MultiFactorLIBORMonteCarlo.java

package org.drip.sample.lmm;

import java.util.List;

import org.drip.analytics.date.JulianDate;
import org.drip.analytics.definition.MarketSurface;
import org.drip.analytics.support.CompositePeriodBuilder;
import org.drip.dynamics.lmm.*;
import org.drip.function.r1tor1.QuadraticRationalShapeControl;
import org.drip.numerical.common.FormatUtil;
import org.drip.param.creator.*;
import org.drip.param.market.CurveSurfaceQuoteContainer;
import org.drip.param.period.*;
import org.drip.param.valuation.*;
import org.drip.product.creator.SingleStreamComponentBuilder;
import org.drip.product.rates.*;
import org.drip.sequence.random.*;
import org.drip.service.env.EnvManager;
import org.drip.spline.basis.PolynomialFunctionSetParams;
import org.drip.spline.grid.OverlappingStretchSpan;
import org.drip.spline.params.*;
import org.drip.spline.stretch.*;
import org.drip.state.creator.*;
import org.drip.state.curve.BasisSplineForwardRate;
import org.drip.state.discount.*;
import org.drip.state.estimator.LatentStateStretchBuilder;
import org.drip.state.forward.ForwardCurve;
import org.drip.state.identifier.*;
import org.drip.state.inference.*;

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

/*!
 * Copyright (C) 2019 Lakshmi Krishnamurthy
 * Copyright (C) 2018 Lakshmi Krishnamurthy
 * Copyright (C) 2017 Lakshmi Krishnamurthy
 * Copyright (C) 2016 Lakshmi Krishnamurthy
 * Copyright (C) 2015 Lakshmi Krishnamurthy
 * 
 *  This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
 *      calculations, valuation adjustment, and portfolio construction within and across fixed income,
 *      credit, commodity, equity, FX, and structured products.
 *  
 *      https://lakshmidrip.github.io/DROP/
 *  
 *  DROP is composed of three modules:
 *  
 *  - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
 *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
 *  - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
 * 
 *  DROP Analytics Core implements libraries for the following:
 *  - Fixed Income Analytics
 *  - Asset Backed Analytics
 *  - XVA Analytics
 *  - Exposure and Margin Analytics
 * 
 *  DROP Portfolio Core implements libraries for the following:
 *  - Asset Allocation Analytics
 *  - Transaction Cost Analytics
 * 
 *  DROP Numerical Core implements libraries for the following:
 *  - Statistical Learning
 *  - Numerical Optimizer
 *  - Spline Builder
 *  - Algorithm Support
 * 
 *  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>MultiFactorLIBORMonteCarlo</i> demonstrates the Monte-Carlo Evolution Sequence of the LIBOR Forward
 * Curve. The References are:
 *  
 * <br><br>
 *  <ul>
 *      <li>
 *          Goldys, B., M. Musiela, and D. Sondermann (1994): Log-normality of Rates and Term Structure
 *              Models, The University of New South Wales.
 *      </li>
 *      <li>
 *          Musiela, M. (1994): Nominal Annual Rates and Log-normal Volatility Structure, The University of
 *              New South Wales.
 *      </li>
 *      <li>
 *          Brace, A., D. Gatarek, and M. Musiela (1997): The Market Model of Interest Rate Dynamics,
 *              Mathematical Finance 7 (2), 127-155.
 *      </li>
 *  </ul>
 *  
 * <br><br>
 *  <ul>
 *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/AnalyticsCore.md">Analytics Core Module</a></li>
 *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FixedIncomeAnalyticsLibrary.md">Fixed Income 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">Sample</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/lmm/README.md">LIBOR Market (LMM-BGM Variant) Evolution</a></li>
 *  </ul>
 * <br><br>
 *
 * @author Lakshmi Krishnamurthy
 */

public class MultiFactorLIBORMonteCarlo {

    /*
     * Construct the Array of Deposit Instruments from the given set of parameters
     * 
     *      USE WITH CARE: This sample ignores errors and does not handle exceptions.
     */

    private static final SingleStreamComponent[] DepositInstrumentsFromMaturityDays (
        final JulianDate dtEffective,
        final String strCurrency,
        final int[] aiDay)
        throws Exception
    {
        SingleStreamComponent[] aDeposit = new SingleStreamComponent[aiDay.length];

