CorrelatedNumeraireXVAGreeks.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>CorrelatedNumeraireXVAGreeks</i> constructs the XVA Greeks arising out of the Joint Evolution of
 * Numeraires - the Continuous Asset, the Collateral, the Bank, and the Counter-Party Numeraires involved in
 * the Dynamic XVA Replication Portfolio of the Burgard and Kjaer (2011) Methodology. 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 CorrelatedNumeraireXVAGreeks
{

	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)
		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 tcm = 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));

		System.out.println ("\t||" +
			FormatUtil.FormatDouble (dblTime, 1, 6, 1.) + " | " +
			FormatUtil.FormatDouble (dblDerivativeXVAValueFinish, 1, 6, 1.) + " | " +
			FormatUtil.FormatDouble (dblDerivativeXVAValueDeltaFinish, 1, 6, 1.) + " | " +
			FormatUtil.FormatDouble (dblDerivativeXVAValueGammaFinish, 1, 6, 1.) + " | " +
			FormatUtil.FormatDouble (dblGainOnBankDefaultFinish, 1, 6, 1.) + " | " +
			FormatUtil.FormatDouble (dblGainOnCounterPartyDefaultFinish, 1, 6, 1.) + " | " +
			FormatUtil.FormatDouble (bker.derivativeXVAStochasticGrowth(), 1, 6, 1.) + " | " +
			FormatUtil.FormatDouble (bker.derivativeXVACollateralGrowth(), 1, 6, 1.) + " | " +
			FormatUtil.FormatDouble (bker.derivativeXVAFundingGrowth(), 1, 6, 1.) + " | " +
			FormatUtil.FormatDouble (bker.derivativeXVADealerDefaultGrowth(), 1, 6, 1.) + " | " +
			FormatUtil.FormatDouble (bker.derivativeXVAClientDefaultGrowth(), 1, 6, 1.) + " | " +
			FormatUtil.FormatDouble (dblThetaAssetNumeraireDown, 1, 6, 1.) + " | " +
			FormatUtil.FormatDouble (dblTheta, 1, 6, 1.) + " | " +
			FormatUtil.FormatDouble (dblThetaAssetNumeraireUp, 1, 6, 1.) + " ||"
		);

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

		double dblCashAccountAccumulationFinish = cae.accumulation();

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

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

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

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

	public static final 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));

		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||            - Derivative XVA Delta                                                                                                                                     ||");

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

		System.out.println ("\t||            - Derivative Gain on Bank Default                                                                                                                          ||");

		System.out.println ("\t||            - Derivative Gain on Counter Party Default                                                                                                                 ||");

		System.out.println ("\t||            - Derivative XVA Stochastic Growth Rate                                                                                                                    ||");

		System.out.println ("\t||            - Derivative XVA Collateral Growth Rate                                                                                                                    ||");

		System.out.println ("\t||            - Derivative XVA Funding Growth Rate                                                                                                                       ||");

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

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

		System.out.println ("\t||            - Derivative XVA Bank Default Growth                                                                                                                       ||");

		System.out.println ("\t||            - Derivative XVA Counter Party Default Growth                                                                                                              ||");

		System.out.println ("\t||            - Derivative XVA Early Termination Growth                                                                                                                  ||");

		System.out.println ("\t||            - Derivative XVA Theta Asset Numeraire Down                                                                                                                ||");

		System.out.println ("\t||            - Derivative XVA Theta Asset Numeraire Flat                                                                                                                ||");

		System.out.println ("\t||            - Derivative XVA Theta Asset Numeraire Up                                                                                                                  ||");

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

		System.out.println ("\t||" +
			FormatUtil.FormatDouble (1., 1, 6, 1.) + " | " +
			FormatUtil.FormatDouble (dblDerivativeXVAValue, 1, 6, 1.) + " | " +
			FormatUtil.FormatDouble (-1., 1, 6, 1.) + " | " +
			FormatUtil.FormatDouble (0., 1, 6, 1.) + " | " +
			FormatUtil.FormatDouble (dblGainOnBankDefaultInitial, 1, 6, 1.) + " | " +
			FormatUtil.FormatDouble (dblGainOnCounterPartyDefaultInitial, 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.) + " | " +
			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.,
				dblGainOnBankDefaultInitial,
				dblGainOnCounterPartyDefaultInitial,
				0.
			),
			agvInitial,
			dblGainOnBankDefaultInitial,
			dblGainOnCounterPartyDefaultInitial,
			0.,
			0.
		);

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

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

		System.out.println();

		EnvManager.TerminateEnv();
	}
}