XVAExplain.java

package org.drip.sample.burgard2011;

import java.util.ArrayList;
import java.util.List;
import java.util.Map;

import org.drip.analytics.date.*;
import org.drip.analytics.support.VertexDateBuilder;
import org.drip.exposure.evolver.*;
import org.drip.exposure.universe.*;
import org.drip.measure.crng.RandomNumberGenerator;
import org.drip.measure.discrete.CorrelatedPathVertexDimension;
import org.drip.measure.dynamics.*;
import org.drip.measure.process.*;
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.*;
import org.drip.xva.definition.*;
import org.drip.xva.derivative.*;
import org.drip.xva.pde.*;

/*
 * -*- 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
 * Copyright (C) 2017 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>XVAExplain</i> demonstrates the Trajectory Attribution of the Bank and Counter-Party Default Based
 * Derivative Evolution of the Dynamic XVA Replication Porfolio. The References are:
 *  
 * <br><br>
 *  <ul>
 *      <li>
 *          Burgard, C., and M. Kjaer (2014): PDE Representations of Derivatives with Bilateral Counter-party
 *              Risk and Funding Costs <i>Journal of Credit Risk</i> <b>7 (3)</b> 1-19
 *      </li>
 *      <li>
 *          Cesari, G., J. Aquilina, N. Charpillon, X. Filipovic, G. Lee, and L. Manda (2009): <i>Modeling,
 *              Pricing, and Hedging Counter-party Credit Exposure - A Technical Guide</i> <b>Springer
 *              Finance</b> New York
 *      </li>
 *      <li>
 *          Gregory, J. (2009): Being Two-faced over Counter-party Credit Risk <i>Risk</i> <b>20 (2)</b>
 *              86-90
 *      </li>
 *      <li>
 *          Li, B., and Y. Tang (2007): <i>Quantitative Analysis, Derivatives Modeling, and Trading
 *              Strategies in the Presence of Counter-party Credit Risk for the Fixed Income Market</i>
 *              <b>World Scientific Publishing</b> Singapore
 *      </li>
 *      <li>
 *          Piterbarg, V. (2010): Funding Beyond Discounting: Collateral Agreements and Derivatives Pricing
 *              <i>Risk</i> <b>21 (2)</b> 97-102
 *      </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/XVAAnalyticsLibrary.md">XVA Analytics Library</a></li>
 *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">DROP API Construction and Usage</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/burgard2011/README.md">Burgard Kjaer (2011) PDE Evolver</a></li>
 *  </ul>
 * <br><br>
 * 
 * @author Lakshmi Krishnamurthy
 */

public class XVAExplain
{

    private static final PrimarySecurity AssetValueReplicator (
        final String currency)
        throws Exception
    {
        double assetValueReplicatorDrift = 0.0025;
        double assetValueReplicatorVolatility = 0.10;
        double assetValueReplicatorRepo = 0.03;
        double assetValueReplicatorDividend = 0.02;

        EntityEquityLabel equityLabel = EntityEquityLabel.Standard (
            "AAPL",
            currency
        );

        return new PrimarySecurity (
            "AAPL",
            equityLabel,
            new DiffusionEvolver (
                DiffusionEvaluatorLogarithmic.Standard (
                    assetValueReplicatorDrift - assetValueReplicatorDividend,
                    assetValueReplicatorVolatility
                )
            ),
            assetValueReplicatorRepo
        );
    }

    private static final PrimarySecurity OvernightReplicator (
        final String currency,
        final List<LatentStateLabel> latentStateLabelList)
        throws Exception
    {
        double overnightReplicatorDrift = 0.0025;
        double overnightReplicatorVolatility = 0.001;
        double overnightReplicatorRepo = 0.0;

        LatentStateLabel overnightLabel = OvernightLabel.Create (currency);

        latentStateLabelList.add (overnightLabel);

        return new PrimarySecurity (
            currency + "_OVERNIGHT",
            overnightLabel,
            new DiffusionEvolver (
                DiffusionEvaluatorLogarithmic.Standard (
                    overnightReplicatorDrift,
                    overnightReplicatorVolatility
                )
            ),
            overnightReplicatorRepo
        );
    }

    private static final PrimarySecurity CSAReplicator (
        final String currency,
        final List<LatentStateLabel> latentStateLabelList)
        throws Exception
    {
        double csaReplicatorDrift = 0.01;
        double csaReplicatorVolatility = 0.002;
        double csaReplicatorRepo = 0.005;

