OvernightArithmeticCompoundingConvexity.java

package org.drip.sample.ois;

import java.util.*;

import org.drip.analytics.cashflow.CompositePeriod;
import org.drip.analytics.date.*;
import org.drip.analytics.support.*;
import org.drip.function.r1tor1.*;
import org.drip.market.otc.*;
import org.drip.numerical.common.FormatUtil;
import org.drip.param.creator.*;
import org.drip.param.market.*;
import org.drip.param.period.*;
import org.drip.param.valuation.*;
import org.drip.product.creator.*;
import org.drip.product.definition.CalibratableComponent;
import org.drip.product.rates.*;
import org.drip.service.env.EnvManager;
import org.drip.spline.basis.PolynomialFunctionSetParams;
import org.drip.spline.params.*;
import org.drip.spline.stretch.*;
import org.drip.state.creator.*;
import org.drip.state.discount.*;
import org.drip.state.estimator.LatentStateStretchBuilder;
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) 2018 Lakshmi Krishnamurthy
 * Copyright (C) 2017 Lakshmi Krishnamurthy
 * Copyright (C) 2016 Lakshmi Krishnamurthy
 * Copyright (C) 2015 Lakshmi Krishnamurthy
 * Copyright (C) 2014 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.
 */

/**
 * OvernightArithmeticCompoundingConvexity contains an assessment of the impact of the Overnight Index
 *  Volatility, the Funding Numeraire Volatility, and the ON Index/Funding Correlation on the Overnight
 *  Floating Stream.
 * 
 * @author Lakshmi Krishnamurthy
 */

public class OvernightArithmeticCompoundingConvexity {

    private static final FixFloatComponent OTCOISFixFloat (
        final JulianDate dtSpot,
        final String strCurrency,
        final String strMaturityTenor,
        final double dblCoupon)
    {
        FixedFloatSwapConvention ffConv = OvernightFixedFloatContainer.FundConventionFromJurisdiction (
            strCurrency
        );

        return ffConv.createFixFloatComponent (
            dtSpot,
            strMaturityTenor,
            dblCoupon,
            0.,
            1.
        );
    }

    /*
     * 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];

        for (int i = 0; i < aiDay.length; ++i)
            aDeposit[i] = SingleStreamComponentBuilder.Deposit (
                dtEffective,
                dtEffective.addBusDays (
                    aiDay[i],
                    strCurrency
                ),
                OvernightLabel.Create (
                    strCurrency
                )
            );

        return aDeposit;
    }

    private static final FixFloatComponent[] OISFromMaturityTenor (
        final JulianDate dtSpot,
        final String strCurrency,
        final String[] astrMaturityTenor,
        final double[] adblCoupon)
        throws Exception
    {
        FixFloatComponent[] aOIS = new FixFloatComponent[astrMaturityTenor.length];

        for (int i = 0; i < astrMaturityTenor.length; ++i)
            aOIS[i] = OTCOISFixFloat (
                dtSpot,
                strCurrency,
                astrMaturityTenor[i],
                adblCoupon[i]
            );

        return aOIS;
    }

    private static final FixFloatComponent[] OISFuturesFromMaturityTenor (
        final JulianDate dtSpot,
        final String strCurrency,
        final String[] astrStartTenor,
        final String[] astrMaturityTenor,
        final double[] adblCoupon)
        throws Exception
    {
        FixFloatComponent[] aOISFutures = new FixFloatComponent[astrMaturityTenor.length];

        for (int i = 0; i < astrMaturityTenor.length; ++i)
            aOISFutures[i] = OTCOISFixFloat (
                dtSpot.addTenor (astrStartTenor[i]),
                strCurrency,
                astrMaturityTenor[i],
                adblCoupon[i]
            );

        return aOISFutures;
    }

    private static final MergedDiscountForwardCurve CustomOISCurveBuilderSample (
        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, 3
            }
        );

        double[] adblDepositQuote = new double[] {
            0.0004, 0.0004, 0.0004       // Deposit
        };

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

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

        /*
         * Construct the Array of Short End OIS Instruments and their Quotes from the given set of parameters
         */

        double[] adblShortEndOISQuote = new double[] {
            0.00070,    //   1W
            0.00069,    //   2W
            0.00078,    //   3W
            0.00074     //   1M
        };

        CalibratableComponent[] aShortEndOISComp = OISFromMaturityTenor (
            dtSpot,
            strCurrency,
            new java.lang.String[] {
                "1W", "2W", "3W", "1M"
            },
            adblShortEndOISQuote
        );

        /*
         * Construct the Short End OIS Instrument Set Stretch Builder
         */

        LatentStateStretchSpec oisShortEndStretch = LatentStateStretchBuilder.ForwardFundingStretchSpec (
            "SHORT END OIS",
            aShortEndOISComp,
            "SwapRate",
            adblShortEndOISQuote
        );

