PrincipalComponentDynamics.java

package org.drip.sample.hjm;

import org.drip.analytics.date.*;
import org.drip.analytics.definition.MarketSurface;
import org.drip.dynamics.hjm.*;
import org.drip.function.definition.R1ToR1;
import org.drip.function.r1tor1.FlatUnivariate;
import org.drip.numerical.common.FormatUtil;
import org.drip.sequence.random.*;
import org.drip.service.env.EnvManager;
import org.drip.spline.basis.PolynomialFunctionSetParams;
import org.drip.spline.params.*;
import org.drip.spline.stretch.MultiSegmentSequenceBuilder;
import org.drip.state.creator.ScenarioMarketSurfaceBuilder;
import org.drip.state.identifier.*;

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

/*!
 * Copyright (C) 2019 Lakshmi Krishnamurthy
 * 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 DROP, an open-source library targeting risk, transaction costs, exposure, margin
 *      calculations, valuation adjustment, and portfolio construction within and across fixed income,
 *      credit, commodity, equity, FX, and structured products.
 *  
 *      https://lakshmidrip.github.io/DROP/
 *  
 *  DROP is composed of three modules:
 *  
 *  - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
 *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
 *  - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
 * 
 *  DROP Analytics Core implements libraries for the following:
 *  - Fixed Income Analytics
 *  - Asset Backed Analytics
 *  - XVA Analytics
 *  - Exposure and Margin Analytics
 * 
 *  DROP Portfolio Core implements libraries for the following:
 *  - Asset Allocation Analytics
 *  - Transaction Cost Analytics
 * 
 *  DROP Numerical Core implements libraries for the following:
 *  - Statistical Learning
 *  - Numerical Optimizer
 *  - Spline Builder
 *  - Algorithm Support
 * 
 *  Documentation for DROP is Spread Over:
 * 
 *  - Main                     => https://lakshmidrip.github.io/DROP/
 *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
 *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
 *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
 *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
 *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
 *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
 *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
 *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
 *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
 *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
 * 
 *  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.
 */

/**
 * <i>PrincipalComponentDynamics</i> demonstrates the Construction and Usage of the PCA-Based Multi-Factor
 * Gaussian Model Dynamics for the Evolution of the Instantaneous Forward Rate, the Price, and the Short
 * Rate.
 *  
 * <br><br>
 *  <ul>
 *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/AnalyticsCore.md">Analytics Core Module</a></li>
 *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FixedIncomeAnalyticsLibrary.md">Fixed Income Analytics Library</a></li>
 *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">Sample</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/hjm/README.md">Generic HJM Evolution</a></li>
 *  </ul>
 * <br><br>
 *
 * @author Lakshmi Krishnamurthy
 */

public class PrincipalComponentDynamics {

    private static final MarketSurface FlatVolatilitySurface (
        final JulianDate dtStart,
        final String strCurrency,
        final double dblFlatVol)
        throws Exception
    {
        return ScenarioMarketSurfaceBuilder.CustomSplineWireSurface (
            "VIEW_TARGET_VOLATILITY_SURFACE",
            dtStart,
            strCurrency,
            new double[] {
                dtStart.julian(),
                dtStart.addYears (2).julian(),
                dtStart.addYears (4).julian(),
                dtStart.addYears (6).julian(),
                dtStart.addYears (8).julian(),
                dtStart.addYears (10).julian()
            },
            new double[] {
                dtStart.julian(),
                dtStart.addYears (2).julian(),
                dtStart.addYears (4).julian(),
                dtStart.addYears (6).julian(),
                dtStart.addYears (8).julian(),
                dtStart.addYears (10).julian()
            },
            new double[][] {
                {dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol},
                {dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol},
                {dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol},
                {dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol},
                {dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol},
                {dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol, dblFlatVol},
            },
            new SegmentCustomBuilderControl (
                MultiSegmentSequenceBuilder.BASIS_SPLINE_POLYNOMIAL,
                new PolynomialFunctionSetParams (4),
                SegmentInelasticDesignControl.Create (
                    2,
                    2
                ),
                null,
                null
            ),
            new SegmentCustomBuilderControl (
                MultiSegmentSequenceBuilder.BASIS_SPLINE_POLYNOMIAL,
                new PolynomialFunctionSetParams (4),
                SegmentInelasticDesignControl.Create (
                    2,
                    2
                ),
                null,
                null
            )
        );
    }

