FokkerPlanckGenerator.java

package org.drip.pricer.option;

/*
 * -*- 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
 * Copyright (C) 2014 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
 *  - 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>FokkerPlanckGenerator</i> holds the base functionality that the performs the PDF evolution oriented
 * Option Pricing.
 *
 *  <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/pricer/README.md">Custom Pricing Algorithms and the Derivative Fokker Planck Trajectory Generators</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/pricer/option/README.md">Deterministic/Stochastic Volatility Settings/Greeks</a></li>
 *  </ul>
 * <br><br>
 * 
 * @author Lakshmi Krishnamurthy
 */

public abstract class FokkerPlanckGenerator implements org.drip.param.pricer.GenericPricer {

    /**
     * Compute the Expected Payoff of the Option from the Inputs
     * 
     * @param dblStrike Option Strike
     * @param dblTimeToExpiry Option Time To Expiry
     * @param dblRiskFreeRate Option Risk Free Rate
     * @param dblUnderlier Option Underlier Value
     * @param bIsPut TRUE - The Option is a Put
     * @param bIsForward TRUE - The Underlier represents the Forward, FALSE - it represents Spot
     * @param dblInitialVolatility Option Initial Volatility Value
     * @param bAsPrice TRUE - Return the Discounted Payoff
     * 
     * @return The Expected Option Payoff
     * 
     * @throws java.lang.Exception Thrown if the Expected Payoff cannot be calculated
     */

    public abstract double payoff (
        final double dblStrike,
        final double dblTimeToExpiry,
        final double dblRiskFreeRate,
        final double dblUnderlier,
        final boolean bIsPut,
        final boolean bIsForward,
        final double dblInitialVolatility,
        final boolean bAsPrice)
        throws java.lang.Exception;

    /**
     * Carry out a Sensitivity Run and generate the Pricing related measure set
     * 
     * @param dblStrike Option Strike
     * @param dblTimeToExpiry Option Time To Expiry
     * @param dblRiskFreeRate Option Risk Free Rate
     * @param dblUnderlier Option Underlier Value
     * @param bIsPut TRUE - The Option is a Put
     * @param bIsForward TRUE - The Underlier represents the Forward, FALSE - it represents Spot
     * @param dblInitialVolatility Option Initial Volatility Value
     * 
     * @return The Greeks Sensitivities Output
     */

    public abstract org.drip.pricer.option.Greeks greeks (
        final double dblStrike,
        final double dblTimeToExpiry,
        final double dblRiskFreeRate,
        final double dblUnderlier,
        final boolean bIsPut,
        final boolean bIsForward,
        final double dblInitialVolatility);

    /**
     * Compute the Expected Payoff of the Option from the Inputs
     * 
     * @param iSpotDate Spot Date
     * @param iExpiryDate Expiry Date
     * @param dblStrike Option Strike
     * @param dcFunding The Funding Curve
     * @param dblUnderlier Option Underlier Value
     * @param bIsPut TRUE - The Option is a Put
     * @param bIsForward TRUE - The Underlier represents the Forward, FALSE - it represents Spot
     * @param dblInitialVolatility Option Initial Volatility Value
     * @param bAsPrice TRUE - Return the Discounted Payoff
     * 
     * @return The Expected Option Payoff
     * 
     * @throws java.lang.Exception Thrown if the Expected Payoff cannot be calculated
     */

    public double payoff (
        final int iSpotDate,
        final int iExpiryDate,
        final double dblStrike,
        final org.drip.state.discount.MergedDiscountForwardCurve dcFunding,
        final double dblUnderlier,
        final boolean bIsPut,
        final boolean bIsForward,
        final double dblInitialVolatility,
        final boolean bAsPrice)
        throws java.lang.Exception
    {
        if (iExpiryDate <= iSpotDate || !org.drip.numerical.common.NumberUtil.IsValid (dblStrike) || null ==
            dcFunding || !org.drip.numerical.common.NumberUtil.IsValid (dblInitialVolatility))
            throw new java.lang.Exception ("FokkerPlanckGenerator::payoff => Invalid Inputs");

        return payoff (dblStrike, 1. * (iExpiryDate - iSpotDate) / 365.25, dcFunding.libor (iSpotDate,
            iExpiryDate), dblUnderlier, bIsPut, bIsForward, dblInitialVolatility, bAsPrice);
    }

