,
        final int iNumStep,
        final double dblTime,
        final double dblTimeWidth,
        final int iNumSwap)
        throws Exception
    {
        double[] adblSwapPortfolioValueRealization = new double[iNumStep + 1];

        for (int i = 0; i < iNumStep; ++i)
            adblSwapPortfolioValueRealization[i] = 0.;

        for (int i = 0; i < iNumSwap; ++i) {
            double[] adblATMSwapRateOffsetRealization = ATMSwapRateOffsetRealization (
                deATMSwapRate,
                dblATMSwapRateStart,
                dblTime,
                dblTimeWidth,
                iNumStep
            );

            for (int j = 0; j <= iNumStep; ++j)
                adblSwapPortfolioValueRealization[j] += dblTimeWidth * (iNumStep - j) * adblATMSwapRateOffsetRealization[j];
        }

        return adblSwapPortfolioValueRealization;
    }

    private static final double[][] SwapPortfolioValueRealization (
        final DiffusionEvolver deATMSwapRate,
        final double dblSwapPortfolioValueStart,
        final int iNumStep,
        final double dblTime,
        final double dblTimeWidth,
        final int iNumSwap,
        final int iNumSimulation)
        throws Exception
    {
        double[][] aadblSwapPortfolioValueRealization = new double[iNumSimulation][];

        for (int i = 0; i < iNumSimulation; ++i)
            aadblSwapPortfolioValueRealization[i] = SwapPortfolioValueRealization (
                deATMSwapRate,
                dblSwapPortfolioValueStart,
                iNumStep,
                dblTime,
                dblTimeWidth,
                iNumSwap
            );

        return aadblSwapPortfolioValueRealization;
    }

    private static final void UDTDump (
        final String strHeader,
        final JulianDate[] adtVertexNode,
        final UnivariateDiscreteThin[] aUDT)
        throws Exception
    {
        System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|");

        System.out.println (strHeader);

        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|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|");

         strDump = "\t|     AVERAGE     =>";

        for (int j = 0; j < aUDT.length; ++j)
            strDump = strDump + "   " + FormatUtil.FormatDouble (aUDT[j].average(), 2, 4, 1.) + "   |";

        System.out.println (strDump);

        strDump = "\t|     MAXIMUM     =>";

        for (int j = 0; j < aUDT.length; ++j)
            strDump = strDump + "   " + FormatUtil.FormatDouble (aUDT[j].maximum(), 2, 4, 1.) + "   |";

        System.out.println (strDump);

        strDump = "\t|     MINIMUM     =>";

        for (int j = 0; j < aUDT.length; ++j)
            strDump = strDump + "   " + FormatUtil.FormatDouble (aUDT[j].minimum(), 2, 4, 1.) + "   |";

        System.out.println (strDump);

        strDump = "\t|      ERROR      =>";

        for (int j = 0; j < aUDT.length; ++j)
            strDump = strDump + "   " + FormatUtil.FormatDouble (aUDT[j].error(), 2, 4, 1.) + "   |";

        System.out.println (strDump);

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

    private static final void UDTDump (
        final String strHeader,
        final UnivariateDiscreteThin udt)
        throws Exception
    {
        System.out.println (
            strHeader +
            FormatUtil.FormatDouble (udt.average(), 3, 2, 100.) + "% | " +
            FormatUtil.FormatDouble (udt.maximum(), 3, 2, 100.) + "% | " +
            FormatUtil.FormatDouble (udt.minimum(), 3, 2, 100.) + "% | " +
            FormatUtil.FormatDouble (udt.error(), 3, 2, 100.) + "% ||"
        );
    }

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

        int iNumStep = 10;
        int iNumSwap = 10;
        double dblTime = 5.;
        int iNumPath = 10000;
        double dblATMSwapRateStart = 0.;
        double dblATMSwapRateDrift = 0.0;
        double dblATMSwapRateVolatility = 0.25;
        double dblOvernightNumeraireDrift = 0.004;
        double dblCSADrift = 0.01;
        double dblBankHazardRate = 0.015;
        double dblBankRecoveryRate = 0.40;
        double dblCounterPartyHazardRate = 0.030;
        double dblCounterPartyRecoveryRate = 0.30;
        double dblBankThreshold = -0.1;
        double dblCounterPartyThreshold = 0.1;

        JulianDate dtSpot = DateUtil.Today();

        double dblTimeWidth = dblTime / iNumStep;
        MarketVertex[] aMV = new MarketVertex[iNumStep + 1];
        JulianDate[] adtVertex = new JulianDate[iNumStep + 1];
        double dblBankFundingSpread = dblBankHazardRate / (1. - dblBankRecoveryRate);
        MonoPathExposureAdjustment[] aMPEA = new MonoPathExposureAdjustment[iNumPath];
        double dblCounterPartyFundingSpread = dblCounterPartyHazardRate / (1. - dblCounterPartyRecoveryRate);

        PositionGroupSpecification positionGroupSpecification = PositionGroupSpecification.FixedThreshold (
            "FIXEDTHRESHOLD",
            dblCounterPartyThreshold,
            dblBankThreshold,
            PositionReplicationScheme.ALBANESE_ANDERSEN_VERTEX,
            BrokenDateScheme.LINEAR_TIME,
            0.,
            CloseOutScheme.ISDA_92
        );

        double[][] aadblSwapPortfolioValueRealization = SwapPortfolioValueRealization (
            new DiffusionEvolver (
                DiffusionEvaluatorLinear.Standard (
                    dblATMSwapRateDrift,
                    dblATMSwapRateVolatility
                )
            ),
            dblATMSwapRateStart,
            iNumStep,
            dblTime,
            dblTimeWidth,
            iNumSwap,
            iNumPath
        );