    private static final MultiFactorStateEvolver HJMInstance (
        final JulianDate dtStart,
        final String strCurrency,
        final MarketSurface mktSurfFlatVol1,
        final MarketSurface mktSurfFlatVol2,
        final MarketSurface mktSurfFlatVol3,
        final R1ToR1 auForwardRate,
        final int iNumFactor)
        throws Exception
    {
        MultiFactorVolatility mfv = new MultiFactorVolatility (
            new MarketSurface[] {
                mktSurfFlatVol1,
                mktSurfFlatVol2,
                mktSurfFlatVol3
            },
            new PrincipalFactorSequenceGenerator (
                new UnivariateSequenceGenerator[] {
                    new BoxMullerGaussian (
                        0.,
                        1.
                    ),
                    new BoxMullerGaussian (
                        0.,
                        1.
                    ),
                    new BoxMullerGaussian (
                        0.,
                        1.
                    )
                },
                new double[][] {
                    {1.0, 0.1, 0.2},
                    {0.1, 1.0, 0.2},
                    {0.2, 0.1, 1.0}
                },
                iNumFactor
            )
        );

        return new MultiFactorStateEvolver (
            FundingLabel.Standard (strCurrency),
            ForwardLabel.Create (
                strCurrency,
                "6M"
            ),
            mfv,
            auForwardRate
        );
    }

    private static final void Evolve (
        final MultiFactorStateEvolver hjm,
        final JulianDate dtStart,
        final String strCurrency,
        final String strViewTenor,
        final String strTargetTenor,
        final double dblStartingForwardRate,
        final double dblStartingPrice)
        throws Exception
    {
        int iViewDate = dtStart.addTenor (strViewTenor).julian();

        int iTargetDate = dtStart.addTenor (strTargetTenor).julian();

        int iDayStep = 2;
        JulianDate dtSpot = dtStart;
        double dblPrice = dblStartingPrice;
        double dblShortRate = dblStartingForwardRate;
        double dblLIBORForwardRate = dblStartingForwardRate;
        double dblInstantaneousForwardRate = dblStartingForwardRate;
        double dblContinuouslyCompoundedShortRate = dblStartingForwardRate;
        double dblShiftedLIBORForwardRate = dblStartingForwardRate + (365.25 / (iTargetDate - iViewDate));

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

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

        System.out.println ("\t|    Multi-Factor PCA-Based Gaussian HJM Run                                                                                    ||");

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

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

        System.out.println ("\t|        Number of Prinicipal Components: " + hjm.mfv().msg().numFactor() + "                                                                                     ||");

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

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

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

        System.out.println ("\t|            Instantaneous Forward Rate (%)                                                                                     ||");

        System.out.println ("\t|            Instantaneous Forward Rate - Change (%)                                                                            ||");

        System.out.println ("\t|            LIBOR Forward Rate (%)                                                                                             ||");

        System.out.println ("\t|            LIBOR Forward Rate - Change (%)                                                                                    ||");

        System.out.println ("\t|            Shifted LIBOR Forward Rate (%)                                                                                     ||");

        System.out.println ("\t|            Shifted LIBOR Forward Rate - Change (%)                                                                            ||");

        System.out.println ("\t|            Short Rate (%)                                                                                                     ||");

        System.out.println ("\t|            Short Rate - Change (%)                                                                                            ||");

        System.out.println ("\t|            Continuously Compounded Short Rate (%)                                                                             ||");

        System.out.println ("\t|            Continuously Compounded Short Rate - Change (%)                                                                    ||");

