PermanentImpactQuasiArbitrage.java

package org.drip.execution.athl;

/*
 * -*- 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
 * 
 *  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>PermanentImpactQuasiArbitrage</i> implements the Linear Permanent Market Impact with Coefficients that
 * have been determined empirically by Almgren, Thum, Hauptmann, and Li (2005), independent of the no Quasi-
 * Arbitrage Criterion identified by Huberman and Stanzl (2004). The References are:
 * 
 * <br><br>
 *  <ul>
 *  <li>
 *      Almgren, R., and N. Chriss (2000): Optimal Execution of Portfolio Transactions <i>Journal of Risk</i>
 *          <b>3 (2)</b> 5-39
 *  </li>
 *  <li>
 *      Almgren, R. (2003): Optimal Execution with Nonlinear Impact Functions and Trading-Enhanced Risk
 *          <i>Applied Mathematical Finance</i> <b>10 (1)</b> 1-18
 *  </li>
 *  <li>
 *      Almgren, R., and N. Chriss (2003): Bidding Principles <i>Risk</i> 97-102
 *  </li>
 *  <li>
 *      Almgren, R., C. Thum, E. Hauptmann, and H. Li (2005): Equity Market Impact <i>Risk</i> <b>18 (7)</b>
 *          57-62
 *  </li>
 *  <li>
 *      Huberman, G., and W. Stanzl (2004): Price Manipulation and Quasi-arbitrage <i>Econometrics</i>
 *          <b>72 (4)</b> 1247-1275
 *  </li>
 *  </ul>
 *
 *  <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/TransactionCostAnalyticsLibrary.md">Transaction Cost Analytics</a></li>
 *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/execution/README.md">Optimal Impact/Capture Based Trading Trajectories - Deterministic, Stochastic, Static, and Dynamic</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/execution/athl/README.md">Almgren-Thum-Hauptmann-Li Calibration</a></li>
 *  </ul>
 * 
 * @author Lakshmi Krishnamurthy
 */

public class PermanentImpactQuasiArbitrage extends org.drip.execution.impact.TransactionFunctionPower {
    private double _dblLiquidityFactor = java.lang.Double.NaN;
    private org.drip.execution.parameters.AssetFlowSettings _afp = null;

    /**
     * PermanentImpactQuasiArbitrage Constructor
     * 
     * @param afp The Asset Flow Parameters
     * 
     * @throws java.lang.Exception Thrown if the Inputs are Invalid
     */

    public PermanentImpactQuasiArbitrage (
        final org.drip.execution.parameters.AssetFlowSettings afp)
        throws java.lang.Exception
    {
        if (null == (_afp = afp))
            throw new java.lang.Exception ("PermanentImpactQuasiArbitrage Constructor => Invalid Inputs");

        _dblLiquidityFactor = java.lang.Math.pow (afp.inverseTurnover(),
            org.drip.execution.athl.CalibrationEmpirics.PERMANENT_IMPACT_INVERSE_TURNOVER_EXPONENT);
    }

    /**
     * Retrieve the Liquidity Factor
     * 
     * @return The Liquidity Factor
     */

    public double liquidityFactor()
    {
        return _dblLiquidityFactor;
    }

    /**
     * Retrieve the Asset Flow Parameters
     * 
     * @return The Asset Flow Parameters
     */

    public org.drip.execution.parameters.AssetFlowSettings assetFlowParameters()
    {
        return _afp;
    }

    @Override public double regularize (
        final double dblTradeInterval)
        throws java.lang.Exception
    {
        if (!org.drip.numerical.common.NumberUtil.IsValid (dblTradeInterval) || 0 >= dblTradeInterval)
            throw new java.lang.Exception ("PermanentImpactQuasiArbitrage::regularize => Invalid Inputs");

        return 1. / (_afp.averageDailyVolume() * dblTradeInterval);
    }

    @Override public double modulate (
        final double dblTradeInterval)
        throws java.lang.Exception
    {
        if (!org.drip.numerical.common.NumberUtil.IsValid (dblTradeInterval) || 0 >= dblTradeInterval)
            throw new java.lang.Exception ("PermanentImpactQuasiArbitrage::modulate => Invalid Inputs");

        return dblTradeInterval * _afp.dailyVolatility();
    }

    @Override public double constant()
    {
        return org.drip.execution.athl.CalibrationEmpirics.PERMANENT_IMPACT_COEFFICIENT *
            _dblLiquidityFactor;
    }

    @Override public double exponent()
    {
        return org.drip.execution.athl.CalibrationEmpirics.PERMANENT_IMPACT_EXPONENT_ATHL2005;
    }

    @Override public double evaluate (
        final double dblNormalizedX)
        throws java.lang.Exception
    {
        if (!org.drip.numerical.common.NumberUtil.IsValid (dblNormalizedX))
            throw new java.lang.Exception ("PermanentImpactQuasiArbitrage::evaluate => Invalid Inputs");

        double dblAlpha = org.drip.execution.athl.CalibrationEmpirics.PERMANENT_IMPACT_EXPONENT_ATHL2005;
        double dblGamma = org.drip.execution.athl.CalibrationEmpirics.PERMANENT_IMPACT_COEFFICIENT;

        return 0.5 * dblGamma * (dblNormalizedX < 0. ? -1. : 1.) * java.lang.Math.pow (java.lang.Math.abs
            (dblNormalizedX), dblAlpha) * _dblLiquidityFactor;
    }

    @Override public double derivative  (
        final double dblNormalizedX,
        final int iOrder)
        throws java.lang.Exception
    {
        if (0 >= iOrder || !org.drip.numerical.common.NumberUtil.IsValid (dblNormalizedX))
            throw new java.lang.Exception ("PermanentImpactQuasiArbitrage::derivative => Invalid Inputs");

        double dblCoefficient = 1.;
        double dblAlpha = org.drip.execution.athl.CalibrationEmpirics.PERMANENT_IMPACT_EXPONENT_ATHL2005;
        double dblGamma = org.drip.execution.athl.CalibrationEmpirics.PERMANENT_IMPACT_COEFFICIENT;

        for (int i = 0; i < iOrder; ++i)
            dblCoefficient = dblCoefficient * (dblAlpha - i);

        return 0.5 * dblGamma * (dblNormalizedX < 0. ? -1. : 1.) * dblCoefficient * java.lang.Math.pow
            (java.lang.Math.abs (dblNormalizedX), dblAlpha - iOrder) * _dblLiquidityFactor;
    }
}