VariableDriftTrajectoryComparator.java

package org.drip.sample.trend;

import org.drip.execution.bayesian.*;
import org.drip.execution.cost.*;
import org.drip.execution.impact.ParticipationRateLinear;
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) 2018 Lakshmi Krishnamurthy
 * Copyright (C) 2017 Lakshmi Krishnamurthy
 * Copyright (C) 2016 Lakshmi Krishnamurthy
 * 
 *  This file is part of DRIP, a free-software/open-source library for buy/side financial/trading model
 *      libraries targeting analysts and developers
 *      https://lakshmidrip.github.io/DRIP/
 *  
 *  DRIP is composed of four main libraries:
 *  
 *  - DRIP Fixed Income - https://lakshmidrip.github.io/DRIP-Fixed-Income/
 *  - DRIP Asset Allocation - https://lakshmidrip.github.io/DRIP-Asset-Allocation/
 *  - DRIP Numerical Optimizer - https://lakshmidrip.github.io/DRIP-Numerical-Optimizer/
 *  - DRIP Statistical Learning - https://lakshmidrip.github.io/DRIP-Statistical-Learning/
 * 
 *  - DRIP Fixed Income: Library for Instrument/Trading Conventions, Treasury Futures/Options,
 *      Funding/Forward/Overnight Curves, Multi-Curve Construction/Valuation, Collateral Valuation and XVA
 *      Metric Generation, Calibration and Hedge Attributions, Statistical Curve Construction, Bond RV
 *      Metrics, Stochastic Evolution and Option Pricing, Interest Rate Dynamics and Option Pricing, LMM
 *      Extensions/Calibrations/Greeks, Algorithmic Differentiation, and Asset Backed Models and Analytics.
 * 
 *  - DRIP Asset Allocation: Library for model libraries for MPT framework, Black Litterman Strategy
 *      Incorporator, Holdings Constraint, and Transaction Costs.
 * 
 *  - DRIP Numerical Optimizer: Library for Numerical Optimization and Spline Functionality.
 * 
 *  - DRIP Statistical Learning: Library for Statistical Evaluation and Machine Learning.
 * 
 *  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.
 */

/**
 * VariableDriftTrajectoryComparator demonstrates the Optimal Trajectory for a Price Process with Bayesian
 *  Drift, Arithmetic Volatility, and Linear Temporary Market Impact across a Set of Drifts. The References
 *  are:
 * 
 *  - Bertsimas, D., and A. W. Lo (1998): Optimal Control of Execution Costs, Journal of Financial Markets 1
 *      1-50.
 * 
 *  - Almgren, R., and N. Chriss (2000): Optimal Execution of Portfolio Transactions, Journal of Risk 3 (2)
 *      5-39.
 * 
 *  - Brunnermeier, L. K., and L. H. Pedersen (2005): Predatory Trading, Journal of Finance 60 (4) 1825-1863.
 *
 *  - Almgren, R., and J. Lorenz (2006): Bayesian Adaptive Trading with a Daily Cycle, Journal of Trading 1
 *      (4) 38-46.
 * 
 *  - Kissell, R., and R. Malamut (2007): Algorithmic Decision Making Framework, Journal of Trading 1 (1)
 *      12-21.
 * 
 * @author Lakshmi Krishnamurthy
 */

public class VariableDriftTrajectoryComparator {

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

        int iN = 50;
        double dblT = 1.;
        double dblX0 = 1.;
        double dblNu = 1.;
        double dblEta = 0.07;
        double dblSigma = 1.5;
        double dblAlphaBarLow = 0.0;
        double dblAlphaBarMid = 0.7;
        double dblAlphaBarHigh = 1.5;

        double dblTime = 0.;
        double dblTimeWidth = dblT / iN;
        double dblXUnconstrained = dblX0;
        double dblXConstrainedLow = dblX0;
        double dblXConstrainedMid = dblX0;
        double dblXConstrainedHigh = dblX0;

        ParticipationRateLinear prlTemporary = ParticipationRateLinear.SlopeOnly (dblEta);

        PriorDriftDistribution pddLow = new PriorDriftDistribution (
            dblAlphaBarLow,
            dblNu
        );

        PriorDriftDistribution pddMid = new PriorDriftDistribution (
            dblAlphaBarMid,
            dblNu
        );

        PriorDriftDistribution pddHigh = new PriorDriftDistribution (
            dblAlphaBarHigh,
            dblNu
        );

        double[] adblAlphaLow = pddLow.realizedDrift (iN);

        double[] adblAlphaMid = pddMid.realizedDrift (iN);

        double[] adblAlphaHigh = pddHigh.realizedDrift (iN);

        System.out.println();

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

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

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

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

        System.out.println ("\t|    - Constrained Trade Rate Low Drift                                          ||");

        System.out.println ("\t|    - Constrained Trade Rate Mid Drift                                          ||");

        System.out.println ("\t|    - Constrained Trade Rate High Drift                                         ||");

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

        System.out.println ("\t|    - Constrained Holdings Low Drift                                            ||");