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

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

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

        while (dtSpot.julian() < iViewDate) {
            int iSpotDate = dtSpot.julian();

            double dblIFRIncrement = hjm.instantaneousForwardRateIncrement (
                iViewDate,
                iTargetDate,
                iDayStep
            );

            dblInstantaneousForwardRate += dblIFRIncrement;

            double dblLIBORForwardRateIncrement = hjm.liborForwardRateIncrement (
                iSpotDate,
                iViewDate,
                iTargetDate,
                dblLIBORForwardRate,
                iDayStep
            );

            dblLIBORForwardRate += dblLIBORForwardRateIncrement;

            double dblShiftedLIBORForwardRateIncrement = hjm.shiftedLIBORForwardIncrement (
                iSpotDate,
                iViewDate,
                iTargetDate,
                dblShiftedLIBORForwardRate,
                iDayStep
            );

            dblShiftedLIBORForwardRate += dblShiftedLIBORForwardRateIncrement;

            double dblShortRateIncrement = hjm.shortRateIncrement (
                iSpotDate,
                iViewDate,
                iDayStep
            );

            dblShortRate += dblShortRateIncrement;

            double dblProportionalPriceIncrement = hjm.proportionalPriceIncrement (
                iSpotDate,
                iViewDate,
                dblShortRate,
                iDayStep
            );

            dblPrice *= (1. + dblProportionalPriceIncrement);

            double dblContinuouslyCompoundedShortRateIncrement = hjm.compoundedShortRateIncrement (
                iSpotDate,
                iViewDate,
                iTargetDate,
                dblContinuouslyCompoundedShortRate,
                dblShortRate,
                iDayStep
            );

            dblContinuouslyCompoundedShortRate += dblContinuouslyCompoundedShortRateIncrement;

            System.out.println ("\t| [" + dtSpot + "] = " +
                FormatUtil.FormatDouble (dblInstantaneousForwardRate, 1, 2, 100.) + "% | " +
                FormatUtil.FormatDouble (dblIFRIncrement, 1, 2, 100.) + "% || " +
                FormatUtil.FormatDouble (dblLIBORForwardRate, 1, 2, 100.) + "% | " +
                FormatUtil.FormatDouble (dblLIBORForwardRateIncrement, 1, 2, 100.) + "% || " +
                FormatUtil.FormatDouble (dblShiftedLIBORForwardRate, 1, 4, 1.) + " | " +
                FormatUtil.FormatDouble (dblShiftedLIBORForwardRateIncrement, 1, 2, 100.) + "% || " +
                FormatUtil.FormatDouble (dblShortRate, 1, 2, 100.) + "% | " +
                FormatUtil.FormatDouble (dblShortRateIncrement, 1, 2, 100.) + "% || " +
                FormatUtil.FormatDouble (dblContinuouslyCompoundedShortRate, 1, 2, 100.) + "% | " +
                FormatUtil.FormatDouble (dblContinuouslyCompoundedShortRateIncrement, 1, 2, 100.) + "% || " +
                FormatUtil.FormatDouble (dblPrice, 2, 2, 100.) + " | " +
                FormatUtil.FormatDouble (dblProportionalPriceIncrement, 1, 2, 100.) + " || "
            );

            dtSpot = dtSpot.addBusDays (iDayStep, strCurrency);
        }

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

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

        String strCurrency = "USD";

        JulianDate dtSpot = DateUtil.Today();

        double dblFlatVol1 = 0.01;
        double dblFlatVol2 = 0.02;
        double dblFlatVol3 = 0.03;
        double dblFlatForwardRate = 0.05;
        double dblStartingPrice = 0.9875;

        MarketSurface mktSurfFlatVol1 = FlatVolatilitySurface (
            dtSpot,
            strCurrency,
            dblFlatVol1
        );

        MarketSurface mktSurfFlatVol2 = FlatVolatilitySurface (
            dtSpot,
            strCurrency,
            dblFlatVol2
        );

        MarketSurface mktSurfFlatVol3 = FlatVolatilitySurface (
            dtSpot,
            strCurrency,
            dblFlatVol3
        );

        int[] aiNumFactor = new int[] {
            1, 2, 3
        };

        for (int iNumFactor : aiNumFactor) {
            MultiFactorStateEvolver hjm = HJMInstance (
                dtSpot,
                strCurrency,
                mktSurfFlatVol1,
                mktSurfFlatVol2,
                mktSurfFlatVol3,
                new FlatUnivariate (dblFlatForwardRate),
                iNumFactor
            );

            Evolve (
                hjm,
                dtSpot,
                strCurrency,
                "3M",
                "6M",
                dblFlatForwardRate,
                dblStartingPrice
            );
        }

        EnvManager.TerminateEnv();
    }
}