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

        double[] adblOISFutureQuote = new double[] {
             0.00046,    //   1M x 1M
             0.00016,    //   2M x 1M
            -0.00007,    //   3M x 1M
            -0.00013,    //   4M x 1M
            -0.00014     //   5M x 1M
        };

        CalibratableComponent[] aOISFutureComp = OISFuturesFromMaturityTenor (
            dtSpot,
            strCurrency,
            new java.lang.String[] {
                "1M", "2M", "3M", "4M", "5M"
            },
            new java.lang.String[] {
                "1M", "1M", "1M", "1M", "1M"
            },
            adblOISFutureQuote
        );

        /*
         * Construct the OIS Future Instrument Set Stretch Builder
         */

        LatentStateStretchSpec oisFutureStretch = LatentStateStretchBuilder.ForwardFundingStretchSpec (
            " OIS FUTURE  ",
            aOISFutureComp,
            "SwapRate",
            adblOISFutureQuote
        );

        /*
         * Construct the Array of Long End OIS Instruments and their Quotes from the given set of parameters
         */

        double[] adblLongEndOISQuote = new double[] {
            0.00002,    //  15M
            0.00008,    //  18M
            0.00021,    //  21M
            0.00036,    //   2Y
            0.00127,    //   3Y
            0.00274,    //   4Y
            0.00456,    //   5Y
            0.00647,    //   6Y
            0.00827,    //   7Y
            0.00996,    //   8Y
            0.01147,    //   9Y
            0.01280,    //  10Y
            0.01404,    //  11Y
            0.01516,    //  12Y
            0.01764,    //  15Y
            0.01939,    //  20Y
            0.02003,    //  25Y
            0.02038     //  30Y
        };

        CalibratableComponent[] aLongEndOISComp = OISFromMaturityTenor (
            dtSpot,
            strCurrency,
            new java.lang.String[] {
                "15M", "18M", "21M", "2Y", "3Y", "4Y", "5Y", "6Y", "7Y", "8Y", "9Y", "10Y", "11Y", "12Y", "15Y", "20Y", "25Y", "30Y"
            },
            adblLongEndOISQuote
        );

        /*
         * Construct the Long End OIS Instrument Set Stretch Builder
         */

        LatentStateStretchSpec oisLongEndStretch = LatentStateStretchBuilder.ForwardFundingStretchSpec (
            "LONG END OIS ",
            aLongEndOISComp,
            "SwapRate",
            adblLongEndOISQuote
        );

        LatentStateStretchSpec[] aStretchSpec = new LatentStateStretchSpec[] {
            depositStretch,
            oisShortEndStretch,
            oisFutureStretch,
            oisLongEndStretch
        };

        /*
         * 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
        );

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

        return ScenarioDiscountCurveBuilder.ShapePreservingDFBuild (
            strCurrency,
            lcc,
            aStretchSpec,
            new ValuationParams (
                dtSpot,
                dtSpot,
                strCurrency
            ),
            null,
            null,
            null,
            1.
        );
    }

    private static final LatentStateFixingsContainer SetFlatOvernightFixings (
        final JulianDate dtStart,
        final JulianDate dtEnd,
        final JulianDate dtValue,
        final ForwardLabel fri,
        final double dblFlatFixing,
        final double dblNotional)
        throws Exception
    {
        LatentStateFixingsContainer lsfc = new LatentStateFixingsContainer();

        JulianDate dt = dtStart.addDays (1);

        while (dt.julian() <= dtEnd.julian()) {
            lsfc.add (
                dt,
                fri,
                dblFlatFixing
            );

            dt = dt.addBusDays (1, "USD");
        }

        return lsfc;
    }

    private static final void SetMarketParams (
        final int iValueDate,
        final CurveSurfaceQuoteContainer mktParams,
        final String strCurrency,
        final ForwardLabel fri,
        final double dblOISVol,
        final double dblUSDFundingVol,
        final double dblUSDFundingUSDOISCorrelation)
        throws Exception
    {
        FundingLabel fundingLabel = FundingLabel.Standard (strCurrency);

        mktParams.setForwardVolatility (
            ScenarioDeterministicVolatilityBuilder.FlatForward (
                iValueDate,
                VolatilityLabel.Standard (fri),
                fri.currency(),
                dblOISVol
            )
        );

        mktParams.setFundingVolatility (
            ScenarioDeterministicVolatilityBuilder.FlatForward (
                iValueDate,
                VolatilityLabel.Standard (fundingLabel),
                "USD",
                dblUSDFundingVol
            )
        );


        mktParams.setForwardFundingCorrelation (
            fri,
            fundingLabel,
            new FlatUnivariate (dblUSDFundingUSDOISCorrelation)
        );
    }

    private static final void VolCorrScenario (
        final Stream[] aFloatStream,
        final String strCurrency,
        final ForwardLabel fri,
        final ValuationParams valParams,
        final CurveSurfaceQuoteContainer mktParams,
        final double dblOISVol,
        final double dblUSDFundingVol,
        final double dblUSDFundingUSDOISCorrelation)
        throws Exception
    {
        SetMarketParams (
            valParams.valueDate(),
            mktParams,
            strCurrency,
            fri,
            dblOISVol,
            dblUSDFundingVol,
            dblUSDFundingUSDOISCorrelation
        );