        System.out.println ("\t|    - Constrained Holdings Mid Drift                                            ||");

        System.out.println ("\t|    - Constrained Holdings High Drift                                           ||");

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

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

        for (int i = 0; i < iN - 1; ++i) {
            dblTime = dblTime + dblTimeWidth;

            ConditionalPriceDistribution cpdLow = new ConditionalPriceDistribution (
                adblAlphaLow[i],
                dblSigma,
                dblTime
            );

            ConditionalPriceDistribution cpdMid = new ConditionalPriceDistribution (
                adblAlphaMid[i],
                dblSigma,
                dblTime
            );

            ConditionalPriceDistribution cpdHigh = new ConditionalPriceDistribution (
                adblAlphaHigh[i],
                dblSigma,
                dblTime
            );

            double dblPriceSwingLow = cpdLow.priceVolatilitySwing();

            double dblPriceSwingMid = cpdMid.priceVolatilitySwing();

            double dblPriceSwingHigh = cpdHigh.priceVolatilitySwing();

            double dblRealizedPriceChangeLow = adblAlphaLow[i] * dblTimeWidth + dblPriceSwingLow;
            double dblRealizedPriceChangeMid = adblAlphaMid[i] * dblTimeWidth + dblPriceSwingMid;
            double dblRealizedPriceChangeHigh = adblAlphaHigh[i] * dblTimeWidth + dblPriceSwingHigh;

            PriorConditionalCombiner pccLow = new PriorConditionalCombiner (
                pddLow,
                cpdLow
            );

            PriorConditionalCombiner pccMid = new PriorConditionalCombiner (
                pddMid,
                cpdMid
            );

            PriorConditionalCombiner pccHigh = new PriorConditionalCombiner (
                pddHigh,
                cpdHigh
            );

            ConstrainedLinearTemporaryImpact cltiLow = ConstrainedLinearTemporaryImpact.Standard (
                0.,
                dblT,
                dblXConstrainedLow,
                pccLow,
                dblRealizedPriceChangeLow,
                prlTemporary
            );

            ConstrainedLinearTemporaryImpact cltiMid = ConstrainedLinearTemporaryImpact.Standard (
                0.,
                dblT,
                dblXConstrainedMid,
                pccMid,
                dblRealizedPriceChangeMid,
                prlTemporary
            );

            ConstrainedLinearTemporaryImpact cltiHigh = ConstrainedLinearTemporaryImpact.Standard (
                0.,
                dblT,
                dblXConstrainedHigh,
                pccHigh,
                dblRealizedPriceChangeHigh,
                prlTemporary
            );

            double dblConstrainedInstantaneousTradeRateLow = cltiLow.instantaneousTradeRate();

            dblXConstrainedLow = dblXConstrainedLow - dblConstrainedInstantaneousTradeRateLow * dblTimeWidth;

            if (0 > dblXConstrainedLow) dblXConstrainedLow = 0.;

            double dblConstrainedInstantaneousTradeRateMid = cltiMid.instantaneousTradeRate();

            dblXConstrainedMid = dblXConstrainedMid - dblConstrainedInstantaneousTradeRateMid * dblTimeWidth;

            if (0 > dblXConstrainedMid) dblXConstrainedMid = 0.;

            double dblConstrainedInstantaneousTradeRateHigh = cltiHigh.instantaneousTradeRate();

            dblXConstrainedHigh = dblXConstrainedHigh - dblConstrainedInstantaneousTradeRateHigh * dblTimeWidth;

            if (0 > dblXConstrainedHigh) dblXConstrainedHigh = 0.;

            LinearTemporaryImpact lti = LinearTemporaryImpact.Unconstrained (
                dblTime,
                dblT,
                dblXUnconstrained,
                pccMid,
                dblRealizedPriceChangeMid,
                prlTemporary
            );

            double dblUnconstrainedInstantaneousTradeRate = lti.instantaneousTradeRate();

            dblXUnconstrained = dblXUnconstrained - dblUnconstrainedInstantaneousTradeRate * dblTimeWidth;

            System.out.println (
                "\t| " + FormatUtil.FormatDouble (dblTime, 1, 2, 1.) + " => " +
                FormatUtil.FormatDouble (dblConstrainedInstantaneousTradeRateLow, 1, 3, 1.) + " | " +
                FormatUtil.FormatDouble (dblConstrainedInstantaneousTradeRateMid, 1, 3, 1.) + " | " +
                FormatUtil.FormatDouble (dblConstrainedInstantaneousTradeRateHigh, 1, 3, 1.) + " | " +
                FormatUtil.FormatDouble (dblUnconstrainedInstantaneousTradeRate, 1, 3, 1.) + " | " +
                FormatUtil.FormatDouble (dblXConstrainedLow, 1, 3, 1.) + " | " +
                FormatUtil.FormatDouble (dblXConstrainedMid, 1, 3, 1.) + " | " +
                FormatUtil.FormatDouble (dblXConstrainedHigh, 1, 3, 1.) + " | " +
                FormatUtil.FormatDouble (dblXUnconstrained, 1, 3, 1.) + " ||"
            );
        }

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