OptimalTrajectoryNoDrift.java

package org.drip.sample.almgrenchriss;

import org.drip.execution.capture.*;
import org.drip.execution.dynamics.*;
import org.drip.execution.impact.*;
import org.drip.execution.nonadaptive.DiscreteAlmgrenChriss;
import org.drip.execution.optimum.AlmgrenChrissDiscrete;
import org.drip.execution.parameters.*;
import org.drip.execution.profiletime.UniformParticipationRateLinear;
import org.drip.function.r1tor1.FlatUnivariate;
import org.drip.measure.gaussian.R1UnivariateNormal;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;

/*
 * -*- 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>OptimalTrajectoryNoDrift</i> demonstrates the Generation of the Optimal Trading Trajectory in
 * accordance with the Specification of Almgren and Chriss (2000) for the given Risk Aversion Parameter
 * without the Asset Drift. 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/sample/README.md">DROP API Construction and Usage</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/almgrenchriss/README.md">Almgren Chriss Efficient Frontier Trajectories</a></li>
 *  </ul>
 * <br><br>
 *
 * @author Lakshmi Krishnamurthy
 */

public class OptimalTrajectoryNoDrift {

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


        double dblS0 = 50.;
        double dblX = 1000000.;
        double dblT = 5.;
        int iN = 5;
        double dblAnnualVolatility = 0.30;
        double dblAnnualReturns = 0.10;
        double dblBidAsk = 0.125;
        double dblDailyVolume = 5.e06;
        double dblDailyVolumePermanentImpact = 0.1;
        double dblDailyVolumeTemporaryImpact = 0.01;
        double dblLambdaU = 1.e-06;

        ArithmeticPriceDynamicsSettings apds = ArithmeticPriceDynamicsSettings.FromAnnualReturnsSettings (
            dblAnnualReturns,
            dblAnnualVolatility,
            0.,
            dblS0
        );

        double dblAlpha = apds.drift();

        double dblSigma = apds.epochVolatility();

        PriceMarketImpactLinear pmil = new PriceMarketImpactLinear (
            new AssetTransactionSettings (
                dblS0,
                dblDailyVolume,
                dblBidAsk
            ),
            dblDailyVolumePermanentImpact,
            dblDailyVolumeTemporaryImpact
        );

        ParticipationRateLinear prlPermanent = (ParticipationRateLinear) pmil.permanentTransactionFunction();

        ParticipationRateLinear prlTemporary = (ParticipationRateLinear) pmil.temporaryTransactionFunction();

        LinearPermanentExpectationParameters lpep = ArithmeticPriceEvolutionParametersBuilder.LinearExpectation (
            new ArithmeticPriceDynamicsSettings (
                0.,
                new FlatUnivariate (dblSigma),
                0.
            ),
            new UniformParticipationRateLinear (prlPermanent),
            new UniformParticipationRateLinear (prlTemporary)
        );

        DiscreteAlmgrenChriss dac = DiscreteAlmgrenChriss.Standard (
            dblX,
            dblT,
            iN,
            lpep,
            dblLambdaU
        );

        AlmgrenChrissDiscrete acd = (AlmgrenChrissDiscrete) dac.generate();

        double[] adblExecutionTimeNode = acd.executionTimeNode();

        double[] adblTradeList = acd.tradeList();

        double[] adblHoldings = acd.holdings();

        LinearImpactTrajectoryEstimator lite = new LinearImpactTrajectoryEstimator (acd);

        TrajectoryShortfallAggregate tsa = lite.totalCostDistributionDetail (lpep);

        double[] adblIncrementalPermanentImpact = tsa.incrementalPermanentImpactExpectation();

        double[] adblIncrementalTemporaryImpact = tsa.incrementalTemporaryImpactExpectation();

        double[] adblCumulativePermanentImpact = tsa.cumulativePermanentImpactExpectation();

        double[] adblCumulativeTemporaryImpact = tsa.cumulativeTemporaryImpactExpectation();

        double[] adblIncrementalShortfallVariance = tsa.incrementalVariance();

        double[] adblCumulativeShortfallVariance = tsa.cumulativeVariance();

        double[] adblIncrementalShortfallMean = tsa.incrementalExpectation();

        double[] adblCumulativeShortfallMean = tsa.cumulativeExpectation();

        R1UnivariateNormal r1un = lite.totalCostDistributionSynopsis (lpep);

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

        System.out.println ("\t| ALMGREN-CHRISS TRAJECTORY GENERATOR INPUTS  ||");

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

        System.out.println ("\t| Initial Stock Price           : " + dblS0);

        System.out.println ("\t| Initial Holdings              : " + dblX);

        System.out.println ("\t| Liquidation Time              : " + dblT);

        System.out.println ("\t| Number of Time Periods        : " + iN);

        System.out.println ("\t| Annual Volatility             :" + FormatUtil.FormatDouble (dblAnnualVolatility, 1, 0, 100.) + "%");

        System.out.println ("\t| Annual Growth                 :" + FormatUtil.FormatDouble (dblAnnualReturns, 1, 0, 100.) + "%");

        System.out.println ("\t| Bid-Ask Spread                : " + dblBidAsk);

        System.out.println ("\t| Daily Volume                  : " + dblDailyVolume);

        System.out.println ("\t| Daily Volume Temporary Impact : " + dblDailyVolumeTemporaryImpact);

