BlackVolatility.java

package org.drip.sample.sabr;

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.
 */

/**
 * BlackVolatility demonstrates the Construction and Usage of the SABR Model to Imply the Black Volatility of
 *  a given Contract.
 *
 * @author Lakshmi Krishnamurthy
 */

public class BlackVolatility {

    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 VolatilitySurface (
        final StochasticVolatilityStateEvolver seSABR,
        final double[] adblStrike,
        final double dblATMForwardRate,
        final double dblTTE,
        final double dblSigma0)
    {
        String strDump = "\t| " + FormatUtil.FormatDouble (dblTTE, 1, 2, 1.) + " => ";

        for (int i = 0; i < adblStrike.length; ++i) {
            ImpliedBlackVolatility ibv = seSABR.computeBlackVolatility (
                adblStrike[i],
                dblATMForwardRate,
                dblTTE,
                dblSigma0
            );

            strDump += FormatUtil.FormatDouble (ibv.impliedVolatility(), 2, 1, 100.) + " | ";
        }

        System.out.println (strDump);
    }

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

        double dblRho = 0.;
        double dblBeta = 0.7;
        double dblATMForwardRate = 0.04;
        double dblVolatilityOfVolatility = 0.5;
        double adblForwardRateVolatility = 0.10;
        double[] adblStrike = {
            0.30, 0.35, 0.40, 0.45, 0.50
        };
        double[] adblTTE = {
            0.25, 0.50, 0.75, 1.00, 2.00, 3.00, 4.00, 5.00, 7.00, 9.99
        };

        StochasticVolatilityStateEvolver seSABR = SABREvolver (
            dblBeta,
            dblRho,
            dblVolatilityOfVolatility
        );

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

        System.out.println ("\t|         SABR IMPLIED BLACK VOLATILITY          |");

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

        for (double dblTTE : adblTTE)
            VolatilitySurface (
                seSABR,
                adblStrike,
                dblATMForwardRate,
                dblTTE,
                adblForwardRateVolatility
            );

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