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

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

            aMV[i] = MarketVertex.Nodal (
                adtVertex[i] = dtSpot.addMonths (6 * i),
                dblOvernightNumeraireDrift,
                Math.exp (-0.5 * dblOvernightNumeraireDrift * (iNumStep - i)),
                dblCSADrift,
                Math.exp (-0.5 * dblCSADrift * (iNumStep - i)),
                new MarketVertexEntity (
                    Math.exp (-0.5 * dblBankHazardRate * i),
                    dblBankHazardRate,
                    dblBankRecoveryRate,
                    dblBankFundingSpread,
                    Math.exp (-0.5 * dblBankHazardRate * (1. - dblBankRecoveryRate) * (iNumStep - i)),
                    Double.NaN,
                    Double.NaN,
                    Double.NaN
                ),
                new MarketVertexEntity (
                    Math.exp (-0.5 * dblCounterPartyHazardRate * i),
                    dblCounterPartyHazardRate,
                    dblCounterPartyRecoveryRate,
                    dblCounterPartyFundingSpread,
                    Math.exp (-0.5 * dblCounterPartyHazardRate * (1. - dblCounterPartyRecoveryRate) * (iNumStep - i)),
                    Double.NaN,
                    Double.NaN,
                    Double.NaN
                ),
                latentStateVertexContainer
            );
        }

        MarketPath mp = MarketPath.FromMarketVertexArray (aMV);

        for (int i = 0; i < iNumPath; ++i) {
            JulianDate dtStart = dtSpot;
            double dblValueStart = dblTime * dblATMSwapRateStart;
            AlbaneseAndersen[] aHGVR = new AlbaneseAndersen[iNumStep + 1];

            for (int j = 0; j <= iNumStep; ++j) {
                JulianDate dtEnd = adtVertex[j];
                double dblCollateralBalance = 0.;
                double dblValueEnd = aadblSwapPortfolioValueRealization[i][j];

                if (0 != j) {
                    CollateralAmountEstimator hae = new CollateralAmountEstimator (
                        positionGroupSpecification,
                        new BrokenDateInterpolatorLinearT (
                            dtStart.julian(),
                            dtEnd.julian(),
                            dblValueStart,
                            dblValueEnd
                        ),
                        Double.NaN
                    );

                    dblCollateralBalance = hae.postingRequirement (dtEnd);
                }

                aHGVR[j] = new AlbaneseAndersen (
                    adtVertex[j],
                    aadblSwapPortfolioValueRealization[i][j],
                    0.,
                    dblCollateralBalance
                );

                dtStart = dtEnd;
                dblValueStart = dblValueEnd;
            }

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

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

        ExposureAdjustmentAggregator eaa = new ExposureAdjustmentAggregator (aMPEA);

        ExposureAdjustmentDigest ead = eaa.digest();

        System.out.println();

        UDTDump (
            "\t|                                                                                COLLATERALIZED EXPOSURE                                                                                |",
            eaa.vertexDates(),
            ead.collateralizedExposure()
        );

        UDTDump (
            "\t|                                                                               UNCOLLATERALIZED EXPOSURE                                                                               |",
            eaa.vertexDates(),
            ead.uncollateralizedExposure()
        );

        UDTDump (
            "\t|                                                                                COLLATERALIZED EXPOSURE PV                                                                             |",
            eaa.vertexDates(),
            ead.collateralizedExposurePV()
        );

        UDTDump (
            "\t|                                                                               UNCOLLATERALIZED EXPOSURE PV                                                                            |",
            eaa.vertexDates(),
            ead.uncollateralizedExposurePV()
        );

        UDTDump (
            "\t|                                                                            COLLATERALIZED POSITIVE EXPOSURE PV                                                                        |",
            eaa.vertexDates(),
            ead.collateralizedPositiveExposure()
        );

        UDTDump (
            "\t|                                                                           UNCOLLATERALIZED POSITIVE EXPOSURE PV                                                                       |",
            eaa.vertexDates(),
            ead.uncollateralizedPositiveExposure()
        );

        UDTDump (
            "\t|                                                                            COLLATERALIZED NEGATIVE EXPOSURE PV                                                                        |",
            eaa.vertexDates(),
            ead.collateralizedNegativeExposure()
        );

        UDTDump (
            "\t|                                                                           UNCOLLATERALIZED NEGATIVE EXPOSURE PV                                                                       |",
            eaa.vertexDates(),
            ead.uncollateralizedNegativeExposure()
        );

        System.out.println();

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

        System.out.println ("\t||  UCVA CVA FTDCVA DVA FCA UNIVARIATE THIN STATISTICS ||");

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

        System.out.println ("\t||    L -> R:                                          ||");

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

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

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

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

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

        UDTDump (
            "\t||  UCVA  => ",
            ead.ucva()
        );

        UDTDump (
            "\t|| FTDCVA => ",
            ead.ftdcva()
        );

        UDTDump (
            "\t||   CVA  => ",
            ead.cva()
        );

        UDTDump (
            "\t||  CVACL => ",
            ead.cvacl()
        );

        UDTDump (
            "\t||   DVA  => ",
            ead.dva()
        );

        UDTDump (
            "\t||   FVA  => ",
            ead.fva()
        );

        UDTDump (
            "\t||   FDA  => ",
            ead.fda()
        );

        UDTDump (
            "\t||   FCA  => ",
            ead.fca()
        );

        UDTDump (
            "\t||   FBA  => ",
            ead.fba()
        );

        UDTDump (
            "\t||  SFVA  => ",
            ead.sfva()
        );

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

        UDTDump (
            "\t||  Total => ",
            ead.totalVA()
        );

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

        System.out.println();

        EnvManager.TerminateEnv();
    }
}