        LatentStateLabel csaLabel = CSALabel.ISDA (currency);

        latentStateLabelList.add (csaLabel);

        return new PrimarySecurity (
            currency + "_CSA",
            csaLabel,
            new DiffusionEvolver (
                DiffusionEvaluatorLogarithmic.Standard (
                    csaReplicatorDrift,
                    csaReplicatorVolatility
                )
            ),
            csaReplicatorRepo
        );
    }

    private static final PrimarySecurity DealerSeniorFundingReplicator (
        final String currency,
        final String dealer,
        final List<LatentStateLabel> latentStateLabelList)
        throws Exception
    {
        double dealerSeniorFundingReplicatorDrift = 0.03;
        double dealerSeniorFundingReplicatorVolatility = 0.002;
        double dealerSeniorFundingReplicatorRepo = 0.028;

        LatentStateLabel dealerSeniorFundingLabel = EntityFundingLabel.Senior (
            dealer,
            currency
        );

        latentStateLabelList.add (dealerSeniorFundingLabel);

        return new PrimarySecurity (
            dealer + "_" + currency + "_SENIOR_ZERO",
            dealerSeniorFundingLabel,
            new JumpDiffusionEvolver (
                DiffusionEvaluatorLogarithmic.Standard (
                    dealerSeniorFundingReplicatorDrift,
                    dealerSeniorFundingReplicatorVolatility
                ),
                HazardJumpEvaluator.Standard (
                    0.3,
                    0.45
                )
            ),
            dealerSeniorFundingReplicatorRepo
        );
    }

    private static final PrimarySecurity DealerSubordinateFundingReplicator (
        final String currency,
        final String dealer,
        final List<LatentStateLabel> latentStateLabelList)
        throws Exception
    {
        double dealerSubordinateFundingReplicatorDrift = 0.045;
        double dealerSubordinateFundingReplicatorVolatility = 0.002;
        double dealerSubordinateFundingReplicatorRepo = 0.028;

        LatentStateLabel dealerSubordinateFundingLabel = EntityFundingLabel.Subordinate (
            dealer,
            currency
        );

        latentStateLabelList.add (dealerSubordinateFundingLabel);

        return new PrimarySecurity (
            dealer + "_" + currency + "_SUBORDINATE_ZERO",
            dealerSubordinateFundingLabel,
            new JumpDiffusionEvolver (
                DiffusionEvaluatorLogarithmic.Standard (
                    dealerSubordinateFundingReplicatorDrift,
                    dealerSubordinateFundingReplicatorVolatility
                ),
                HazardJumpEvaluator.Standard (
                    0.3,
                    0.25
                )
            ),
            dealerSubordinateFundingReplicatorRepo
        );
    }

    private static final PrimarySecurity ClientFundingReplicator (
        final String currency,
        final String client,
        final List<LatentStateLabel> latentStateLabelList)
        throws Exception
    {
        double clientFundingReplicatorDrift = 0.03;
        double clientFundingReplicatorVolatility = 0.003;
        double clientFundingReplicatorRepo = 0.028;

        LatentStateLabel clientFundingLabel = EntityFundingLabel.Senior (
            client,
            currency
        );

        latentStateLabelList.add (clientFundingLabel);

        return new PrimarySecurity (
            client + "_" + currency + "_SENIOR_ZERO",
            clientFundingLabel,
            new JumpDiffusionEvolver (
                DiffusionEvaluatorLogarithmic.Standard (
                    clientFundingReplicatorDrift,
                    clientFundingReplicatorVolatility
                ),
                HazardJumpEvaluator.Standard (
                    0.5,
                    0.30
                )
            ),
            clientFundingReplicatorRepo
        );
    }

    private static final PrimarySecurityDynamicsContainer PrimarySecurityEvolver (
        final String currency,
        final String dealer,
        final String client,
        final List<LatentStateLabel> latentStateLabelList)
        throws Exception
    {
        List<PrimarySecurity> assetList = new ArrayList<PrimarySecurity>();

        assetList.add (AssetValueReplicator (currency));

