DiscreteAlmgrenChriss.java

package org.drip.execution.nonadaptive;

/*
 * -*- 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>DiscreteAlmgrenChriss</i> generates the Trade/Holdings List of Optimal Execution Schedule for the
 * Equally Spaced Trading Intervals based on the No-Drift Linear Impact Evolution Walk Parameters specified.
 * The References are:
 * 
 * <br><br>
 *  <ul>
 *      <li>
 *          Almgren, R., and N. Chriss (1999): Value under Liquidation <i>Risk</i> <b>12 (12)</b>
 *      </li>
 *      <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>
 *          Bertsimas, D., and A. W. Lo (1998): Optimal Control of Execution Costs <i>Journal of Financial
 *              Markets</i> <b>1</b> 1-50
 *      </li>
 *      <li>
 *          Chan, L. K. C., and J. Lakonishak (1995): The Behavior of Stock Prices around Institutional
 *              Trades <i>Journal of Finance</i> <b>50</b> 1147-1174
 *      </li>
 *      <li>
 *          Keim, D. B., and A. Madhavan (1997): Transaction Costs and Investment Style: An Inter-exchange
 *              Analysis of Institutional Equity Trades <i>Journal of Financial Economics</i> <b>46</b>
 *              265-292
 *      </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/nonadaptive/README.md">Almgren-Chriss Static Optimal Trajectory</a></li>
 *  </ul>
 * 
 * @author Lakshmi Krishnamurthy
 */

public class DiscreteAlmgrenChriss extends org.drip.execution.nonadaptive.StaticOptimalSchemeDiscrete {

    private double KappaTau (
        final double dblKappaTildaSquared,
        final double dblTau)
    {
        double dblKappaTildaSquaredTauSquared = dblKappaTildaSquared * dblTau * dblTau;

        return java.lang.Math.log (0.5 * (2. + dblKappaTildaSquaredTauSquared + dblTau * java.lang.Math.sqrt
            (dblKappaTildaSquared * (dblKappaTildaSquaredTauSquared + 4.))));
    }

    /**
     * Create the Standard DiscreteAlmgrenChriss Instance
     * 
     * @param dblStartHoldings Trajectory Start Holdings
     * @param dblFinishTime Trajectory Finish Time
     * @param iNumInterval The Number of Fixed Intervals
     * @param lpep Linear Impact Price Walk Parameters
     * @param dblRiskAversion The Risk Aversion Parameter
     * 
     * @return The DiscreteAlmgrenChriss Instance
     */

    public static final DiscreteAlmgrenChriss Standard (
        final double dblStartHoldings,
        final double dblFinishTime,
        final int iNumInterval,
        final org.drip.execution.dynamics.LinearPermanentExpectationParameters lpep,
        final double dblRiskAversion)
    {
        try {
            return new DiscreteAlmgrenChriss
                (org.drip.execution.strategy.DiscreteTradingTrajectoryControl.FixedInterval (new
                    org.drip.execution.strategy.OrderSpecification (dblStartHoldings, dblFinishTime),
                        iNumInterval), lpep, new org.drip.execution.risk.MeanVarianceObjectiveUtility
                            (dblRiskAversion));
        } catch (java.lang.Exception e) {
            e.printStackTrace();
        }

        return null;
    }

    private DiscreteAlmgrenChriss (
        final org.drip.execution.strategy.DiscreteTradingTrajectoryControl dttc,
        final org.drip.execution.dynamics.LinearPermanentExpectationParameters lpep,
        final org.drip.execution.risk.MeanVarianceObjectiveUtility mvou)
        throws java.lang.Exception
    {
        super (dttc, lpep, mvou);
    }

