ForwardContract.java

package org.drip.sample.piterbarg2010;

import org.drip.analytics.date.*;
import org.drip.analytics.support.Helper;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
import org.drip.service.template.LatentMarketStateBuilder;
import org.drip.state.discount.*;

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

/*!
 * Copyright (C) 2018 Lakshmi Krishnamurthy
 * Copyright (C) 2017 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.
 */

/**
 * ForwardContract examines the Valuation of Forward Contract under CSA and non-CSA Settle Agreements. CSA is
 *  proxied using the OIS Curve, and non-CSA using the Issuer Hedge Funding Curve. The corresponding
 *  Convexity Adjustments using Spread/CSA Covariance are also calculated. The References are:
 *  
 *  - Barden, P. (2009): Equity Forward Prices in the Presence of Funding Spreads, ICBI Conference, Rome.
 *  
 *  - Burgard, C., and M. Kjaer (2009): Modeling and successful Management of Credit Counter-party Risk of
 *      Derivative Portfolios, ICBI Conference, Rome.
 *  
 *  - Gregory, J. (2009): Being Two-faced over Counter-party Credit Risk, Risk 20 (2) 86-90.
 *  
 *  - Johannes, M., and S. Sundaresan (2007): Pricing Collateralized Swaps, Journal of Finance 62 383-410.
 * 
 *  - Piterbarg, V. (2010): Funding Beyond Discounting: Collateral Agreements and Derivatives Pricing, Risk
 *      21 (2) 97-102.
 * 
 * @author Lakshmi Krishnamurthy
 */

public class ForwardContract {

    private static final DiscountCurve CSACurve (
        final String strCurrency,
        final JulianDate dtSpot)
        throws Exception
    {
        String[] astrDepositMaturityTenor = new String[] {
            "1D",
            // "2D",
            // "3D"
        };

        double[] adblDepositQuote = new double[] {
            0.0004,     // 1D
            // 0.0004,      // 2D
            // 0.0004       // 3D
        };

        String[] astrShortEndOISMaturityTenor = new String[] {
            "1W",
            "2W",
            "3W",
            "1M"
        };

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

        String[] astrOISFuturesEffectiveTenor = new String[] {
            "1M",
            "2M",
            "3M",
            "4M",
            "5M"
        };

        String[] astrOISFuturesMaturityTenor = new String[] {
            "1M",
            "1M",
            "1M",
            "1M",
            "1M"
        };

        double[] adblOISFuturesQuote = 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
        };

        String[] astrLongEndOISMaturityTenor = new String[] {
            "15M",
            "18M",
            "21M",
            "02Y",
            "03Y",
            "04Y",
            "05Y",
            "06Y",
            "07Y",
            "08Y",
            "09Y",
            "10Y",
            "11Y",
            "12Y",
            "15Y",
            "20Y",
            "25Y",
            "30Y"
        };

        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
        };

        return LatentMarketStateBuilder.SmoothOvernightCurve (
            dtSpot,
            strCurrency,
            astrDepositMaturityTenor,
            adblDepositQuote,
            "Rate",
            astrShortEndOISMaturityTenor,
            adblShortEndOISQuote,
            "SwapRate",
            astrOISFuturesEffectiveTenor,
            astrOISFuturesMaturityTenor,
            adblOISFuturesQuote,
            "SwapRate",
            astrLongEndOISMaturityTenor,
            adblLongEndOISQuote,
            "SwapRate"
        );
    }

    private static final DiscountCurve NonCSACurve (
        final String strCurrency,
        final JulianDate dtSpot)
        throws Exception
    {
        String[] astrDepositMaturityTenor = new String[] {
            "01D",
            "04D",
            "07D",
            "14D",
            "30D",
            "60D"
        };

        double[] adblDepositQuote = new double[] {
            0.0013,     //  1D
            0.0017,     //  2D
            0.0017,     //  7D
            0.0018,     // 14D
            0.0020,     // 30D
            0.0023      // 60D
        };

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

        String[] astrFixFloatMaturityTenor = new String[] {
            "04Y",
            "05Y",
            "06Y",
            "07Y",
            "08Y",
            "09Y",
            "10Y",
            "11Y",
            "12Y",
            "15Y",
            "20Y",
            "25Y",
            "30Y",
            "40Y",
            "50Y"
        };

        double[] adblFixFloatQuote = new double[] {
            0.0166,     //   4Y
            0.0206,     //   5Y
            0.0241,     //   6Y
            0.0269,     //   7Y
            0.0292,     //   8Y
            0.0311,     //   9Y
            0.0326,     //  10Y
            0.0340,     //  11Y
            0.0351,     //  12Y
            0.0375,     //  15Y
            0.0393,     //  20Y
            0.0402,     //  25Y
            0.0407,     //  30Y
            0.0409,     //  40Y
            0.0409      //  50Y
        };

        return LatentMarketStateBuilder.SmoothFundingCurve (
            dtSpot,
            strCurrency,
            astrDepositMaturityTenor,
            adblDepositQuote,
            "ForwardRate",
            adblFuturesQuote,
            "ForwardRate",
            astrFixFloatMaturityTenor,
            adblFixFloatQuote,
            "SwapRate"
        );
    }

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

        String strCurrency = "USD";
        double dblATMForward = 50.;
        double dblCSAVolatility = 0.1;
        double dblCSANonCSASpreadVolatility = 0.2;
        double dblCSANonCSASpreadCorrelation = 0.2;

        JulianDate dtSpot = DateUtil.Today().addBusDays (
            0,
            strCurrency
        );

        String[] astrTenor = new String[] {
             "1W",
             "2W",
             "3W",
             "1M",
             "2M",
             "3M",
             "6M",
             "9M",
            "12M",
            "18M",
             "2Y",
             "3Y",
             "4Y",
             "5Y",
             "7Y",
            "10Y",
            "12Y",
            "15Y",
            "20Y",
            "25Y",
            "30Y",
            "40Y",
            "50Y"
        };

        DiscountCurve dcOvernight = CSACurve (
            strCurrency,
            dtSpot
        );

        DiscountCurve dcFunding = NonCSACurve (
            strCurrency,
            dtSpot
        );

        System.out.println();

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

        System.out.println ("\t||     FORWARD CONTRACT CONVEXITY ADJUSTMENT     ||");

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

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

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

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

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

        System.out.println ("\t||        - CSA-Funding Convexity Adjustment     ||");

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

        for (String strTenor : astrTenor) {
            JulianDate dt = dtSpot.addTenor (strTenor);

            double dblTenorToYF = Helper.TenorToYearFraction (strTenor);

            double dblSpreadNumeraire = dcFunding.df (dt) / dcOvernight.df (dt);

            double dblConvexityAdjustment = dblCSANonCSASpreadCorrelation * dblCSANonCSASpreadVolatility * dblCSAVolatility;

            System.out.println ("\t|| " + dt + " | " +
                FormatUtil.FormatDouble (dblSpreadNumeraire, 1, 4, 1.) + " | " +
                FormatUtil.FormatDouble (dblConvexityAdjustment * dblTenorToYF, 1, 6, 1.) + " | " +
                FormatUtil.FormatDouble (dblConvexityAdjustment * dblATMForward * dblSpreadNumeraire * dblTenorToYF, 1, 6, 1.) + " ||"
            );
        }

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

        System.out.println();
    }
}