    /**
     * Compute the Expected Payoff of the Option from the Inputs
     * 
     * @param iSpotDate Spot Date
     * @param iExpiryDate Expiry Date
     * @param dblStrike Option Strike
     * @param dcFunding The Funding Curve
     * @param dblUnderlier Option Underlier Value
     * @param bIsPut TRUE - The Option is a Put
     * @param bIsForward TRUE - The Underlier represents the Forward, FALSE - it represents Spot
     * @param funcVolatilityR1ToR1 The R^1 To R^1 Volatility Term Structure
     * @param bAsPrice TRUE - Return the Discounted Payoff
     * 
     * @return The Expected Option Payoff
     * 
     * @throws java.lang.Exception Thrown if the Expected Payoff cannot be calculated
     */

    public double payoff (
        final int iSpotDate,
        final int iExpiryDate,
        final double dblStrike,
        final org.drip.state.discount.MergedDiscountForwardCurve dcFunding,
        final double dblUnderlier,
        final boolean bIsPut,
        final boolean bIsForward,
        final org.drip.function.definition.R1ToR1 funcVolatilityR1ToR1,
        final boolean bAsPrice)
        throws java.lang.Exception
    {
        if (iExpiryDate <= iSpotDate || !org.drip.numerical.common.NumberUtil.IsValid (dblStrike) || null ==
            dcFunding || null == funcVolatilityR1ToR1)
            throw new java.lang.Exception ("FokkerPlanckGenerator::payoff => Invalid Inputs");

        int iDaysToExpiry = iExpiryDate - iSpotDate;

        double dblRiskFreeRate = dcFunding.libor (iSpotDate, iExpiryDate);

        org.drip.function.definition.R1ToR1 funcVarianceR1ToR1 = new org.drip.function.definition.R1ToR1
            (null) {
            @Override public double evaluate (
                final double dblX)
                throws java.lang.Exception
            {
                return funcVolatilityR1ToR1.evaluate (dblX) * funcVolatilityR1ToR1.evaluate (dblX);
            }
        };

        double dblEffectiveVolatility = java.lang.Math.sqrt (funcVarianceR1ToR1.integrate (iSpotDate,
            iExpiryDate) / iDaysToExpiry);

        return payoff (dblStrike, 1. * iDaysToExpiry / 365.25, dblRiskFreeRate, dblUnderlier, bIsPut,
            bIsForward, dblEffectiveVolatility, bAsPrice);
    }

    /**
     * Carry out a Sensitivity Run and generate the Pricing related measure set
     * 
     * @param iSpotDate Spot Date
     * @param iExpiryDate Expiry Date
     * @param dblStrike Option Strike
     * @param dcFunding The Funding Curve
     * @param dblUnderlier Option Underlier Value
     * @param bIsPut TRUE - The Option is a Put
     * @param bIsForward TRUE - The Underlier represents the Forward, FALSE - it represents Spot
     * @param dblIntegratedSurfaceVariance The Integrated Surface Variance
     * 
     * @return The Greeks Output generated from the Sensitivities Run
     */

    public org.drip.pricer.option.Greeks greeks (
        final int iSpotDate,
        final int iExpiryDate,
        final double dblStrike,
        final org.drip.state.discount.MergedDiscountForwardCurve dcFunding,
        final double dblUnderlier,
        final boolean bIsPut,
        final boolean bIsForward,
        final double dblIntegratedSurfaceVariance)
    {
        if (iExpiryDate <= iSpotDate || !org.drip.numerical.common.NumberUtil.IsValid (dblStrike) || null ==
            dcFunding || !org.drip.numerical.common.NumberUtil.IsValid (dblIntegratedSurfaceVariance))
            return null;

