MultiFactorVolatility.java

package org.drip.dynamics.hjm;

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

/*!
 * Copyright (C) 2020 Lakshmi Krishnamurthy
 * 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 analytics/risk, transaction cost analytics,
 *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
 *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
 *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
 *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
 *      and computational support.
 *  
 *      https://lakshmidrip.github.io/DROP/
 *  
 *  DROP is composed of three modules:
 *  
 *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
 *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
 *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
 * 
 *  DROP Product Core implements libraries for the following:
 *  - Fixed Income Analytics
 *  - Loan Analytics
 *  - Transaction Cost Analytics
 * 
 *  DROP Portfolio Core implements libraries for the following:
 *  - Asset Allocation Analytics
 *  - Asset Liability Management Analytics
 *  - Capital Estimation Analytics
 *  - Exposure Analytics
 *  - Margin Analytics
 *  - XVA Analytics
 * 
 *  DROP Computational Core implements libraries for the following:
 *  - Algorithm Support
 *  - Computation Support
 *  - Function Analysis
 *  - Model Validation
 *  - Numerical Analysis
 *  - Numerical Optimizer
 *  - Spline Builder
 *  - Statistical Learning
 * 
 *  Documentation for DROP is Spread Over:
 * 
 *  - Main                     => https://lakshmidrip.github.io/DROP/
 *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
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 *  - 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
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 *  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
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 */

/**
 * <i>MultiFactorVolatility</i> implements the Volatility of the Multi-factor Stochastic Evolution Process.
 * The Factors may come from the Underlying Stochastic Variables, or from Principal Components.
 *
 *  <br><br>
 *  <ul>
 *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ProductCore.md">Product Core Module</a></li>
 *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FixedIncomeAnalyticsLibrary.md">Fixed Income Analytics</a></li>
 *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/dynamics/README.md">HJM, Hull White, LMM, and SABR Dynamic Evolution Models</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/dynamics/hjm/README.md">HJM Based Latent State Evolution</a></li>
 *  </ul>
 *
 * @author Lakshmi Krishnamurthy
 */

public class MultiFactorVolatility {
    private org.drip.analytics.definition.MarketSurface[] _aMSVolatility = null;
    private org.drip.sequence.random.PrincipalFactorSequenceGenerator _pfsg = null;

    /**
     * MultiFactorVolatility Constructor
     * 
     * @param aMSVolatility Array of the Multi-Factor Volatility Surfaces
     * @param pfsg Principal Factor Sequence Generator
     * 
     * @throws java.lang.Exception Thrown if Inputs are Invalid
     */

    public MultiFactorVolatility (
        final org.drip.analytics.definition.MarketSurface[] aMSVolatility,
        final org.drip.sequence.random.PrincipalFactorSequenceGenerator pfsg)
        throws java.lang.Exception
    {
        if (null == (_aMSVolatility = aMSVolatility) || null == (_pfsg = pfsg))
            throw new java.lang.Exception ("MultiFactorVolatility ctr: Invalid Inputs");

        int iNumFactor = _pfsg.numFactor();

        if (0 == iNumFactor || _aMSVolatility.length < iNumFactor)
            throw new java.lang.Exception ("MultiFactorVolatility ctr: Invalid Inputs");
    }

    /**
     * Retrieve the Array of Volatility Surfaces
     * 
     * @return The Array of Volatility Surfaces
     */

    public org.drip.analytics.definition.MarketSurface[] volatilitySurface()
    {
        return _aMSVolatility;
    }

    /**
     * Retrieve the Principal Factor Sequence Generator
     * 
     * @return The Principal Factor Sequence Generator
     */

    public org.drip.sequence.random.PrincipalFactorSequenceGenerator msg()
    {
        return _pfsg;
    }

