ExposurePathBrownianBridge.java

package org.drip.sample.pykhtin2009;

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

import org.drip.analytics.date.DateUtil;
import org.drip.analytics.date.JulianDate;
import org.drip.exposure.csatimeline.AndersenPykhtinSokolLag;
import org.drip.exposure.evolver.EntityDynamicsContainer;
import org.drip.exposure.evolver.LatentStateDynamicsContainer;
import org.drip.exposure.evolver.LatentStateVertexContainer;
import org.drip.exposure.evolver.PrimarySecurity;
import org.drip.exposure.evolver.PrimarySecurityDynamicsContainer;
import org.drip.exposure.evolver.TerminalLatentState;
import org.drip.exposure.generator.NumeraireMPoR;
import org.drip.exposure.mpor.PathVariationMarginTrajectoryEstimator;
import org.drip.exposure.regression.LocalVolatilityGenerationControl;
import org.drip.exposure.regression.PykhtinBrownianBridgeStretch;
import org.drip.exposure.regression.PykhtinPillarDynamics;
import org.drip.exposure.universe.LatentStateWeiner;
import org.drip.exposure.universe.MarketPath;
import org.drip.exposure.universe.MarketVertex;
import org.drip.exposure.universe.MarketVertexGenerator;
import org.drip.function.definition.R1ToR1;
import org.drip.measure.crng.RandomNumberGenerator;
import org.drip.measure.discrete.CorrelatedPathVertexDimension;
import org.drip.measure.dynamics.DiffusionEvaluatorLinear;
import org.drip.measure.dynamics.DiffusionEvaluatorLogarithmic;
import org.drip.measure.dynamics.HazardJumpEvaluator;
import org.drip.measure.gaussian.NormalQuadrature;
import org.drip.measure.process.DiffusionEvolver;
import org.drip.measure.process.JumpDiffusionEvolver;
import org.drip.measure.statistics.UnivariateDiscreteThin;
import org.drip.numerical.common.FormatUtil;
import org.drip.numerical.linearalgebra.Matrix;
import org.drip.service.env.EnvManager;
import org.drip.state.identifier.CSALabel;
import org.drip.state.identifier.EntityEquityLabel;
import org.drip.state.identifier.EntityFundingLabel;
import org.drip.state.identifier.EntityHazardLabel;
import org.drip.state.identifier.EntityRecoveryLabel;
import org.drip.state.identifier.LatentStateLabel;
import org.drip.state.identifier.OvernightLabel;

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

/*!
 * Copyright (C) 2018 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.
 */

/**
 * ExposurePathBrownianBridge sets up a Brownian Bridge Scheme base on the Pykhtin (2009) local Volatility
 *  Methodology to estimate Exposures at Secondary Nodes. The References are:
 *  
 *  - Andersen, L. B. G., M. Pykhtin, and A. Sokol (2017): Re-thinking Margin Period of Risk,
 *      https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2902737, eSSRN.
 *  
 *  - Andersen, L. B. G., M. Pykhtin, and A. Sokol (2017): Credit Exposure in the Presence of Initial Margin,
 *      https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2806156, eSSRN.
 *  
 *  - Albanese, C., and L. Andersen (2014): Accounting for OTC Derivatives: Funding Adjustments and the
 *      Re-Hypothecation Option, eSSRN, https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2482955.
 *  
 *  - Burgard, C., and M. Kjaer (2017): Derivatives Funding, Netting, and Accounting, eSSRN,
 *      https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2534011.
 * 
 *  - Pykhtin, M. (2009): Modeling Counter-party Credit Exposure in the Presence of Margin Agreements,
 *      http://www.risk-europe.com/protected/michael-pykhtin.pdf.
 * 
 * @author Lakshmi Krishnamurthy
 */

public class ExposurePathBrownianBridge
{

    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 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 PrimarySecurityDynamicsContainer PrimarySecurityEvolver (
        final String currency,
        final String dealer,
        final String client,
        final List<LatentStateLabel> latentStateLabelList)
        throws Exception
    {
        return new PrimarySecurityDynamicsContainer (
            null,
            OvernightReplicator (
                currency,
                latentStateLabelList
            ),
            CSAReplicator (
                currency,
                latentStateLabelList
            ),
            DealerSeniorFundingReplicator (
                currency,
                dealer,
                latentStateLabelList
            ),
            DealerSubordinateFundingReplicator (
                currency,
                dealer,
                latentStateLabelList
            ),
            ClientFundingReplicator (
                currency,
                client,
                latentStateLabelList
            )
        );
    }

    private static final LatentStateDynamicsContainer LatentStateEvolver (
        final EntityEquityLabel equityLabel,
        final List<LatentStateLabel> latentStateLabelList)
        throws Exception
    {
        double equityNumeraireDrift = 0.05;
        double equityNumeraireVolatility = 0.10;

        latentStateLabelList.add (equityLabel);