        ComposableFloatingUnitSetting cfus = new ComposableFloatingUnitSetting (
            "3M",
            CompositePeriodBuilder.EDGE_DATE_SEQUENCE_SINGLE,
            null,
            ForwardLabel.Create (
                strCurrency,
                "3M"
            ),
            CompositePeriodBuilder.REFERENCE_PERIOD_IN_ADVANCE,
            0.
        );

        CompositePeriodSetting cps = new CompositePeriodSetting (
            4,
            "3M",
            strCurrency,
            null,
            1.,
            null,
            null,
            null,
            null
        );

        CashSettleParams csp = new CashSettleParams (
            0,
            strCurrency,
            0
        );

        for (int i = 0; i < aiDay.length; ++i) {
            aDeposit[i] = new SingleStreamComponent (
                "DEPOSIT_" + aiDay[i],
                new Stream (
                    CompositePeriodBuilder.FloatingCompositeUnit (
                        CompositePeriodBuilder.EdgePair (
                            dtEffective,
                            dtEffective.addBusDays (
                                aiDay[i],
                                strCurrency
                            )
                        ),
                        cps,
                        cfus
                    )
                ),
                csp
            );

            aDeposit[i].setPrimaryCode (aiDay[i] + "D");
        }

        return aDeposit;
    }

    /*
     * Construct the Array of Swap Instruments from the given set of parameters
     * 
     *      USE WITH CARE: This sample ignores errors and does not handle exceptions.
     */

    private static final FixFloatComponent[] SwapInstrumentsFromMaturityTenor (
        final JulianDate dtEffective,
        final String strCurrency,
        final String[] astrMaturityTenor)
        throws Exception
    {
        FixFloatComponent[] aIRS = new FixFloatComponent[astrMaturityTenor.length];

        UnitCouponAccrualSetting ucasFixed = new UnitCouponAccrualSetting (
            4,
            "Act/360",
            false,
            "Act/360",
            false,
            strCurrency,
            true,
            CompositePeriodBuilder.ACCRUAL_COMPOUNDING_RULE_GEOMETRIC
        );

        ComposableFloatingUnitSetting cfusFloating = new ComposableFloatingUnitSetting (
            "3M",
            CompositePeriodBuilder.EDGE_DATE_SEQUENCE_REGULAR,
            null,
            ForwardLabel.Create (
                strCurrency,
                "3M"
            ),
            CompositePeriodBuilder.REFERENCE_PERIOD_IN_ADVANCE,
            0.
        );

        ComposableFixedUnitSetting cfusFixed = new ComposableFixedUnitSetting (
            "3M",
            CompositePeriodBuilder.EDGE_DATE_SEQUENCE_REGULAR,
            null,
            0.,
            0.,
            strCurrency
        );

        CompositePeriodSetting cpsFloating = new CompositePeriodSetting (
            4,
            "3M",
            strCurrency,
            null,
            -1.,
            null,
            null,
            null,
            null
        );

        CompositePeriodSetting cpsFixed = new CompositePeriodSetting (
            4,
            "3M",
            strCurrency,
            null,
            1.,
            null,
            null,
            null,
            null
        );

        CashSettleParams csp = new CashSettleParams (
            0,
            strCurrency,
            0
        );

        for (int i = 0; i < astrMaturityTenor.length; ++i) {
            List<Integer> lsFixedStreamEdgeDate = CompositePeriodBuilder.RegularEdgeDates (
                dtEffective,
                "3M",
                astrMaturityTenor[i],
                null
            );

            List<Integer> lsFloatingStreamEdgeDate = CompositePeriodBuilder.RegularEdgeDates (
                dtEffective,
                "3M",
                astrMaturityTenor[i],
                null
            );

            Stream floatingStream = new Stream (
                CompositePeriodBuilder.FloatingCompositeUnit (
                    lsFloatingStreamEdgeDate,
                    cpsFloating,
                    cfusFloating
                )
            );

