R1JointJumpDiffusion.java

package org.drip.sample.numeraire;

import org.drip.measure.discrete.SequenceGenerator;
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;

/*
 * -*- 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.
 */

/**
 * R1JointJumpDiffusion demonstrates the Joint Evolution of R^1 Jump Diffusion Variates - 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:
 *  
 *  - Burgard, C., and M. Kjaer (2014): PDE Representations of Derivatives with Bilateral Counter-party Risk
 *      and Funding Costs, Journal of Credit Risk, 7 (3) 1-19.
 *  
 *  - Cesari, G., J. Aquilina, N. Charpillon, X. Filipovic, G. Lee, and L. Manda (2009): Modeling, Pricing,
 *      and Hedging Counter-party Credit Exposure - A Technical Guide, Springer Finance, New York.
 *  
 *  - Gregory, J. (2009): Being Two-faced over Counter-party Credit Risk, Risk 20 (2) 86-90.
 *  
 *  - Li, B., and Y. Tang (2007): Quantitative Analysis, Derivatives Modeling, and Trading Strategies in the
 *      Presence of Counter-party Credit Risk for the Fixed Income Market, World Scientific Publishing,
 *      Singapore.
 * 
 *  - Piterbarg, V. (2010): Funding Beyond Discounting: Collateral Agreements and Derivatives Pricing, Risk
 *      21 (2) 97-102.
 * 
 * @author Lakshmi Krishnamurthy
 */

public class R1JointJumpDiffusion {

    private static final double[][] NumeraireSequence (
        final int iCount,
        final double[][] aadblCorrelation,
        final String strHeader)
        throws Exception
    {
        double[][] aadblGaussianJoint = SequenceGenerator.GaussianJoint (
            iCount,
            aadblCorrelation
        );

        System.out.println();

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

        System.out.println (strHeader);

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

        for (int i = 0; i < iCount; ++i) {
            String strDump = "\t||" + FormatUtil.FormatDouble (i, 2, 0, 1.) + " |";

            for (int j = 0; j < aadblCorrelation.length; ++j)
                strDump = strDump + " " + FormatUtil.FormatDouble (aadblGaussianJoint[i][j], 1, 6, 1.) + " |";

            System.out.println (strDump + "|");
        }

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

        System.out.println();

        return Matrix.Transpose (aadblGaussianJoint);
    }

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

        double dblTimeWidth = 1. / 24.;
        double dblTime = 0.;
        double[][] aadblCorrelation = new double[][] {
            {1.00, 0.20, 0.15, 0.05}, // #0 ASSET
            {0.20, 1.00, 0.13, 0.25}, // #1 COLLATERAL
            {0.15, 0.13, 1.00, 0.00}, // #2 BANK
            {0.05, 0.25, 0.00, 1.00}  // #3 COUNTER PARTY
        };
        double dblAssetDrift = 0.06;
        double dblAssetVolatility = 0.15;
        double dblInitialAssetNumeraire = 1.;

        double dblZeroCouponBankBondDrift = 0.03;
        double dblZeroCouponBankBondVolatility = 0.10;
        double dblBankHazardRate = 0.03;
        double dblBankRecoveryRate = 0.45;
        double dblInitialBankNumeraire = 1.;

        double dblZeroCouponCollateralBondDrift = 0.01;
        double dblZeroCouponCollateralBondVolatility = 0.05;
        double dblInitialCollateralNumeraire = 1.;

        double dblZeroCouponCounterPartyBondDrift = 0.03;
        double dblZeroCouponCounterPartyBondVolatility = 0.10;
        double dblCounterPartyHazardRate = 0.05;
        double dblCounterPartyRecoveryRate = 0.30;
        double dblInitialCounterPartyNumeraire = 1.;

        int iNumTimeStep = (int) (1. / dblTimeWidth);

        DiffusionEvolver meAsset = new DiffusionEvolver (
            DiffusionEvaluatorLogarithmic.Standard (
                dblAssetDrift,
                dblAssetVolatility
            )
        );

        DiffusionEvolver meZeroCouponCollateralBond = new DiffusionEvolver (
            DiffusionEvaluatorLogarithmic.Standard (
                dblZeroCouponCollateralBondDrift,
                dblZeroCouponCollateralBondVolatility
            )
        );

        JumpDiffusionEvolver meZeroCouponBankBond = new JumpDiffusionEvolver (
            DiffusionEvaluatorLogarithmic.Standard (
                dblZeroCouponBankBondDrift,
                dblZeroCouponBankBondVolatility
            ),
            HazardJumpEvaluator.Standard (
                dblBankHazardRate,
                dblBankRecoveryRate
            )
        );

        JumpDiffusionEvolver meZeroCouponCounterPartyBond = new JumpDiffusionEvolver (
            DiffusionEvaluatorLogarithmic.Standard (
                dblZeroCouponCounterPartyBondDrift,
                dblZeroCouponCounterPartyBondVolatility
            ),
            HazardJumpEvaluator.Standard (
                dblCounterPartyHazardRate,
                dblCounterPartyRecoveryRate
            )
        );

        double[][] aadblNumeraireTimeSeries = NumeraireSequence (
            iNumTimeStep,
            aadblCorrelation,
            "\t|| ASSET, COLLATERAL, BANK, COUNTER PARTY REALIZATION ||"
        );

        double[] adblBankDefaultIndicator = SequenceGenerator.Uniform (iNumTimeStep);

        double[] adblCounterPartyDefaultIndicator = SequenceGenerator.Uniform (iNumTimeStep);

        double[] adblTimeWidth = new double[iNumTimeStep];

        for (int i = 0; i < iNumTimeStep; ++i)
            adblTimeWidth[i] = dblTimeWidth;