    @Override public org.drip.execution.optimum.EfficientTradingTrajectoryDiscrete generate()
    {
        org.drip.execution.strategy.DiscreteTradingTrajectoryControl dttc = control();

        double[] adblTNode = dttc.executionTimeNodes();

        org.drip.execution.dynamics.LinearPermanentExpectationParameters lpep =
            (org.drip.execution.dynamics.LinearPermanentExpectationParameters) priceEvolutionParameters();

        org.drip.execution.impact.TransactionFunction tfTemporaryExpectation =
            lpep.temporaryExpectation().epochImpactFunction();

        if (!(tfTemporaryExpectation instanceof org.drip.execution.impact.TransactionFunctionLinear))
            return null;

        double dblEpochVolatility = java.lang.Double.NaN;
        org.drip.execution.impact.TransactionFunctionLinear tflTemporaryExpectation =
            (org.drip.execution.impact.TransactionFunctionLinear) tfTemporaryExpectation;

        try {
            dblEpochVolatility = lpep.arithmeticPriceDynamicsSettings().epochVolatility();
        } catch (java.lang.Exception e) {
            e.printStackTrace();

            return null;
        }

        double dblGamma = lpep.linearPermanentExpectation().epochLiquidityFunction().slope();

        double dblEta = tflTemporaryExpectation.slope();

        double dblX = dttc.startHoldings();

        int iNumNode = adblTNode.length;
        double dblXSquared = dblX * dblX;
        final double dblSigma = dblEpochVolatility;
        double dblTau = adblTNode[1] - adblTNode[0];
        double dblSigmaSquared = dblSigma * dblSigma;
        double[] adblHoldings = new double[iNumNode];
        double[] adblTradeList = new double[iNumNode - 1];
        double dblT = adblTNode[iNumNode - 1] - adblTNode[0];
        double dblEtaTilda = dblEta - 0.5 * dblGamma * dblTau;

        double dblKappaTildaSquared = ((org.drip.execution.risk.MeanVarianceObjectiveUtility)
            objectiveUtility()).riskAversion() * dblSigmaSquared / dblEtaTilda;

        double dblKappaTau = KappaTau (dblKappaTildaSquared, dblTau);

        double dblHalfKappaTau = 0.5 * dblKappaTau;
        double dblKappa = dblKappaTau / dblTau;
        double dblKappaT = dblKappa * dblT;

        double dblSinhKappaT = java.lang.Math.sinh (dblKappaT);

        double dblSinhKappaTau = java.lang.Math.sinh (dblKappaTau);

        double dblSinhHalfKappaTau = java.lang.Math.sinh (dblHalfKappaTau);

        double dblTSinhKappaTau = dblT * dblSinhKappaTau;
        double dblInverseSinhKappaT = 1. / dblSinhKappaT;
        double dblTrajectoryScaler = dblInverseSinhKappaT * dblX;
        double dblTradeListScaler = 2. * dblSinhHalfKappaTau * dblTrajectoryScaler;
        double dblReciprocalSinhKappaTSquared = dblInverseSinhKappaT * dblInverseSinhKappaT;

        for (int i = 0; i < iNumNode; ++i) {
            adblHoldings[i] = dblTrajectoryScaler * java.lang.Math.sinh (dblKappa * (dblT - adblTNode[i]));

            if (i < iNumNode - 1)
                adblTradeList[i] = -1. * dblTradeListScaler * java.lang.Math.cosh (dblKappa * (dblT - dblTau
                    * (0.5 + i)));
        }

        try {
            return new org.drip.execution.optimum.AlmgrenChrissDiscrete (adblTNode, adblHoldings,
                adblTradeList, java.lang.Math.sqrt (dblKappaTildaSquared), dblKappa, 0.5 * dblGamma *
                    dblXSquared + tflTemporaryExpectation.offset() * dblX + dblEtaTilda * dblXSquared *
                        dblReciprocalSinhKappaTSquared * java.lang.Math.tanh (dblHalfKappaTau) * (dblTau *
                            java.lang.Math.sinh (2. * dblKappaT) + 2. * dblTSinhKappaTau) / (2. * dblTau *
                                dblTau), 0.5 * dblSigmaSquared * dblXSquared * dblReciprocalSinhKappaTSquared
                                    * (dblTau * dblSinhKappaT * java.lang.Math.cosh (dblKappa * (dblT -
                                        dblTau)) - dblTSinhKappaTau) / dblSinhKappaTau, dblEpochVolatility *
                                            dblX / (dblT * dblEpochVolatility * java.lang.Math.sqrt (dblT)));
        } catch (java.lang.Exception e) {
            e.printStackTrace();
        }

        return null;
    }
}