LocalVolatilityTermStructure.java

package org.drip.sample.option;

import org.drip.analytics.date.*;
import org.drip.analytics.definition.*;
import org.drip.numerical.common.FormatUtil;
import org.drip.spline.basis.PolynomialFunctionSetParams;
import org.drip.spline.params.*;
import org.drip.spline.stretch.MultiSegmentSequenceBuilder;
import org.drip.state.creator.ScenarioMarketSurfaceBuilder;

/*
 * -*- 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.
 */

/**
 * LocalVolatilityTermStructure contains an illustration of the Calibration and Extraction of the Implied and
 *  the Local Volatility Surfaces and their eventual Strike and Maturity Anchor Term Structures.
 * 
 * @author Lakshmi Krishnamurthy
 */

public class LocalVolatilityTermStructure {
    private static final SegmentCustomBuilderControl scbc()
        throws Exception
    {
        return new SegmentCustomBuilderControl (
            MultiSegmentSequenceBuilder.BASIS_SPLINE_POLYNOMIAL,
            new PolynomialFunctionSetParams (4),
            SegmentInelasticDesignControl.Create (
                2,
                2
            ),
            null,
            null
        );
    }

    private static final void EvaluateLocalVolSurface (
        final MarketSurface volSurface,
        final double[] adblStrikeATMFactor,
        final String[] astrMaturityTenor)
        throws Exception
    {
        System.out.println ("\n\t  " + volSurface.label());

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

        System.out.print ("\t|------------------------------------------------------------|\n\t|  ATM/TTE  =>");

        NodeStructure[] aTSMaturityAnchor = new NodeStructure[astrMaturityTenor.length];

        for (int j = 0; j < astrMaturityTenor.length; ++j) {
            aTSMaturityAnchor[j] = volSurface.maturityAnchorTermStructure (astrMaturityTenor[j]);

            System.out.print ("    " + astrMaturityTenor[j] + "  ");
        }

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

        for (int i = 0; i < adblStrikeATMFactor.length; ++i) {
            System.out.print ("\t|  " + FormatUtil.FormatDouble (adblStrikeATMFactor[i], 1, 2, 1.) + "    =>");

            NodeStructure tsStrikeAnchor = volSurface.xAnchorTermStructure (adblStrikeATMFactor[i]);

            for (int j = 0; j < astrMaturityTenor.length; ++j) {
                double dblLocalVol = Math.sqrt (2. * (tsStrikeAnchor.nodeDerivative (astrMaturityTenor[j], 1) +
                    0.0 * adblStrikeATMFactor[i] * aTSMaturityAnchor[j].nodeDerivative ((int) adblStrikeATMFactor[i], 1)) /
                        (adblStrikeATMFactor[i] * adblStrikeATMFactor[i] *
                            aTSMaturityAnchor[j].nodeDerivative ((int) adblStrikeATMFactor[i], 2)));

                System.out.print ("  " + FormatUtil.FormatDouble (dblLocalVol, 2, 2, 100.) + "%");
            }

            System.out.print ("  |\n");
        }

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

    public static final void main (
        final String[] astrArgs)
        throws Exception
    {
        JulianDate dtStart = DateUtil.Today();

        double[] adblStrikeATMFactorCalib = new double[] {
            0.8, 0.9, 1.0, 1.1, 1.2
        };
        String[] astrMaturityTenorCalib = new String[] {
            "12M", "24M", "36M", "48M", "60M"
        };
        double[][] aadblVol = new double[][] {
            {0.171, 0.169, 0.168, 0.168, 0.168},
            {0.159, 0.161, 0.161, 0.162, 0.164},
            {0.138, 0.145, 0.149, 0.152, 0.154},
            {0.115, 0.130, 0.137, 0.143, 0.148},
            {0.103, 0.119, 0.128, 0.135, 0.140}
        };

        MarketSurface priceSurfCubicPoly = ScenarioMarketSurfaceBuilder.CustomWireSurface (
            "HESTON1993_CUBICPOLY_CALLPRICE_SURFACE",
            dtStart,
            "USD",
            adblStrikeATMFactorCalib,
            astrMaturityTenorCalib,
            aadblVol,
            scbc(),
            scbc()
        );

        double[] adblStrikeATMFactor = new double[] {
            0.850, 0.925, 1.000, 1.075, 1.150
        };
        String[] astrMaturityTenor = new String[] {
            "18M", "27M", "36M", "45M", "54M"
        };

        NodeStructure[] aTSMaturityAnchor = new NodeStructure[astrMaturityTenor.length];

        for (int j = 0; j < astrMaturityTenor.length; ++j)
            aTSMaturityAnchor[j] = priceSurfCubicPoly.maturityAnchorTermStructure (astrMaturityTenor[j]);

        for (int i = 0; i < adblStrikeATMFactor.length; ++i) {
            NodeStructure tsStrikeAnchor = priceSurfCubicPoly.xAnchorTermStructure (adblStrikeATMFactor[i]);

            for (int j = 0; j < astrMaturityTenor.length; ++j) {
                System.out.println (Math.sqrt (2. * (tsStrikeAnchor.nodeDerivative (astrMaturityTenor[j], 1) +
                    0.0 * adblStrikeATMFactor[i] * aTSMaturityAnchor[j].nodeDerivative ((int) adblStrikeATMFactor[i], 1)) /
                        (adblStrikeATMFactor[i] * adblStrikeATMFactor[i] *
                            aTSMaturityAnchor[j].nodeDerivative ((int) adblStrikeATMFactor[i], 2))) + " | " +
                                aTSMaturityAnchor[j].nodeDerivative ((int) adblStrikeATMFactor[i], 2));
            }
        }

        EvaluateLocalVolSurface (
            priceSurfCubicPoly,
            adblStrikeATMFactor,
            astrMaturityTenor
        );
    }
}