        return new PrimarySecurityDynamicsContainer (
            assetList,
            OvernightReplicator (
                currency,
                latentStateLabelList
            ),
            CSAReplicator (
                currency,
                latentStateLabelList
            ),
            DealerSeniorFundingReplicator (
                currency,
                dealer,
                latentStateLabelList
            ),
            DealerSubordinateFundingReplicator (
                currency,
                dealer,
                latentStateLabelList
            ),
            ClientFundingReplicator (
                currency,
                client,
                latentStateLabelList
            )
        );
    }

    private static final TerminalLatentState DealerHazard (
        final String currency,
        final String dealer,
        final List<LatentStateLabel> latentStateLabelList)
        throws Exception
    {
        double dealerHazardDrift = 0.0002;
        double dealerHazardVolatility = 0.02;

        LatentStateLabel dealerHazardLabel = EntityHazardLabel.Standard (
            dealer,
            currency
        );

        latentStateLabelList.add (dealerHazardLabel);

        return new TerminalLatentState (
            dealerHazardLabel,
            new DiffusionEvolver (
                DiffusionEvaluatorLogarithmic.Standard (
                    dealerHazardDrift,
                    dealerHazardVolatility
                )
            )
        );
    }

    private static final TerminalLatentState DealerRecovery (
        final String currency,
        final String dealer,
        final List<LatentStateLabel> latentStateLabelList)
        throws Exception
    {
        double dealerRecoveryDrift = 0.0002;
        double dealerRecoveryVolatility = 0.02;

        LatentStateLabel dealerRecoveryLabel = EntityRecoveryLabel.Senior (
            dealer,
            currency
        );

        latentStateLabelList.add (dealerRecoveryLabel);

        return new TerminalLatentState (
            dealerRecoveryLabel,
            new DiffusionEvolver (
                DiffusionEvaluatorLogarithmic.Standard (
                    dealerRecoveryDrift,
                    dealerRecoveryVolatility
                )
            )
        );
    }

    private static final TerminalLatentState ClientHazard (
        final String currency,
        final String client,
        final List<LatentStateLabel> latentStateLabelList)
        throws Exception
    {
        double clientHazardDrift = 0.0002;
        double clientHazardVolatility = 0.02;

        LatentStateLabel clientHazardLabel = EntityHazardLabel.Standard (
            client,
            currency
        );

        latentStateLabelList.add (clientHazardLabel);

        return new TerminalLatentState (
            clientHazardLabel,
            new DiffusionEvolver (
                DiffusionEvaluatorLogarithmic.Standard (
                    clientHazardDrift,
                    clientHazardVolatility
                )
            )
        );
    }

    private static final TerminalLatentState ClientRecovery (
        final String currency,
        final String client,
        final List<LatentStateLabel> latentStateLabelList)
        throws Exception
    {
        double clientRecoveryDrift = 0.0002;
        double clientRecoveryVolatility = 0.02;

        LatentStateLabel clientRecoveryLabel = EntityRecoveryLabel.Senior (
            client,
            currency
        );

        latentStateLabelList.add (clientRecoveryLabel);

        return new TerminalLatentState (
            clientRecoveryLabel,
            new DiffusionEvolver (
                DiffusionEvaluatorLogarithmic.Standard (
                    clientRecoveryDrift,
                    clientRecoveryVolatility
                )
            )
        );
    }

    private static final EntityDynamicsContainer EntityEvolver (
        final String currency,
        final String dealer,
        final String client,
        final List<LatentStateLabel> latentStateLabelList)
        throws Exception
    {
        return new EntityDynamicsContainer (
            DealerHazard (
                currency,
                dealer,
                latentStateLabelList
            ),
            DealerRecovery (
                currency,
                dealer,
                latentStateLabelList
            ),
            null,
            ClientHazard (
                currency,
                client,
                latentStateLabelList
            ),
            ClientRecovery (
                currency,
                client,
                latentStateLabelList
            )
        );
    }

    private static final LatentStateDynamicsContainer LatentStateEvolver (
        final EntityEquityLabel equityLabel,
        final List<LatentStateLabel> latentStateLabelList)
        throws Exception
    {
        double assetValueReplicatorDrift = 0.0025;
        double assetValueReplicatorVolatility = 0.10;

        latentStateLabelList.add (equityLabel);