        String strDump = "\t[" +
            FormatUtil.FormatDouble (dblOISVol, 2, 0, 100.) + "%," +
            FormatUtil.FormatDouble (dblUSDFundingVol, 2, 0, 100.) + "%," +
            FormatUtil.FormatDouble (dblUSDFundingUSDOISCorrelation, 2, 0, 100.) + "%] = ";

        for (int i = 0; i < aFloatStream.length; ++i) {
            Map<String, Double> mapValue = aFloatStream[i].value (
                valParams,
                null,
                mktParams,
                null
            );

            if (0 != i) strDump += " || ";

            strDump +=
                FormatUtil.FormatDouble (mapValue.get ("UnadjustedFairPremium"), 1, 4, 100.) + "% | " +
                FormatUtil.FormatDouble (mapValue.get ("CompoundingAdjustmentFactor") - 1, 1, 2, 100.) + "% | " +
                FormatUtil.FormatDouble (mapValue.get ("CumulativeConvexityAdjustmentFactor") - 1, 1, 2, 100.) + "%";
        }

        System.out.println (strDump);
    }

    public static final void main (
        final String[] astrArgs)
        throws Exception
    {
        /*
         * Initialize the Credit Analytics Library
         */

        EnvManager.InitEnv ("");

        JulianDate dtToday = DateUtil.Today().addTenor ("0D");

        String strCurrency = "USD";

        MergedDiscountForwardCurve dc = CustomOISCurveBuilderSample (
            dtToday,
            strCurrency
        );

        JulianDate dtCustomOISStart = dtToday.subtractTenor ("2M");

        JulianDate dtCustomOISMaturity = dtToday.addTenor ("4M");

        ForwardLabel fri = OvernightLabel.Create (strCurrency);

        ComposableFloatingUnitSetting cfusFloating = new ComposableFloatingUnitSetting (
            "ON",
            CompositePeriodBuilder.EDGE_DATE_SEQUENCE_OVERNIGHT,
            null,
            OvernightLabel.Create (
                strCurrency
            ),
            CompositePeriodBuilder.REFERENCE_PERIOD_IN_ADVANCE,
            0.
        );

        CompositePeriodSetting cpsFloating = new CompositePeriodSetting (
            360,
            "ON",
            strCurrency,
            null,
            -1.,
            null,
            null,
            null,
            null
        );

        List<Integer> lsFloatingStreamEdgeDate = CompositePeriodBuilder.RegularEdgeDates (
            dtCustomOISStart,
            "6M",
            "6M",
            null
        );

        List<CompositePeriod> lsCP = CompositePeriodBuilder.FloatingCompositeUnit (
            lsFloatingStreamEdgeDate,
            cpsFloating,
            cfusFloating
        );

        Stream floatStream = new Stream (lsCP);

        CurveSurfaceQuoteContainer mktParams = MarketParamsBuilder.Create (
            dc,
            null,
            null,
            null,
            null,
            null,
            SetFlatOvernightFixings (
                dtCustomOISStart,
                dtCustomOISMaturity,
                dtToday,
                fri,
                0.003,
                -1.
            )
        );

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

        double[] adblOISVol = new double [] {
            0.1, 0.3, 0.5
        };
        double[] adblUSDFundingVol = new double [] {
            0.1, 0.3, 0.5
        };
        double[] adblUSDFundingUSDOISCorrelation = new double [] {
            -0.3, 0.0, 0.3
        };

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

        System.out.println ("\tInput Order (LHS) L->R:");

        System.out.println ("\t\tOIS Volatility, Funding Volatility, OIS/Funding Correlation\n");

        System.out.println ("\tOutput Order (RHS) L->R:");

        System.out.println ("\t\tUnadjusted Fair Premium, Compounding Adjustment Factor (% - Relative), Convexity Adjustment Factor (% - Relative)\n");

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

        for (double dblOISVol : adblOISVol) {
            for (double dblUSDFundingVol : adblUSDFundingVol) {
                for (double dblUSDFundingUSDOISCorrelation : adblUSDFundingUSDOISCorrelation)
                    VolCorrScenario (
                        new Stream[] {floatStream},
                        strCurrency,
                        fri,
                        valParams,
                        mktParams,
                        dblOISVol,
                        dblUSDFundingVol,
                        dblUSDFundingUSDOISCorrelation
                    );
            }
        }

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