        JumpDiffusionEdge[] aR1AssetLR = meAsset.incrementSequence (
            new JumpDiffusionVertex (
                dblTime,
                dblInitialAssetNumeraire,
                0.,
                false
            ),
            JumpDiffusionEdgeUnit.Diffusion (
                adblTimeWidth,
                aadblNumeraireTimeSeries[0]
            ),
            dblTimeWidth
        );

        JumpDiffusionEdge[] aR1CollateralLR = meZeroCouponCollateralBond.incrementSequence (
            new JumpDiffusionVertex (
                dblTime,
                dblInitialCollateralNumeraire,
                0.,
                false
            ),
            JumpDiffusionEdgeUnit.Diffusion (
                adblTimeWidth,
                aadblNumeraireTimeSeries[1]
            ),
            dblTimeWidth
        );

        JumpDiffusionEdge[] aR1BankLR = meZeroCouponBankBond.incrementSequence (
            new JumpDiffusionVertex (
                dblTime,
                dblInitialBankNumeraire,
                0.,
                false
            ),
            JumpDiffusionEdgeUnit.JumpDiffusion (
                adblTimeWidth,
                aadblNumeraireTimeSeries[2],
                adblBankDefaultIndicator
            ),
            dblTimeWidth
        );

        JumpDiffusionEdge[] aR1CounterPartyLR = meZeroCouponCounterPartyBond.incrementSequence (
            new JumpDiffusionVertex (
                dblTime,
                dblInitialCounterPartyNumeraire,
                0.,
                false
            ),
            JumpDiffusionEdgeUnit.JumpDiffusion (
                adblTimeWidth,
                aadblNumeraireTimeSeries[3],
                adblCounterPartyDefaultIndicator
            ),
            dblTimeWidth
        );

        System.out.println();

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

        System.out.println("\t||                  BURGARD & KJAER (2011) CORRELATED JOINT ASSET/COLLATERAL/BANK/COUNTER-PARTY NUMERAIRE EVOLUTION                 ||");

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

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

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

        System.out.println("\t||          - Asset Numeraire Finish Value                                                                                          ||");

        System.out.println("\t||          - Asset Numeraire Start Value                                                                                           ||");

        System.out.println("\t||          - Asset Numeraire Continuous Wander Realization                                                                         ||");

        System.out.println("\t||          - Collateral Numeraire Finish Value                                                                                     ||");

        System.out.println("\t||          - Collateral Numeraire Start Value                                                                                      ||");

        System.out.println("\t||          - Collateral Numeraire Continuous Wander Realization                                                                    ||");

        System.out.println("\t||          - Bank Numeraire Finish Value                                                                                           ||");

        System.out.println("\t||          - Bank Numeraire Start Value                                                                                            ||");

        System.out.println("\t||          - Bank Numeraire Continuous Wander Realization                                                                          ||");

        System.out.println("\t||          - Counter-Party Numeraire Finish Value                                                                                  ||");

        System.out.println("\t||          - Counter-Party Numeraire Start Value                                                                                   ||");

        System.out.println("\t||          - Counter-Party Numeraire Continuous Wander Realization                                                                 ||");

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

        for (int i = 0; i < iNumTimeStep; ++i) {
            dblTime = dblTime + dblTimeWidth;

            System.out.println (
                "\t|| " +
                FormatUtil.FormatDouble (dblTime, 1, 4, 1.) + " => " +
                FormatUtil.FormatDouble (aR1AssetLR[i].start(), 1, 4, 1.) + " | " +
                FormatUtil.FormatDouble (aR1AssetLR[i].finish(), 1, 4, 1.) + " | " +
                FormatUtil.FormatDouble (aR1AssetLR[i].diffusionWander(), 1, 4, 1.) + " ||" +
                FormatUtil.FormatDouble (aR1CollateralLR[i].start(), 1, 4, 1.) + " | " +
                FormatUtil.FormatDouble (aR1CollateralLR[i].finish(), 1, 4, 1.) + " | " +
                FormatUtil.FormatDouble (aR1CollateralLR[i].diffusionWander(), 1, 4, 1.) + " ||" +
                FormatUtil.FormatDouble (aR1BankLR[i].start(), 1, 4, 1.) + " | " +
                FormatUtil.FormatDouble (aR1BankLR[i].finish(), 1, 4, 1.) + " | " +
                FormatUtil.FormatDouble (aR1BankLR[i].diffusionWander(), 1, 4, 1.) + " ||" +
                FormatUtil.FormatDouble (aR1CounterPartyLR[i].start(), 1, 4, 1.) + " | " +
                FormatUtil.FormatDouble (aR1CounterPartyLR[i].finish(), 1, 4, 1.) + " | " +
                FormatUtil.FormatDouble (aR1CounterPartyLR[i].diffusionWander(), 1, 4, 1.) + " ||"
            );
        }

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

        System.out.println();
    }
}