        double dblTimeToExpiry = 1. * (iExpiryDate - iSpotDate) / 365.25;

        try {
            return greeks (dblStrike, dblTimeToExpiry, dcFunding.libor (iSpotDate, iExpiryDate),
                dblUnderlier, bIsPut, bIsForward, java.lang.Math.sqrt (dblIntegratedSurfaceVariance /
                    dblTimeToExpiry));
        } catch (java.lang.Exception e) {
            e.printStackTrace();
        }

        return null;
    }

    /**
     * Carry out a Sensitivity Run and generate the Pricing related measure set
     * 
     * @param iSpotDate Spot Date
     * @param iExpiryDate Expiry Date
     * @param dblStrike Option Strike
     * @param dcFunding The Funding Curve
     * @param dblUnderlier Option Underlier Value
     * @param bIsPut TRUE - The Option is a Put
     * @param bIsForward TRUE - The Underlier represents the Forward, FALSE - it represents Spot
     * @param funcVolatilityR1ToR1 The R^1 To R^1 Volatility Term Structure
     * 
     * @return The Greeks Output generated from the Sensitivities Run
     */

    public org.drip.pricer.option.Greeks greeks (
        final int iSpotDate,
        final int iExpiryDate,
        final double dblStrike,
        final org.drip.state.discount.MergedDiscountForwardCurve dcFunding,
        final double dblUnderlier,
        final boolean bIsPut,
        final boolean bIsForward,
        final org.drip.function.definition.R1ToR1 funcVolatilityR1ToR1)
    {
        if (iExpiryDate <= iSpotDate || !org.drip.numerical.common.NumberUtil.IsValid (dblStrike) || null ==
            dcFunding || null == funcVolatilityR1ToR1)
            return null;

        double dblRiskFreeRate = java.lang.Double.NaN;
        double dblEffectiveVolatility = java.lang.Double.NaN;
        double dblTimeToExpiry = 1. * (iExpiryDate - iSpotDate) / 365.25;

        org.drip.function.definition.R1ToR1 funcVarianceR1ToR1 = new org.drip.function.definition.R1ToR1
            (null) {
            @Override public double evaluate (
                final double dblX)
                throws java.lang.Exception
            {
                return funcVolatilityR1ToR1.evaluate (dblX) * funcVolatilityR1ToR1.evaluate (dblX);
            }
        };

        try {
            dblRiskFreeRate = dcFunding.libor (iSpotDate, iExpiryDate);

            dblEffectiveVolatility = java.lang.Math.sqrt (funcVarianceR1ToR1.integrate (iSpotDate,
                iExpiryDate) / (365.25 * dblTimeToExpiry));
        } catch (java.lang.Exception e) {
            e.printStackTrace();

            return null;
        }

        return greeks (dblStrike, dblTimeToExpiry, dblRiskFreeRate, dblUnderlier, bIsPut, bIsForward,
            dblEffectiveVolatility);
    }

    /**
     * Imply the Effective Volatility From the Option Price
     * 
     * @param dblStrike Strike
     * @param dblTimeToExpiry Time To Expiry
     * @param dblRiskFreeRate Risk Free Rate
     * @param dblUnderlier The Underlier
     * @param bIsPut TRUE - The Option is a Put
     * @param bIsForward TRUE - The Underlier represents the Forward, FALSE - it represents Spot
     * @param dblPrice The Price
     * 
     * @return The Implied Effective Volatility
     * 
     * @throws java.lang.Exception Thrown if the Effective Volatility cannot be implied
     */

