PowerLawOptimalTrajectory.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.ArithmeticPriceDynamicsSettings;
import org.drip.execution.profiletime.*;
import org.drip.function.definition.R1ToR1;
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>PowerLawOptimalTrajectory</i> sketches out the Optimal Trajectories for 3 different values of k -
* representing Concave, Linear, and Convex Power's respectively. 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 PowerLawOptimalTrajectory {
private static final void RiskAversionRun (
final double dblLambda)
throws Exception
{
double dblGamma = 0.;
double dblHRef = 0.50;
double dblVRef = 100000.;
double dblDrift = 0.;
double dblVolatility = 1.;
double dblSerialCorrelation = 0.;
double dblX = 100000.;
double dblFinishTime = 10.;
int iNumInterval = 10;
double[] adblK = new double[] {
0.25,
0.50,
0.75,
1.00,
1.25,
1.50,
1.75,
2.00,
2.25,
2.50,
2.75,
3.00
};
System.out.println ("\n\t|------------------------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t|\tPOWER LAW OPTIMAL TRAJECTORY; RISK TOLERANCE (thousands) => " + FormatUtil.FormatDouble (1. / dblLambda, 1, 0, 1.e-03));
System.out.println ("\t|");
System.out.println ("\t|\t\tL -> R:");
System.out.println ("\t|\t\t\tTime Node Trajectory Realization (Percent)");
System.out.println ("\t|\t\t\tCharacteristic Time (Days)");
System.out.println ("\t|\t\t\tMaximum Execution Time (Days)");
System.out.println ("\t|\t\t\tTransaction Cost Expectation (Thousands)");
System.out.println ("\t|\t\t\tTransaction Cost Variance (Thousands)");
System.out.println ("\t|------------------------------------------------------------------------------------------------------------------------------------||");
ArithmeticPriceDynamicsSettings apds = new ArithmeticPriceDynamicsSettings (
dblDrift,
new FlatUnivariate (dblVolatility),
dblSerialCorrelation
);
ParticipationRateLinear prlPermanent = new ParticipationRateLinear (
0.,
dblGamma
);
double[] adblExecutionTime = new double[iNumInterval];
for (int i = 1; i <= iNumInterval; ++i)
adblExecutionTime[i - 1] = ((double) i) / ((double) iNumInterval);
for (int i = 0; i < adblK.length; ++i) {
double dblEta = dblHRef / java.lang.Math.pow (dblVRef, adblK[i]);
LinearPermanentExpectationParameters lpep = ArithmeticPriceEvolutionParametersBuilder.Almgren2003 (
apds,
new UniformParticipationRateLinear (prlPermanent),
new UniformParticipationRate (
new ParticipationRatePower (
dblEta,
adblK[i]
)
)
);
ContinuousPowerImpact cpi = ContinuousPowerImpact.Standard (
dblX,
dblFinishTime,
lpep,
dblLambda
);
PowerImpactContinuous pic = (PowerImpactContinuous) cpi.generate();
if (0 == i) {
String strExecutionTime = "\t| | ";
for (int j = 0; j < adblExecutionTime.length; ++j)
strExecutionTime = strExecutionTime + " " + FormatUtil.FormatDouble (adblExecutionTime[j], 1, 2, 1.);
System.out.println (strExecutionTime);
System.out.println ("\t|------------------------------------------------------------------------------------------------------------------------------------||");
}
R1ToR1 r1ToR1Holdings = pic.holdings();
String strHoldings = "\t| k =" + FormatUtil.FormatDouble (adblK[i], 1, 2, 1.) + " | ";
for (int j = 0; j < iNumInterval; ++j)
strHoldings = strHoldings + " " + FormatUtil.FormatDouble (r1ToR1Holdings.evaluate (adblExecutionTime[j]) / dblX, 2, 2, 100.);
double dblExecutionTimeUpperBound = pic.executionTimeUpperBound();
System.out.println (
strHoldings + " | " +
FormatUtil.FormatDouble (pic.characteristicTime(), 2, 1, 1.) + " | " +
FormatUtil.FormatDouble (Double.isNaN (dblExecutionTimeUpperBound) ? 0. : dblExecutionTimeUpperBound, 2, 1, 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|------------------------------------------------------------------------------------------------------------------------------------||");
}
public static final void main (
final String[] astrArgs)
throws Exception
{
EnvManager.InitEnv (
"",
true
);
double[] adblLambda = new double[] {
1.e-04,
5.e-06,
5.e-07
};
for (double dblLambda : adblLambda)
RiskAversionRun (dblLambda);
EnvManager.TerminateEnv();
}
}