    /**
     * Retrieve the Factor-Specific Univariate Volatility Function for the Specified Date
     * 
     * @param iFactorIndex The Factor Index
     * @param iXDate The X Date
     * 
     * @return The Factor-Specific Univariate Volatility Function for the Specified Date
     */

    public org.drip.function.definition.R1ToR1 xDateVolatilityFunction (
        final int iFactorIndex,
        final int iXDate)
    {
        int iNumFactor = _pfsg.numFactor();

        if (iFactorIndex >= iNumFactor) return null;

        final int iNumVariate = _aMSVolatility.length;

        return new org.drip.function.definition.R1ToR1 (null) {
            @Override public double evaluate (
                final double dblX)
                throws java.lang.Exception
            {
                double dblMultiFactorVol = 0.;

                double[] adblFactor = _pfsg.factors()[iFactorIndex];

                for (int i = 0; i < iNumVariate; ++i) {
                    org.drip.analytics.definition.NodeStructure tsVolatilityXDate =
                        _aMSVolatility[iFactorIndex].xAnchorTermStructure (iXDate);

                    dblMultiFactorVol += adblFactor[i] * tsVolatilityXDate.node ((int) dblX);
                }

                return _pfsg.factorWeight()[iFactorIndex] * dblMultiFactorVol;
            }
        };
    }

    /**
     * Compute the Factor Volatility Integral
     * 
     * @param iFactorIndex The Factor Index
     * @param iXDate The X Date
     * @param iYDate The Y Date
     * 
     * @return The Factor Volatility Integral
     * 
     * @throws java.lang.Exception Thrown if the Factor Volatility Integral cannot be computed
     */

    public double volatilityIntegral (
        final int iFactorIndex,
        final int iXDate,
        final int iYDate)
        throws java.lang.Exception
    {
        org.drip.function.definition.R1ToR1 auVolatilityFunction = xDateVolatilityFunction (iFactorIndex,
            iXDate);

        if (null == auVolatilityFunction)
            throw new java.lang.Exception
                ("MultiFactorVolatility::volatilityIntegral => Cannot extract X Date Volatility Function");

        return auVolatilityFunction.integrate (iXDate, iYDate) / 365.25;
    }

    /**
     * Compute the Factor Point Volatility
     * 
     * @param iFactorIndex The Factor Index
     * @param iXDate The X Date
     * @param iYDate The Y Date
     * 
     * @return The Factor Point Volatility
     * 
     * @throws java.lang.Exception Thrown if the Factor Point Volatility cannot be computed
     */

    public double factorPointVolatility (
        final int iFactorIndex,
        final int iXDate,
        final int iYDate)
        throws java.lang.Exception
    {
        int iNumFactor = _pfsg.numFactor();

        if (iFactorIndex >= iNumFactor)
            throw new java.lang.Exception
                ("MultiFactorVolatility::factorPointVolatility => Invalid Factor Index");

        double[] adblFactor = _pfsg.factors()[iFactorIndex];

        int iNumVariate = adblFactor.length;
        double dblFactorPointVolatility = 0.;

        for (int i = 0; i < iNumVariate; ++i)
            dblFactorPointVolatility += adblFactor[i] * _aMSVolatility[i].node (iXDate, iYDate);

        return dblFactorPointVolatility;
    }

    /**
     * Compute the Array of Factor Point Volatilities
     * 
     * @param iXDate The X Date
     * @param iYDate The Y Date
     * 
     * @return The Array of Factor Point Volatilities
     */

    public double[] factorPointVolatility (
        final int iXDate,
        final int iYDate)
    {
        int iNumFactor = _pfsg.numFactor();

        double[][] aadblFactor = _pfsg.factors();

        int iNumVariate = aadblFactor[0].length;
        double[] adblVariateVolatility = new double[iNumVariate];
        double[] adblFactorPointVolatility = new double[iNumFactor];

        for (int iVariateIndex = 0; iVariateIndex < iNumVariate; ++iVariateIndex) {
            try {
                adblVariateVolatility[iVariateIndex] = _aMSVolatility[iVariateIndex].node (iXDate, iYDate);
            } catch (java.lang.Exception e) {
                e.printStackTrace();