        LatentStateDynamicsContainer latentStateDynamicsContainer = new LatentStateDynamicsContainer();

        latentStateDynamicsContainer.addEntityEquity (
            new TerminalLatentState (
                equityLabel,
                new DiffusionEvolver (
                    DiffusionEvaluatorLinear.Standard (
                        assetValueReplicatorDrift,
                        assetValueReplicatorVolatility
                    )
                )
            )
        );

        return latentStateDynamicsContainer;
    }

    private static final MarketVertexGenerator ConstructMarketVertexGenerator (
        final JulianDate spotDate,
        final int[] eventVertexArray,
        final String currency,
        final String dealer,
        final String client,
        final EntityEquityLabel equityLabel,
        final List<LatentStateLabel> latentStateLabelList)
        throws Exception
    {
        return new MarketVertexGenerator (
            spotDate.julian(),
            eventVertexArray,
            EntityEvolver (
                currency,
                dealer,
                client,
                latentStateLabelList
            ),
            PrimarySecurityEvolver (
                currency,
                dealer,
                client,
                latentStateLabelList
            ),
            LatentStateEvolver (
                equityLabel,
                latentStateLabelList
            )
        );
    }

    private static final MarketVertex[] MarketVertexArray (
        final Map<Integer, MarketVertex> marketVertexMap)
        throws Exception
    {
        int marketVertexCount = marketVertexMap.size();

        int marketVertexIndex = 0;
        MarketVertex[] marketVertexArray = new MarketVertex[marketVertexCount];

        for (Map.Entry<Integer, MarketVertex> marketVertexMapEntry : marketVertexMap.entrySet())
        {
            marketVertexArray[marketVertexIndex++] = marketVertexMapEntry.getValue();
        }

        return marketVertexArray;
    }

    private static final EvolutionTrajectoryVertex RunStep (
        final TrajectoryEvolutionScheme tes,
        final BurgardKjaerOperator bko,
        final EvolutionTrajectoryVertex etvStart,
        final MarketVertex mvStart,
        final MarketVertex mvFinish,
        final LatentStateLabel equityLabel)
        throws Exception
    {
        PositionGreekVertex agvStart = etvStart.positionGreekVertex();

        ReplicationPortfolioVertex rpvStart = etvStart.replicationPortfolioVertex();

        double dblDerivativeXVAValueStart = agvStart.derivativeXVAValue();

        double dblTimeWidth = (mvFinish.anchorDate().julian() - mvStart.anchorDate().julian()) / 365.;

        double dblTimeStart = etvStart.time();

        double dblTime = dblTimeStart + dblTimeWidth;

        PrimarySecurityDynamicsContainer tc = tes.tradeablesContainer();

        double dblCollateralSchemeNumeraire = mvStart.csaReplicator();

        BurgardKjaerEdgeRun bker = bko.edgeRun (
            new MarketEdge (
                mvStart,
                mvFinish
            ),
            etvStart,
            0.
        );

        double dblTheta = bker.theta();

        double dblAssetNumeraireBump = bker.positionValueBump();

        double dblThetaAssetNumeraireUp = bker.thetaPositionValueUp();

        double dblThetaAssetNumeraireDown = bker.thetaPositionValueDown();

        double dblDerivativeXVAValueDeltaFinish = agvStart.derivativeXVAValueDelta() -
            0.5 * (dblThetaAssetNumeraireUp - dblThetaAssetNumeraireDown) * dblTimeWidth / dblAssetNumeraireBump;

        double dblDerivativeXVAValueGammaFinish = agvStart.derivativeXVAValueGamma() -
            (dblThetaAssetNumeraireUp + dblThetaAssetNumeraireDown - 2. * dblTheta) * dblTimeWidth /
                (dblAssetNumeraireBump * dblAssetNumeraireBump);

        double dblDerivativeXVAValueFinish = dblDerivativeXVAValueStart + dblTheta * dblTimeWidth;

