ContinuousTrajectoryConvexImpact.java

package org.drip.sample.almgren2003;

import org.drip.execution.dynamics.*;
import org.drip.execution.impact.*;
import org.drip.execution.nonadaptive.ContinuousPowerImpact;
import org.drip.execution.optimum.PowerImpactContinuous;
import org.drip.execution.parameters.*;
import org.drip.execution.profiletime.*;
import org.drip.function.r1tor1.FlatUnivariate;
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>ContinuousTrajectoryConvexImpact</i> reconciles the Characteristic Times of the Optimal Continuous
 * Trading Trajectory resulting from the Application of the Almgren (2003) Scheme to a Convex Power Law
 * Temporary Market Impact Function. The Power Exponent Considered here is
 * 
 * k = 2.0
 * 
 * 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>
 * 			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>
 * 			Bertsimas, D., and A. W. Lo (1998): Optimal Control of Execution Costs <i>Journal of Financial
 * 				Markets</i> <b>1</b> 1-50
 *  	</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/almgren2003/README.md">Almgren (2003) Power Law Liquidity</a></li>
 *  </ul>
 * <br><br>
 * 
 * @author Lakshmi Krishnamurthy
 */

public class ContinuousTrajectoryConvexImpact {

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

		double dblS0 = 50.;
		double dblDailyVolume = 1000000.;
		double dblBidAskSpread = 0.;
		double dblPermanentImpactFactor = 0.;
		double dblTemporaryImpactFactor = 0.01;
		double dblK = 2.0;
		double dblGamma = 0.;
		double dblDailyVolumeExecutionFactor = 0.1;
		double dblDrift = 0.;
		double dblVolatility = 1.;
		double dblSerialCorrelation = 0.;
		double dblX = 100000.;
		double dblFinishTime = 1.;

		double[] adblLambda = new double[] {
			1.e-03,
			1.e-04,
			1.e-05,
			1.e-06,
			1.e-07
		};

		double[][] aadblAlmgren2003Reconciler = new double[][] {
			{0.22, 462.,  30.},
			{0.46,  99.,  45.},
			{1.00,  21.,  65.},
			{2.15,   5.,  96.},
			{4.64,   1., 141.}
		};

		PriceMarketImpactPower pmip = new PriceMarketImpactPower (
			new AssetTransactionSettings (
				dblS0,
				dblDailyVolume,
				dblBidAskSpread
			),
			dblPermanentImpactFactor,
			dblTemporaryImpactFactor,
			dblDailyVolumeExecutionFactor,
			dblK
		);

		LinearPermanentExpectationParameters lpep = ArithmeticPriceEvolutionParametersBuilder.Almgren2003 (
			new ArithmeticPriceDynamicsSettings (
				dblDrift,
				new FlatUnivariate (dblVolatility),
				dblSerialCorrelation
			),
			new UniformParticipationRateLinear (
				new ParticipationRateLinear (
					0.,
					dblGamma
				)
			),
			new UniformParticipationRate ((ParticipationRatePower) pmip.temporaryTransactionFunction())
		);

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

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

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

		System.out.println ("\t| LAMBDAINV || T_STAR | COST_EXP | COST_STD ||");

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

		for (int i = 0; i < adblLambda.length; ++i) {
			ContinuousPowerImpact cpi = ContinuousPowerImpact.Standard (
				dblX,
				dblFinishTime,
				lpep,
				adblLambda[i]
			);

			PowerImpactContinuous pic = (PowerImpactContinuous) cpi.generate();

			System.out.println ("\t|  " +
				FormatUtil.FormatDouble (1. / adblLambda[i], 5, 0, 1.e-03) + "   || " +
				FormatUtil.FormatDouble (pic.characteristicTime(), 1, 2, 1.) + "      " +
				FormatUtil.FormatDouble (pic.transactionCostExpectation(), 3, 0, 1.e-03) + "       " +
				FormatUtil.FormatDouble (Math.sqrt (pic.transactionCostVariance()), 3, 0, 1.e-03) + "   ||"
			);
		}

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

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

		System.out.println ("\t|               ALMGREN (2003)              ||");

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

		System.out.println ("\t| LAMBDAINV || T_STAR | COST_EXP | COST_STD ||");

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

		for (int i = 0; i < adblLambda.length; ++i)
			System.out.println ("\t|  " +
				FormatUtil.FormatDouble (1. / adblLambda[i], 5, 0, 1.e-03) + "   || " +
				FormatUtil.FormatDouble (aadblAlmgren2003Reconciler[i][0], 1, 2, 1.) + "      " +
				FormatUtil.FormatDouble (aadblAlmgren2003Reconciler[i][1], 3, 0, 1.) + "       " +
				FormatUtil.FormatDouble (aadblAlmgren2003Reconciler[i][2], 3, 0, 1.) + "   ||"
			);

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

		EnvManager.TerminateEnv();
	}
}