    public double impliedVolatilityFromPrice (
        final double dblStrike,
        final double dblTimeToExpiry,
        final double dblRiskFreeRate,
        final double dblUnderlier,
        final boolean bIsPut,
        final boolean bIsForward,
        final double dblPrice)
        throws java.lang.Exception
    {
        org.drip.function.definition.R1ToR1 au = new org.drip.function.definition.R1ToR1 (null) {
            @Override public double evaluate (
                final double dblSpotVolatility)
                throws java.lang.Exception
            {
                return payoff (dblStrike, dblTimeToExpiry, dblRiskFreeRate, dblUnderlier, bIsPut, bIsForward,
                    dblSpotVolatility, true) - dblPrice;
            }
        };

        org.drip.function.r1tor1solver.FixedPointFinderOutput fpop = new
            org.drip.function.r1tor1solver.FixedPointFinderBrent (0., au, true).findRoot();

        if (null == fpop || !fpop.containsRoot())
            throw new java.lang.Exception
                ("FokkerPlanckGenerator::impliedVolatilityFromPrice => Cannot imply Volatility");

        return java.lang.Math.abs (fpop.getRoot());
    }

    /**
     * Imply the Effective Volatility From the Option Price
     * 
     * @param iSpotDate Spot Date
     * @param iExpiryDate Expiry Date
     * @param dblStrike Option Strike
     * @param dcFunding The Funding Curve
     * @param dblUnderlier Option Underlier Value
     * @param bIsPut TRUE - The Option is a Put
     * @param bIsForward TRUE - The Underlier represents the Forward, FALSE - it represents Spot
     * @param dblPrice The Price
     * 
     * @return The Implied Effective Volatility
     * 
     * @throws java.lang.Exception Thrown if the Effective Volatility cannot be implied
     */

    public double impliedVolatilityFromPrice (
        final int iSpotDate,
        final int iExpiryDate,
        final double dblStrike,
        final org.drip.state.discount.MergedDiscountForwardCurve dcFunding,
        final double dblUnderlier,
        final boolean bIsPut,
        final boolean bIsForward,
        final double dblPrice)
        throws java.lang.Exception
    {
        org.drip.function.definition.R1ToR1 au = new org.drip.function.definition.R1ToR1 (null) {
            @Override public double evaluate (
                final double dblInitialVolatility)
                throws java.lang.Exception
            {
                return payoff (iSpotDate, iExpiryDate, dblStrike, dcFunding, dblUnderlier, bIsPut,
                    bIsForward, dblInitialVolatility, true) - dblPrice;
            }
        };

        org.drip.function.r1tor1solver.FixedPointFinderOutput fpop = new
            org.drip.function.r1tor1solver.FixedPointFinderBrent (0., au, true).findRoot();

        if (null == fpop || !fpop.containsRoot())
            throw new java.lang.Exception
                ("FokkerPlanckGenerator::impliedVolatilityFromPrice => Cannot imply Volatility");

        return java.lang.Math.abs (fpop.getRoot());
    }

    /**
     * Imply the Effective Black-Scholes Volatility From the Option Price
     * 
     * @param dblStrike Strike
     * @param dblTimeToExpiry Time To Expiry
     * @param dblRiskFreeRate Risk Free Rate
     * @param dblUnderlier The Underlier
     * @param bIsPut TRUE - The Option is a Put
     * @param bIsForward TRUE - The Underlier represents the Forward, FALSE - it represents Spot
     * @param dblPrice The Price
     * 
     * @return The Implied Black Scholes Effective Volatility
     * 
     * @throws java.lang.Exception Thrown if the Black Scholes Effective Volatility cannot be implied
     */

    public double impliedBlackScholesVolatility (
        final double dblStrike,
        final double dblTimeToExpiry,
        final double dblRiskFreeRate,
        final double dblUnderlier,
        final boolean bIsPut,
        final boolean bIsForward,
        final double dblPrice)
        throws java.lang.Exception
    {
        return new org.drip.pricer.option.BlackScholesAlgorithm().impliedVolatilityFromPrice (dblStrike,
            dblTimeToExpiry, dblRiskFreeRate, dblUnderlier, bIsPut, bIsForward, dblPrice);
    }
}