        CloseOut cog = new CloseOutBilateral (
            mvStart.dealer().seniorRecoveryRate(),
            mvStart.client().seniorRecoveryRate()
        );

        double dblGainOnBankDefaultFinish = -1. * (dblDerivativeXVAValueFinish - cog.dealerDefault
            (dblDerivativeXVAValueFinish));

        double dblGainOnCounterPartyDefaultFinish = -1. * (dblDerivativeXVAValueFinish - cog.clientDefault
            (dblDerivativeXVAValueFinish));

        org.drip.xva.derivative.CashAccountEdge cae = tes.rebalanceCash (
                etvStart,
                new MarketEdge (
                    mvStart,
                    mvFinish
                )
            ).cashAccountEdge();

        double dblCashAccountAccumulationFinish = cae.accumulation();

        double dblAssetNumeraireFinish = mvFinish.latentStateValue (equityLabel);

        double dblBankSeniorFundingNumeraireFinish = mvFinish.dealer().seniorFundingReplicator();

        double dblCounterPartyFundingNumeraireFinish = mvFinish.client().seniorFundingReplicator();

        ReplicationPortfolioVertex rpvFinish = ReplicationPortfolioVertex.Standard (
            -1. * dblDerivativeXVAValueDeltaFinish,
            dblGainOnBankDefaultFinish / dblBankSeniorFundingNumeraireFinish,
            dblGainOnCounterPartyDefaultFinish / dblCounterPartyFundingNumeraireFinish,
            rpvStart.cashAccount() + dblCashAccountAccumulationFinish
        );

        System.out.println ("\t||" +
            FormatUtil.FormatDouble (dblTime, 1, 6, 1.) + " | " +
            FormatUtil.FormatDouble (dblDerivativeXVAValueFinish, 1, 6, 1.) + " | " +
            FormatUtil.FormatDouble (dblAssetNumeraireFinish, 1, 6, 1.) + " | " +
            FormatUtil.FormatDouble (dblBankSeniorFundingNumeraireFinish, 1, 6, 1.) + " | " +
            FormatUtil.FormatDouble (dblCounterPartyFundingNumeraireFinish, 1, 6, 1.) + " | " +
            FormatUtil.FormatDouble (dblCollateralSchemeNumeraire, 1, 6, 1.) + " | " +
            FormatUtil.FormatDouble (rpvFinish.positionHoldings(), 1, 6, 1.) + " | " +
            FormatUtil.FormatDouble (rpvFinish.dealerSeniorNumeraireHoldings(), 1, 6, 1.) + " | " +
            FormatUtil.FormatDouble (rpvFinish.clientNumeraireHoldings(), 1, 6, 1.) + " | " +
            FormatUtil.FormatDouble (rpvFinish.cashAccount(), 1, 6, 1.) + " | " +
            FormatUtil.FormatDouble (dblCashAccountAccumulationFinish, 1, 6, 1.) + " | " +
            FormatUtil.FormatDouble (cae.assetAccumulation(), 1, 6, 1.) + " | " +
            FormatUtil.FormatDouble (cae.dealerAccumulation(), 1, 6, 1.) + " | " +
            FormatUtil.FormatDouble (cae.clientAccumulation(), 1, 6, 1.) + " ||"
        );

        return new EvolutionTrajectoryVertex (
            dblTimeStart + dblTimeWidth,
            rpvFinish,
            new PositionGreekVertex (
                dblDerivativeXVAValueFinish,
                dblDerivativeXVAValueDeltaFinish,
                dblDerivativeXVAValueGammaFinish,
                agvStart.derivativeFairValue() * Math.exp (
                    -1. * dblTimeWidth * tc.csa().evolver().evaluator().drift().value (
                        new JumpDiffusionVertex (
                            dblTime,
                            dblCollateralSchemeNumeraire,
                            0.,
                            false
                        )
                    )
                )
            ),
            dblGainOnBankDefaultFinish,
            dblGainOnCounterPartyDefaultFinish,
            0.,
            0.
        );
    }