        System.out.println ("\t| Daily Volume Permanent Impact : " + dblDailyVolumePermanentImpact);

        System.out.println ("\t| Daily Volume 5 million Shares : " + prlPermanent.slope());

        System.out.println ("\t| Static Holdings 11,000 Shares : " + dblLambdaU);

        System.out.println ("\t|");

        System.out.println (
            "\t| Daily Volatility              : " +
            FormatUtil.FormatDouble (dblSigma, 1, 4, 1.)
        );

        System.out.println (
            "\t| Daily Returns                 : " +
            FormatUtil.FormatDouble (dblAlpha, 1, 4, 1.)
        );

        System.out.println ("\t| Temporary Impact Fixed Offset :  " + prlTemporary.offset());

        System.out.println ("\t| Eta                           :  " + prlTemporary.slope());

        System.out.println ("\t| Gamma                         :  " + prlPermanent.slope());

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

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

        System.out.println ("\t| AC2000 Optimal Trajectory   ||");

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

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

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

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

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

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

        for (int i = 0; i <= iN; ++i) {
            if (i == 0)
                System.out.println (
                    "\t|" + FormatUtil.FormatDouble (adblExecutionTimeNode[i], 1, 0, 1.) + " => " +
                    FormatUtil.FormatDouble (adblHoldings[i], 7, 1, 1.) + " | " +
                    FormatUtil.FormatDouble (0., 6, 1, 1.) + " ||"
                );
            else
                System.out.println (
                    "\t|" + FormatUtil.FormatDouble (adblExecutionTimeNode[i], 1, 0, 1.) + " => " +
                    FormatUtil.FormatDouble (adblHoldings[i], 7, 1, 1.) + " | " +
                    FormatUtil.FormatDouble (adblTradeList[i - 1], 6, 1, 1.) + " ||"
                );
        }

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

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

        System.out.println ("\t|               PERIOD LEVEL COST DISTRIBUTION              ||");

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

        System.out.println ("\t|  PERIOD   |          MEAN         |        VARIANCE       ||");

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

        System.out.println ("\t|  PERIOD   |    INCR   |    CUML   |    INCR   |    CUML   ||");

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

        for (int i = 0; i < adblIncrementalShortfallMean.length; ++i)
            System.out.println (
                "\t| PERIOD #" + (i + 1) + " | " +
                FormatUtil.FormatDouble (adblIncrementalShortfallMean[i], 6, 1, 1.) + " | " +
                FormatUtil.FormatDouble (adblCumulativeShortfallMean[i], 6, 1, 1.) + " | " +
                FormatUtil.FormatDouble (adblIncrementalShortfallVariance[i], 6, 1, 1.e-06) + " | " +
                FormatUtil.FormatDouble (adblCumulativeShortfallVariance[i], 6, 1, 1.e-06) + " ||"
            );

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

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

        System.out.println ("\t|            PERIOD LEVEL COST IMPACT CONTRIBUTION          ||");

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

        System.out.println ("\t|  PERIOD   |       PERMANENT       |       TEMPORARY       ||");

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

        System.out.println ("\t|  PERIOD   |    INCR   |    CUML   |    INCR   |    CUML   ||");

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

        for (int i = 0; i < adblIncrementalPermanentImpact.length; ++i)
            System.out.println (
                "\t| PERIOD #" + (i + 1) + " | " +
                FormatUtil.FormatDouble (adblIncrementalPermanentImpact[i], 6, 1, 1.) + " | " +
                FormatUtil.FormatDouble (adblCumulativePermanentImpact[i], 6, 1, 1.) + " | " +
                FormatUtil.FormatDouble (adblIncrementalTemporaryImpact[i], 6, 1, 1.) + " | " +
                FormatUtil.FormatDouble (adblCumulativeTemporaryImpact[i], 6, 1, 1.) + " ||"
            );

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

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

        System.out.println ("\t| TRANSACTION COST RECONCILIATION: AC2000 vs. EXPLICIT LINEAR  ||");

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

        System.out.println (
            "\t| Transaction Cost Expectation         : " +
            FormatUtil.FormatDouble (r1un.mean(), 6, 1, 1.) + " | " +
            FormatUtil.FormatDouble (acd.transactionCostExpectation(), 6, 1, 1.) + " ||"
        );

        System.out.println (
            "\t| Transaction Cost Variance (X 10^-06) : " +
            FormatUtil.FormatDouble (r1un.variance(), 6, 1, 1.e-06) + " | " +
            FormatUtil.FormatDouble (acd.transactionCostVariance(), 6, 1, 1.e-06) + " ||"
        );

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

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

        System.out.println ("\t|  AC2000 METRICS DUMP  ||");

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

        System.out.println ("\t| Kappa       : " + FormatUtil.FormatDouble (acd.kappa(), 1, 4, 1.) + " ||");

        System.out.println ("\t| Kappa Tilda : " + FormatUtil.FormatDouble (acd.kappaTilda(), 1, 4, 1.) + " ||");

        System.out.println ("\t| Half Life   : " + FormatUtil.FormatDouble (acd.halfLife(), 1, 4, 1.) + " ||");

        System.out.println ("\t| Market Power: " + FormatUtil.FormatDouble (acd.marketPower(), 1, 4, 1.) + " ||");

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

        EnvManager.TerminateEnv();
    }
}