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();
}
}