ContinuousTrajectoryConcaveImpact.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>ContinuousTrajectoryConcaveImpact</i> reconciles the Characteristic Times of the Optimal Continuous
* Trading Trajectory resulting from the Application of the Almgren (2003) Scheme to a Concave Power Law
* Temporary Market Impact Function. The Power Exponent Considered here is
*
* k = 0.5
*
* 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 ContinuousTrajectoryConcaveImpact {
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 = 0.5;
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[][] {
{0.02, 221., 11.},
{0.09, 103., 23.},
{0.40, 48., 49.},
{1.84, 22., 105.},
{8.55, 10., 226.}
};
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();
}
}