                return null;
            }
        }

        for (int iFactorIndex = 0; iFactorIndex < iNumFactor; ++iFactorIndex) {
            adblFactorPointVolatility[iFactorIndex] = 0.;
            double[] adblFactor = aadblFactor[iFactorIndex];

            for (int iVariateIndex = 0; iVariateIndex < iNumVariate; ++iVariateIndex)
                adblFactorPointVolatility[iFactorIndex] += adblFactor[iVariateIndex] *
                    adblVariateVolatility[iVariateIndex];
        }

        return adblFactorPointVolatility;
    }

    /**
     * Compute the Weighted Factor Point Volatility
     * 
     * @param iFactorIndex The Factor Index
     * @param iXDate The X Date
     * @param iYDate The Y Date
     * 
     * @return The Weighted Factor Point Volatility
     * 
     * @throws java.lang.Exception Thrown if the Weighted Factor Point Volatility cannot be computed
     */

    public double weightedFactorPointVolatility (
        final int iFactorIndex,
        final int iXDate,
        final int iYDate)
        throws java.lang.Exception
    {
        int iNumFactor = _pfsg.numFactor();

        if (iFactorIndex >= iNumFactor)
            throw new java.lang.Exception
                ("MultiFactorVolatility::weightedFactorPointVolatility => Invalid Factor Index");

        double[] adblFactor = _pfsg.factors()[iFactorIndex];

        int iNumVariate = adblFactor.length;
        double dblFactorPointVolatility = 0.;

        for (int i = 0; i < iNumVariate; ++i)
            dblFactorPointVolatility += adblFactor[i] * _aMSVolatility[i].node (iXDate, iYDate);

        return _pfsg.factorWeight()[iFactorIndex] * dblFactorPointVolatility;
    }

    /**
     * Compute the Point Volatility Modulus
     * 
     * @param iXDate The X Date
     * @param iYDate The Y Date
     * 
     * @return The Point Volatility Modulus
     * 
     * @throws java.lang.Exception Thrown if the Point Volatility Modulus cannot be computed
     */

    public double pointVolatilityModulus (
        final int iXDate,
        final int iYDate)
        throws java.lang.Exception
    {
        int iNumFactor = _pfsg.numFactor();

        double dblPointVolatilityModulus = 0.;

        for (int i = 0; i < iNumFactor; ++i) {
            double dblWeightedFactorPointVolatility = weightedFactorPointVolatility (i, iXDate, iYDate);

            dblPointVolatilityModulus += dblWeightedFactorPointVolatility * dblWeightedFactorPointVolatility;
        }

        return dblPointVolatilityModulus;
    }

    /**
     * Compute the Point Volatility Modulus Derivative
     * 
     * @param iXDate The X Date
     * @param iYDate The Y Date
     * @param iOrder The Derivative Order
     * @param bTerminal TRUE - Derivative off of the Y Date; FALSE - Derivative off of the X Date
     * 
     * @return The Point Volatility Modulus Derivative
     * 
     * @throws java.lang.Exception Thrown if the Point Volatility Modulus Derivative cannot be computed
     */

    public double pointVolatilityModulusDerivative (
        final int iXDate,
        final int iYDate,
        final int iOrder,
        final boolean bTerminal)
        throws java.lang.Exception
    {
        org.drip.function.definition.R1ToR1 pointVolatilityR1ToR1 = new
            org.drip.function.definition.R1ToR1 (null) {
            @Override public double evaluate (
                final double dblVariate)
                throws java.lang.Exception
            {
                return bTerminal ? pointVolatilityModulus (iXDate, (int) dblVariate) : pointVolatilityModulus
                    ((int) dblVariate, iYDate);
            }
        };

        return bTerminal ? pointVolatilityR1ToR1.derivative (iXDate, iOrder) :
            pointVolatilityR1ToR1.derivative (iXDate, iOrder);
    }
}