ForwardRateEvolution.java

package org.drip.sample.sabr;

import org.drip.analytics.date.*;
import org.drip.dynamics.sabr.*;
import org.drip.numerical.common.FormatUtil;
import org.drip.sequence.random.BoxMullerGaussian;
import org.drip.service.env.EnvManager;
import org.drip.state.identifier.ForwardLabel;

/*
 * -*- 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
 * 
 *  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.
 */

/**
 * ForwardRateEvolution demonstrates the Construction and Usage of the SABR Model Dynamics for the Evolution
 *  of Forward Rate.
 *
 * @author Lakshmi Krishnamurthy
 */

public class ForwardRateEvolution {

    private static StochasticVolatilityStateEvolver SABREvolver (
        final double dblBeta,
        final double dblRho,
        final double dblVolatilityOfVolatility)
        throws Exception
    {
        return new StochasticVolatilityStateEvolver (
            ForwardLabel.Create (
                "USD",
                "6M"
            ),
            dblBeta,
            dblRho,
            dblVolatilityOfVolatility,
            new BoxMullerGaussian (
                0.,
                1.
            ),
            new BoxMullerGaussian (
                0.,
                1.
            )
        );
    }

    private static void SABREvolution (
        final StochasticVolatilityStateEvolver seSABR1,
        final StochasticVolatilityStateEvolver seSABR2,
        final StochasticVolatilityStateEvolver seSABR3,
        final int iSpotDate,
        final int iTerminalDate,
        final ForwardRateUpdate lsqmInitial1,
        final ForwardRateUpdate lsqmInitial2,
        final ForwardRateUpdate lsqmInitial3)
        throws Exception
    {
        int iDayStep = 2;
        int iDate = iSpotDate;
        ForwardRateUpdate lsqm1 = lsqmInitial1;
        ForwardRateUpdate lsqm2 = lsqmInitial2;
        ForwardRateUpdate lsqm3 = lsqmInitial3;

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

        System.out.println ("\t||     SABR  EVOLUTION  DYNAMICS                                                   ||");

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

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

        System.out.println ("\t||        Forward Rate (%)  - Gaussian (beta = 0.0)                                ||");

        System.out.println ("\t||        Forward Rate Vol (%)  - Gaussian (beta = 0.0)                            ||");

        System.out.println ("\t||        Forward Rate (%)  - beta = 0.5                                           ||");

        System.out.println ("\t||        Forward Rate Vol (%)  - beta = 0.5                                       ||");

        System.out.println ("\t||        Forward Rate (%)  - Lognormal (beta = 1.0)                               ||");

        System.out.println ("\t||        Forward Rate Vol (%)  - Lognormal (beta = 1.0)                           ||");

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

        while (iDate < iTerminalDate) {
            lsqm1 = (ForwardRateUpdate) seSABR1.evolve (
                iSpotDate,
                iDate,
                iDayStep,
                lsqm1
            );

            lsqm2 = (ForwardRateUpdate) seSABR2.evolve (
                iSpotDate,
                iDate,
                iDayStep,
                lsqm2
            );

            lsqm3 = (ForwardRateUpdate) seSABR3.evolve (
                iSpotDate,
                iDate,
                iDayStep,
                lsqm3
            );

            System.out.println (
                "\t|| " + new JulianDate (iDate) + " => " +
                FormatUtil.FormatDouble (lsqm1.forwardRate(), 1, 4, 100.) + " % | " +
                FormatUtil.FormatDouble (lsqm1.forwardRateVolatility(), 1, 2, 100.) + " % || " +
                FormatUtil.FormatDouble (lsqm2.forwardRate(), 1, 4, 100.) + " % | " +
                FormatUtil.FormatDouble (lsqm2.forwardRateVolatility(), 1, 1, 100.) + " % || " +
                FormatUtil.FormatDouble (lsqm3.forwardRate(), 1, 4, 100.) + " % | " +
                FormatUtil.FormatDouble (lsqm3.forwardRateVolatility(), 1, 1, 100.) + " % ||"
            );

            iDate += iDayStep;
        }

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

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

        JulianDate dtSpot = DateUtil.Today();

        double dblRho = 0.1;
        double dblForwardRate = 0.04;
        double dblVolatilityOfVolatility = 0.59;
        String strViewTenor = "3M";
        double[] adblBeta = {
            0.00, 0.50, 1.00
        };
        double[] adblForwardRateVolatility = {
            0.03, 0.26, 0.51
        };

        int iViewDate = dtSpot.addTenor (strViewTenor).julian();

        StochasticVolatilityStateEvolver seSABR1 = SABREvolver (
            adblBeta[0],
            dblRho,
            dblVolatilityOfVolatility
        );

        StochasticVolatilityStateEvolver seSABR2 = SABREvolver (
            adblBeta[1],
            dblRho,
            dblVolatilityOfVolatility
        );

        StochasticVolatilityStateEvolver seSABR3 = SABREvolver (
            adblBeta[2],
            dblRho,
            dblVolatilityOfVolatility
        );

        ForwardRateUpdate lsqmInitial1 = ForwardRateUpdate.Create (
            ForwardLabel.Create (
                "USD",
                "6M"
            ),
            dtSpot.julian(),
            dtSpot.julian(),
            iViewDate,
            dblForwardRate,
            0.,
            adblForwardRateVolatility[0],
            0.
        );

        ForwardRateUpdate lsqmInitial2 = ForwardRateUpdate.Create (
            ForwardLabel.Create (
                "USD",
                "6M"
            ),
            dtSpot.julian(),
            dtSpot.julian(),
            iViewDate,
            dblForwardRate,
            0.,
            adblForwardRateVolatility[1],
            0.
        );

        ForwardRateUpdate lsqmInitial3 = ForwardRateUpdate.Create (
            ForwardLabel.Create (
                "USD",
                "6M"
            ),
            dtSpot.julian(),
            dtSpot.julian(),
            iViewDate,
            dblForwardRate,
            0.,
            adblForwardRateVolatility[2],
            0.
        );

        SABREvolution (
            seSABR1,
            seSABR2,
            seSABR3,
            dtSpot.julian(),
            iViewDate,
            lsqmInitial1,
            lsqmInitial2,
            lsqmInitial3
        );
    }
}