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

        String dealer = "WFC";
        String client = "BAC";
        int vertexCount = 24;
        String currency = "USD";
        int simulationDuration = 365;

        double dealerHazardRateInitial = 0.03;
        double clientHazardRateInitial = 0.05;
        double dealerSeniorRecoveryRateInitial = 0.40;
        double clientRecoveryRateInitial = 0.40;

        double[][] latentStateCorrelationMatrix = new double[][]
        {
            {1.00, 0.00, 0.20, 0.15, 0.05, 0.00, 0.00, 0.00, 0.00, 0.00}, // #0  DEALER HAZARD
            {0.00, 1.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00}, // #1  DEALER SENIOR RECOVERY
            {0.20, 0.00, 1.00, 0.13, 0.25, 0.00, 0.00, 0.00, 0.00, 0.00}, // #2  CLIENT HAZARD
            {0.15, 0.00, 0.13, 1.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00}, // #3  CLIENT RECOVERY
            {0.05, 0.00, 0.25, 0.00, 1.00, 0.00, 0.00, 0.00, 0.00, 0.00}, // #4  OVERNIGHT REPLICATOR
            {0.00, 0.00, 0.00, 0.00, 0.00, 1.00, 0.00, 0.00, 0.00, 0.00}, // #5  CSA REPLICATOR
            {0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 1.00, 0.00, 0.00, 0.00}, // #6  DEALER SENIOR FUNDING REPLICATOR
            {0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 1.00, 0.00, 0.00}, // #7  DEALER SUBORDINATE FUNDING REPLICATOR
            {0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 1.00, 0.00}, // #8  CLIENT FUNDING REPLICATOR
            {0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 1.00}, // #9  EQUITY REPLICATOR
        };

        double dblTerminalXVADerivativeValue = 1.;

        double dblSensitivityShiftFactor = 0.001;

        JulianDate spotDateJulian = DateUtil.Today();

        int spotDate = spotDateJulian.julian();

        int[] eventVertexArray = VertexDateBuilder.EqualWidth (
            spotDate,
            spotDate + simulationDuration,
            vertexCount
        );

        List<LatentStateLabel> latentStateLabelList = new ArrayList<LatentStateLabel>();

        EntityEquityLabel equityLabel = EntityEquityLabel.Standard (
            "AAPL",
            currency
        );

        MarketVertexGenerator marketVertexGenerator = ConstructMarketVertexGenerator (
            spotDateJulian,
            eventVertexArray,
            currency,
            dealer,
            client,
            equityLabel,
            latentStateLabelList
        );

        System.out.println ("marketVertexGenerator = " + marketVertexGenerator);

        LatentStateVertexContainer latentStateVertexContainer = new LatentStateVertexContainer();

        latentStateVertexContainer.add (
            equityLabel,
            1.
        );

        MarketVertex initialMarketVertex = MarketVertex.Epochal (
            spotDateJulian,
            1.000,
            1.000,
            dealerHazardRateInitial,
            dealerSeniorRecoveryRateInitial,
            dealerHazardRateInitial / (1 - dealerSeniorRecoveryRateInitial),
            clientHazardRateInitial,
            clientRecoveryRateInitial,
            clientHazardRateInitial / (1 - clientRecoveryRateInitial),
            latentStateVertexContainer
        );

        CorrelatedPathVertexDimension correlatedPathVertexDimension = new CorrelatedPathVertexDimension (
            new RandomNumberGenerator(),
            latentStateCorrelationMatrix,
            vertexCount,
            1,
            true,
            null
        );

        MarketVertex[] aMV = MarketVertexArray (
            marketVertexGenerator.marketVertex (
                initialMarketVertex,
                LatentStateWeiner.FromUnitRandom (
                    latentStateLabelList,
                    Matrix.Transpose (correlatedPathVertexDimension.straightPathVertexRd().flatform())
                )
            )
        );

        System.out.println ("aMV = " + aMV);

        double dblDerivativeValue = dblTerminalXVADerivativeValue;
        double dblDerivativeXVAValue = dblTerminalXVADerivativeValue;

        PDEEvolutionControl pdeec = new PDEEvolutionControl (
            PDEEvolutionControl.CLOSEOUT_GREGORY_LI_TANG,
            dblSensitivityShiftFactor
        );

        CloseOutBilateral cob = new CloseOutBilateral (
            dealerSeniorRecoveryRateInitial,
            clientRecoveryRateInitial
        );

        TrajectoryEvolutionScheme tes = new TrajectoryEvolutionScheme (
            marketVertexGenerator.primarySecurityDynamicsContainer(),
            pdeec
        );

        BurgardKjaerOperator bko = new BurgardKjaerOperator (
            marketVertexGenerator.primarySecurityDynamicsContainer(),
            pdeec
        );