            Stream fixedStream = new Stream (
                CompositePeriodBuilder.FixedCompositeUnit (
                    lsFixedStreamEdgeDate,
                    cpsFixed,
                    ucasFixed,
                    cfusFixed
                )
            );

            FixFloatComponent irs = new FixFloatComponent (
                fixedStream,
                floatingStream,
                csp
            );

            irs.setPrimaryCode ("IRS." + astrMaturityTenor[i] + "." + strCurrency);

            aIRS[i] = irs;
        }

        return aIRS;
    }

    /*
     * This sample demonstrates discount curve calibration and input instrument calibration quote recovery.
     *  It shows the following:
     *  - Construct the Array of Cash/Swap Instruments and their Quotes from the given set of parameters.
     *  - Construct the Cash/Swap Instrument Set Stretch Builder.
     *  - Set up the Linear Curve Calibrator using the following parameters:
     *      - Cubic Exponential Mixture Basis Spline Set
     *      - Ck = 2, Segment Curvature Penalty = 2
     *      - Quadratic Rational Shape Controller
     *      - Natural Boundary Setting
     *  - Construct the Shape Preserving Discount Curve by applying the linear curve calibrator to the array
     *      of Cash and Swap Stretches.
     *  - Cross-Comparison of the Cash/Swap Calibration Instrument "Rate" metric across the different curve
     *      construction methodologies.
     * 
     *      USE WITH CARE: This sample ignores errors and does not handle exceptions.
     */

    private static final MergedDiscountForwardCurve OTCInstrumentCurve (
        final JulianDate dtSpot,
        final String strCurrency)
        throws Exception
    {
        /*
         * Construct the Array of Deposit Instruments and their Quotes from the given set of parameters
         */

        SingleStreamComponent[] aDepositComp = DepositInstrumentsFromMaturityDays (
            dtSpot,
            strCurrency,
            new int[] {
                1, 2, 7, 14, 30, 60
            }
        );

        double[] adblDepositQuote = new double[] {
            0.0013, 0.0017, 0.0017, 0.0018, 0.0020, 0.0023
        };

        /*
         * Construct the Deposit Instrument Set Stretch Builder
         */

        LatentStateStretchSpec depositStretch = LatentStateStretchBuilder.ForwardFundingStretchSpec (
            "DEPOSIT",
            aDepositComp,
            "ForwardRate",
            adblDepositQuote
        );

        /*
         * Construct the Array of EDF Instruments and their Quotes from the given set of parameters
         */

        SingleStreamComponent[] aEDFComp = SingleStreamComponentBuilder.ForwardRateFuturesPack (
            dtSpot,
            8,
            strCurrency
        );

        double[] adblEDFQuote = new double[] {
            0.0027, 0.0032, 0.0041, 0.0054, 0.0077, 0.0104, 0.0134, 0.0160
        };

        /*
         * Construct the EDF Instrument Set Stretch Builder
         */

        LatentStateStretchSpec edfStretch = LatentStateStretchBuilder.ForwardFundingStretchSpec (
            "EDF",
            aEDFComp,
            "ForwardRate",
            adblEDFQuote
        );

        /*
         * Construct the Array of Swap Instruments and their Quotes from the given set of parameters
         */

        FixFloatComponent[] aSwapComp = SwapInstrumentsFromMaturityTenor (
            dtSpot,
            strCurrency,
            new java.lang.String[] {
                "4Y", "5Y", "6Y", "7Y", "8Y", "9Y", "10Y", "11Y", "12Y", "15Y", "20Y", "25Y", "30Y", "40Y", "50Y"
            }
        );

        double[] adblSwapQuote = new double[] {
            0.0166, 0.0206, 0.0241, 0.0269, 0.0292, 0.0311, 0.0326, 0.0340, 0.0351, 0.0375, 0.0393, 0.0402, 0.0407, 0.0409, 0.0409
        };