        LatentStateDynamicsContainer latentStateDynamicsContainer = new LatentStateDynamicsContainer();

        latentStateDynamicsContainer.addEntityEquity (
            new TerminalLatentState (
                equityLabel,
                new DiffusionEvolver (
                    DiffusionEvaluatorLinear.Standard (
                        equityNumeraireDrift,
                        equityNumeraireVolatility
                    )
                )
            )
        );

        return latentStateDynamicsContainer;
    }

    private static final MarketVertexGenerator ConstructMarketVertexGenerator (
        final JulianDate spotDate,
        final String exposureSamplingTenor,
        final int exposureSamplingNodeCount,
        final String currency,
        final String dealer,
        final String client,
        final EntityEquityLabel equityLabel,
        final List<LatentStateLabel> latentStateLabelList)
        throws Exception
    {
        JulianDate terminationDate = spotDate;
        int[] eventVertexArray = new int[exposureSamplingNodeCount];

        for (int i = 0; i < exposureSamplingNodeCount; ++i)
        {
            terminationDate = terminationDate.addTenor (exposureSamplingTenor);

            eventVertexArray[i] = terminationDate.julian();
        }

        return new MarketVertexGenerator (
            spotDate.julian(),
            eventVertexArray,
            EntityEvolver (
                currency,
                dealer,
                client,
                latentStateLabelList
            ),
            PrimarySecurityEvolver (
                currency,
                dealer,
                client,
                latentStateLabelList
            ),
            LatentStateEvolver (
                equityLabel,
                latentStateLabelList
            )
        );
    }

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

        JulianDate spotDateJulian = DateUtil.CreateFromYMD (
            2018,
            DateUtil.APRIL,
            19
        );

        int pathCount = 1000;
        String sparseExposureTenor = "3M";
        int sparseExposurePeriodCount = 20;
        String currency = "USD";
        String dealer = "NOM";
        String client = "SSGA";
        double[][] correlationMatrix = 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  OTC FIX FLOAT REPLICATOR
        };
        String referenceEntity = "HYG";
        double equityNotional = 10.;

        int spotDate = spotDateJulian.julian();

        LocalVolatilityGenerationControl localVolatilityGenerationControl =
            LocalVolatilityGenerationControl.Standard (pathCount);

        EntityEquityLabel equityLabel = EntityEquityLabel.Standard (
            referenceEntity,
            currency
        );

        NumeraireMPoR numeraireMPoR = new NumeraireMPoR (
            equityLabel,
            equityNotional
        );

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

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

        LatentStateVertexContainer latentStateVertexContainer = new LatentStateVertexContainer();

        latentStateVertexContainer.add (
            equityLabel,
            10.
        );

        MarketVertex initialMarketVertex = MarketVertex.Epochal (
            spotDateJulian,
            1.000,              // dblOvernightNumeraireInitial
            1.000,              // dblCSANumeraire
            0.015,              // dblBankHazardRate
            0.400,              // dblBankRecoveryRate
            0.015 / (1 - 0.40), // dblBankFundingSpread
            0.030,              // dblCounterPartyHazardRate
            0.300,              // dblCounterPartyRecoveryRate
            0.030 / (1 - 0.30), // dblCounterPartyFundingSpread
            latentStateVertexContainer
        );

        AndersenPykhtinSokolLag andersenPykhtinSokolLag = AndersenPykhtinSokolLag.ClassicalMinus();

        CorrelatedPathVertexDimension correlatedPathVertexDimension = new CorrelatedPathVertexDimension (
            new RandomNumberGenerator(),
            correlationMatrix,
            sparseExposurePeriodCount,
            1,
            true,
            null
        );

        JulianDate sparseExposureDate = spotDateJulian;
        int[] sparseExposureDateArray = new int[sparseExposurePeriodCount + 1];
        double[][] pathSparseExposureArray = new double[sparseExposurePeriodCount + 1][pathCount];

        for (int i = 0; i <= sparseExposurePeriodCount; ++i)
        {
            sparseExposureDateArray[i] = sparseExposureDate.julian();

            sparseExposureDate = sparseExposureDate.addTenor (sparseExposureTenor);
        }