        PositionGreekVertex agvInitial = new PositionGreekVertex (
            dblDerivativeXVAValue,
            -1.,
            0.,
            dblDerivativeValue
        );

        double dblGainOnBankDefaultInitial = -1. * (dblDerivativeXVAValue - cob.dealerDefault
            (dblDerivativeXVAValue));

        double dblGainOnCounterPartyDefaultInitial = -1. * (dblDerivativeXVAValue - cob.clientDefault
            (dblDerivativeXVAValue));

        ReplicationPortfolioVertex rpvInitial = ReplicationPortfolioVertex.Standard (
            1.,
            dblGainOnBankDefaultInitial,
            dblGainOnCounterPartyDefaultInitial,
            0.
        );

        System.out.println();

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

        System.out.println ("\t||                                            BILATERAL XVA EVOLVER - BURGARD & KJAER (2011) REPLICATION PORTFOLIO EVOLUTION                                             ||");

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

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

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

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

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

        System.out.println ("\t||            - Realization of the Zero Coupon Bank Bond Price                                                                                                           ||");

        System.out.println ("\t||            - Realization of the Zero Coupon Counter Party Bond Price                                                                                                  ||");

        System.out.println ("\t||            - Realization of the Zero Coupon Collateral Bond Price                                                                                                     ||");

        System.out.println ("\t||            - Derivative XVA Asset Replication Units                                                                                                                   ||");

        System.out.println ("\t||            - Derivative XVA Value Bank Bond Replication Units                                                                                                         ||");

        System.out.println ("\t||            - Derivative XVA Value Counter Party Bond Replication Units                                                                                                ||");

        System.out.println ("\t||            - Derivative XVA Value Cash Account Replication Units                                                                                                      ||");

        System.out.println ("\t||            - Derivative Cash Account Accumulation Component                                                                                                           ||");

        System.out.println ("\t||            - Asset Cash Account Accumulation Component                                                                                                                ||");

        System.out.println ("\t||            - Bank Cash Account Accumulation Component                                                                                                                 ||");

        System.out.println ("\t||            - Counter Party Cash Account Accumulation Component                                                                                                        ||");

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

        System.out.println ("\t||" +
            FormatUtil.FormatDouble (1., 1, 6, 1.) + " | " +
            FormatUtil.FormatDouble (agvInitial.derivativeXVAValue(), 1, 6, 1.) + " | " +
            FormatUtil.FormatDouble (aMV[aMV.length - 1].latentStateValue (equityLabel), 1, 6, 1.) + " | " +
            FormatUtil.FormatDouble (1., 1, 6, 1.) + " | " +
            FormatUtil.FormatDouble (1., 1, 6, 1.) + " | " +
            FormatUtil.FormatDouble (1., 1, 6, 1.) + " | " +
            FormatUtil.FormatDouble (rpvInitial.positionHoldings(), 1, 6, 1.) + " | " +
            FormatUtil.FormatDouble (rpvInitial.dealerSeniorNumeraireHoldings(), 1, 6, 1.) + " | " +
            FormatUtil.FormatDouble (rpvInitial.clientNumeraireHoldings(), 1, 6, 1.) + " | " +
            FormatUtil.FormatDouble (rpvInitial.cashAccount(), 1, 6, 1.) + " | " +
            FormatUtil.FormatDouble (0., 1, 6, 1.) + " | " +
            FormatUtil.FormatDouble (0., 1, 6, 1.) + " | " +
            FormatUtil.FormatDouble (0., 1, 6, 1.) + " | " +
            FormatUtil.FormatDouble (0., 1, 6, 1.) + " ||"
        );

        EvolutionTrajectoryVertex etv = new EvolutionTrajectoryVertex (
            1.,
            ReplicationPortfolioVertex.Standard (
                1.,
                0.,
                0.,
                0.
            ),
            agvInitial,
            dblGainOnBankDefaultInitial,
            dblGainOnCounterPartyDefaultInitial,
            0.,
            0.
        );

        for (int i = vertexCount - 1; i >= 0; --i)
            etv = RunStep (
                tes,
                bko,
                etv,
                aMV[i + 1],
                aMV[i],
                equityLabel
            );

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

        System.out.println();

        EnvManager.TerminateEnv();
    }
}