        /*
         * Construct the Swap Instrument Set Stretch Builder
         */

        LatentStateStretchSpec swapStretch = LatentStateStretchBuilder.ForwardFundingStretchSpec (
            "SWAP",
            aSwapComp,
            "SwapRate",
            adblSwapQuote
        );

        LatentStateStretchSpec[] aStretchSpec = new LatentStateStretchSpec[] {
            depositStretch,
            edfStretch,
            swapStretch
        };

        /*
         * Set up the Linear Curve Calibrator using the following parameters:
         *  - Cubic Exponential Mixture Basis Spline Set
         *  - Ck = 2, Segment Curvature Penalty = 2
         *  - Quadratic Rational Shape Controller
         *  - Natural Boundary Setting
         */

        LinearLatentStateCalibrator lcc = new LinearLatentStateCalibrator (
            new SegmentCustomBuilderControl (
                MultiSegmentSequenceBuilder.BASIS_SPLINE_POLYNOMIAL,
                new PolynomialFunctionSetParams (4),
                SegmentInelasticDesignControl.Create (
                    2,
                    2
                ),
                new ResponseScalingShapeControl (
                    true,
                    new QuadraticRationalShapeControl (0.)
                ),
                null
            ),
            BoundarySettings.NaturalStandard(),
            MultiSegmentSequence.CALIBRATE,
            null,
            null
        );

        ValuationParams valParams = new ValuationParams (
            dtSpot,
            dtSpot,
            strCurrency
        );

        /*
         * Construct the Shape Preserving Discount Curve by applying the linear curve calibrator to the array
         *  of Deposit, Futures, and Swap Stretches.
         */

        MergedDiscountForwardCurve dc = ScenarioDiscountCurveBuilder.ShapePreservingDFBuild (
            strCurrency,
            lcc,
            aStretchSpec,
            valParams,
            null,
            null,
            null,
            1.
        );

        CurveSurfaceQuoteContainer csqs = MarketParamsBuilder.Create (
            dc,
            null,
            null,
            null,
            null,
            null,
            null
        );

        /*
         * Cross-Comparison of the Deposit Calibration Instrument "Rate" metric across the different curve
         *  construction methodologies.
         */

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

        System.out.println ("\t     DEPOSIT INSTRUMENTS CALIBRATION RECOVERY");

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

        for (int i = 0; i < aDepositComp.length; ++i)
            System.out.println ("\t[" + aDepositComp[i].maturityDate() + "] = " +
                FormatUtil.FormatDouble (aDepositComp[i].measureValue (valParams, null, csqs,
                    null, "Rate"), 1, 6, 1.) + " | " + FormatUtil.FormatDouble (adblDepositQuote[i], 1, 6, 1.));

        /*
         * Cross-Comparison of the EDF Calibration Instrument "Rate" metric across the different curve
         *  construction methodologies.
         */

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

        System.out.println ("\t     EDF INSTRUMENTS CALIBRATION RECOVERY");

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

        for (int i = 0; i < aEDFComp.length; ++i)
            System.out.println ("\t[" + aEDFComp[i].maturityDate() + "] = " +
                FormatUtil.FormatDouble (aEDFComp[i].measureValue (valParams, null, csqs, null, "Rate"), 1, 6, 1.)
                    + " | " + FormatUtil.FormatDouble (adblEDFQuote[i], 1, 6, 1.));

        /*
         * Cross-Comparison of the Swap Calibration Instrument "Rate" metric across the different curve
         *  construction methodologies.
         */

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

        System.out.println ("\t     SWAP INSTRUMENTS CALIBRATION RECOVERY");

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

        for (int i = 0; i < aSwapComp.length; ++i)
            System.out.println ("\t[" + aSwapComp[i].maturityDate() + "] = " +
                FormatUtil.FormatDouble (aSwapComp[i].measureValue (valParams, null, csqs, null, "CalibSwapRate"), 1, 6, 1.)
                    + " | " + FormatUtil.FormatDouble (adblSwapQuote[i], 1, 6, 1.) + " | " +
                        FormatUtil.FormatDouble (aSwapComp[i].measureValue (valParams, null, csqs, null, "FairPremium"), 1, 6, 1.));

        return dc;
    }

    private static final ForwardCurve LIBORSpan (
        final MergedDiscountForwardCurve dc,
        final ForwardLabel forwardLabel,
        final SegmentCustomBuilderControl scbc,
        final JulianDate dtView,
        final int iNumForwardTenor)
        throws Exception
    {
        int[] aiDate = new int[iNumForwardTenor + 1];
        double[] adblLIBOR = new double[iNumForwardTenor + 1];
        SegmentCustomBuilderControl[] aSCBC = new SegmentCustomBuilderControl[iNumForwardTenor];