        List<Map<Integer, Double>> wanderTrajectoryList = new ArrayList<Map<Integer, Double>>();

        for (int pathIndex = 0; pathIndex < pathCount; ++pathIndex)
        {
            Map<Integer, Double> wanderTrajectory = new TreeMap<Integer, Double>();

            for (int denseExposureDate = spotDate;
                denseExposureDate <= sparseExposureDateArray[sparseExposurePeriodCount];
                ++denseExposureDate)
            {
                wanderTrajectory.put (
                    denseExposureDate,
                    NormalQuadrature.Random()
                );
            }

            wanderTrajectoryList.add (wanderTrajectory);
        }

        for (int pathIndex = 0; pathIndex < pathCount; ++pathIndex)
        {
            MarketPath marketPath = new MarketPath (
                marketVertexGenerator.marketVertex (
                    initialMarketVertex,
                    LatentStateWeiner.FromUnitRandom (
                        latentStateLabelList,
                        Matrix.Transpose (correlatedPathVertexDimension.straightPathVertexRd().flatform())
                    )
                )
            );

            Map<Integer, Double> variationMarginEstimateTrajectory =
                PathVariationMarginTrajectoryEstimator.Standard (
                    sparseExposureDateArray,
                    currency,
                    numeraireMPoR,
                    marketPath,
                    andersenPykhtinSokolLag
                ).variationMarginEstimateTrajectory();

            int sparseExposureDateIndex = 0;

            for (Map.Entry<Integer, Double> variationMarginEstimateTrajectoryEntry :
                variationMarginEstimateTrajectory.entrySet())
            {
                pathSparseExposureArray[sparseExposureDateIndex++][pathIndex] =
                    variationMarginEstimateTrajectoryEntry.getValue();
            }
        }

        Map<Integer, R1ToR1> localVolatilityTrajectory = new TreeMap<Integer, R1ToR1>();

        for (int exposureDateIndex = 0; exposureDateIndex <= sparseExposurePeriodCount; ++exposureDateIndex)
        {
            PykhtinPillarDynamics vertexRealization = PykhtinPillarDynamics.Standard
                (pathSparseExposureArray [exposureDateIndex]);

            localVolatilityTrajectory.put (
                sparseExposureDateArray[exposureDateIndex],
                null == vertexRealization ? null :
                    vertexRealization.localVolatilityR1ToR1 (localVolatilityGenerationControl)
            );
        }

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

        System.out.println ("\t||           EXPOSURE DATE LOCAL VOLATILITY              ||");

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

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

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

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

        System.out.println ("\t||            - The Spot/Forward Dates                   ||");

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

        int denseExposureDateCount = sparseExposureDateArray[sparseExposurePeriodCount] - spotDate + 1;
        double[][] pathDenseExposureDistribution = new double[denseExposureDateCount][pathCount];
        UnivariateDiscreteThin[] univariateDiscreteThinArray = new
            UnivariateDiscreteThin[denseExposureDateCount];

        for (int pathIndex = 0; pathIndex < pathCount; ++pathIndex)
        {
            Map<Integer, Double> sparseExposureTrajectory = new TreeMap<Integer, Double>();

            for (int sparseExposureDateIndex = 0;
                sparseExposureDateIndex <= sparseExposurePeriodCount;
                ++sparseExposureDateIndex)
            {
                sparseExposureTrajectory.put (
                    sparseExposureDateArray[sparseExposureDateIndex],
                    pathSparseExposureArray[sparseExposureDateIndex][pathIndex]
                );
            }

            Map<Integer, Double> pathDenseExposureTrajectory = new PykhtinBrownianBridgeStretch (
                sparseExposureTrajectory,
                localVolatilityTrajectory
            ).denseExposure (wanderTrajectoryList.get (pathIndex));

            if (null != pathDenseExposureTrajectory)
            {
                for (int denseExposureDate = spotDate;
                    denseExposureDate <= sparseExposureDateArray[sparseExposurePeriodCount];
                    ++denseExposureDate)
                {
                    pathDenseExposureDistribution[denseExposureDate - spotDate][pathIndex] =
                        pathDenseExposureTrajectory.get (denseExposureDate);
                }
            }
        }

        for (int denseExposureDate = spotDate;
            denseExposureDate <= sparseExposureDateArray[sparseExposurePeriodCount];
            ++denseExposureDate)
        {
            int dateIndex = denseExposureDate - spotDate;

            univariateDiscreteThinArray[dateIndex] = new UnivariateDiscreteThin
                (pathDenseExposureDistribution[dateIndex]);

            System.out.println (
                "\t|| " +
                new JulianDate (denseExposureDate) + " => " +
                FormatUtil.FormatDouble (univariateDiscreteThinArray[dateIndex].average(), 3, 3, 1.) + " |" +
                FormatUtil.FormatDouble (univariateDiscreteThinArray[dateIndex].minimum(), 3, 3, 1.) + " |" +
                FormatUtil.FormatDouble (univariateDiscreteThinArray[dateIndex].maximum(), 3, 3, 1.) + " |" +
                FormatUtil.FormatDouble (univariateDiscreteThinArray[dateIndex].error(), 3, 3, 1.) + " ||"
            );
        }

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

        EnvManager.TerminateEnv();
    }
}