        JulianDate dtForward = dtView.subtractTenor (forwardLabel.tenor());

        for (int i = 0; i <= iNumForwardTenor; ++i) {
            if (iNumForwardTenor != i) aSCBC[i] = scbc;

            aiDate[i] = dtForward.julian();

            adblLIBOR[i] = dc.libor (dtForward, forwardLabel.tenor());

            dtForward = dtForward.addTenor (forwardLabel.tenor());
        }

        return new BasisSplineForwardRate (
            forwardLabel,
            new OverlappingStretchSpan (
                MultiSegmentSequenceBuilder.CreateCalibratedStretchEstimator (
                    "SPOT_QM_LIBOR",
                    aiDate,
                    adblLIBOR,
                    aSCBC,
                    null,
                    BoundarySettings.NaturalStandard(),
                    MultiSegmentSequence.CALIBRATE
                )
            )
        );
    }

    private static final MarketSurface FlatVolatilitySurface (
        final JulianDate dtStart,
        final String strCurrency,
        final double dblFlatVol)
        throws Exception
    {
        return ScenarioMarketSurfaceBuilder.CustomSplineWireSurface (
            "VIEW_TARGET_VOLATILITY_SURFACE",
            dtStart,
            strCurrency,
            new double[] {
                dtStart.julian(),
                dtStart.addYears (2).julian(),
                dtStart.addYears (4).julian(),
                dtStart.addYears (6).julian(),
                dtStart.addYears (8).julian(),
                dtStart.addYears (10).julian()
            },
            new double[] {
                dtStart.julian(),
                dtStart.addYears (2).julian(),
                dtStart.addYears (4).julian(),
                dtStart.addYears (6).julian(),
                dtStart.addYears (8).julian(),
                dtStart.addYears (10).julian()
            },
            new double[][] {
                {dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol},
                {dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol},
                {dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol},
                {dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol},
                {dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol},
                {dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol},
            },
            new SegmentCustomBuilderControl (
                MultiSegmentSequenceBuilder.BASIS_SPLINE_POLYNOMIAL,
                new PolynomialFunctionSetParams (4),
                SegmentInelasticDesignControl.Create (
                    2,
                    2
                ),
                null,
                null
            ),
            new SegmentCustomBuilderControl (
                MultiSegmentSequenceBuilder.BASIS_SPLINE_POLYNOMIAL,
                new PolynomialFunctionSetParams (4),
                SegmentInelasticDesignControl.Create (
                    2,
                    2
                ),
                null,
                null
            )
        );
    }

    private static final LognormalLIBORVolatility LLVInstance (
        final int iSpotDate,
        final ForwardLabel forwardLabel,
        final MarketSurface[] aMS,
        final double[][] aadblCorrelation,
        final int iNumFactor)
        throws Exception
    {
        UnivariateSequenceGenerator[] aUSG = new UnivariateSequenceGenerator[aMS.length];

        for (int i = 0; i < aUSG.length; ++i)
            aUSG[i] = new BoxMullerGaussian (
                0.,
                1.
            );

        return new LognormalLIBORVolatility (
            iSpotDate,
            forwardLabel,
            aMS,
            new PrincipalFactorSequenceGenerator (
                aUSG,
                aadblCorrelation,
                iNumFactor
            )
        );
    }

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

        String strForwardTenor = "3M";
        String strViewTenor = "1Y";
        String strSimulationTenor = "1M";
        String strCurrency = "USD";
        double dblFlatVol1 = 0.35;
        double dblFlatVol2 = 0.42;
        double dblFlatVol3 = 0.27;
        int iNumForwardTenor = 5;
        int iNumFactor = 2;

        double[][] aadblCorrelation = new double[][] {
            {1.0, 0.1, 0.2},
            {0.1, 1.0, 0.2},
            {0.2, 0.1, 1.0}
        };

        SegmentCustomBuilderControl scbc = new SegmentCustomBuilderControl (
            MultiSegmentSequenceBuilder.BASIS_SPLINE_POLYNOMIAL,
            new PolynomialFunctionSetParams (4),
            SegmentInelasticDesignControl.Create (
                2,
                2
            ),
            new ResponseScalingShapeControl (
                true,
                new QuadraticRationalShapeControl (1.)
            ),
            null
        );

        JulianDate dtSpot = org.drip.analytics.date.DateUtil.Today();

        MarketSurface[] aMS = new MarketSurface[] {
            FlatVolatilitySurface (
                dtSpot,
                strCurrency,
                dblFlatVol1
            ),
            FlatVolatilitySurface (
                dtSpot,
                strCurrency,
                dblFlatVol2
            ),
            FlatVolatilitySurface (
                dtSpot,
                strCurrency,
                dblFlatVol3
            )
        };

        FundingLabel fundingLabel = FundingLabel.Standard (
            strCurrency
        );

        ForwardLabel forwardLabel = ForwardLabel.Create (
            strCurrency,
            strForwardTenor
        );

        MergedDiscountForwardCurve dc = OTCInstrumentCurve (
            dtSpot,
            strCurrency
        );

        JulianDate dtView = dtSpot.addTenor (strViewTenor);

        ForwardCurve fc = LIBORSpan (
            dc,
            forwardLabel,
            scbc,
            dtView,
            iNumForwardTenor
        );

        LognormalLIBORCurveEvolver llce = LognormalLIBORCurveEvolver.Create (
            fundingLabel,
            forwardLabel,
            iNumForwardTenor,
            scbc
        );

        BGMCurveUpdate bgmInitial = BGMCurveUpdate.Create (
            fundingLabel,
            forwardLabel,
            dtSpot.julian(),
            dtSpot.julian(),
            fc,
            null,
            dc,
            null,
            null,
            null,
            null,
            null,
            LLVInstance (
                dtSpot.julian(),
                forwardLabel,
                aMS,
                aadblCorrelation,
                iNumFactor
            )
        );

        double[][] aadblTenorLIBOR = llce.simulatePrincipalMetric (
            dtSpot.julian(),
            dtSpot.addTenor (strSimulationTenor).julian(),
            1,
            dtView.julian(),
            bgmInitial,
            2
        );

        String strBoundary = "\t|---";
        String strTenorDump = "\t|              |";
        JulianDate[] adtForward = new JulianDate[iNumForwardTenor + 1];

        for (int iTenorDate = 0; iTenorDate <= iNumForwardTenor; ++iTenorDate) {
            adtForward[iTenorDate] = 0 == iTenorDate ?
                dtView.addTenor (forwardLabel.tenor()) :
                adtForward[iTenorDate - 1].addTenor (forwardLabel.tenor());

            strBoundary += "-----------------";
            strTenorDump += "  " + adtForward[iTenorDate] + "  |";
        }

        System.out.println ("\n\n" +
            strBoundary + "\n" +
            strTenorDump + "\n" +
            strBoundary
        );

        for (int iSimulationDate = 0; iSimulationDate < aadblTenorLIBOR.length; ++iSimulationDate) {
            double[] adblCurveNode = aadblTenorLIBOR[iSimulationDate];

            String strCurveNodeDump = "\t|  " + dtSpot.addDays (iSimulationDate + 1) + " =>";

            for (int i = 0; i < aadblTenorLIBOR[i].length; ++i)
                strCurveNodeDump += "   " + FormatUtil.FormatDouble (adblCurveNode[i], 1, 3, 100.) +  "%    |";

            System.out.println (strCurveNodeDump);
        }

        System.out.println (strBoundary);

        EnvManager.TerminateEnv();
    }
}