StaticContinuousOptimalTrajectory.java
package org.drip.sample.almgren2009;
import org.drip.execution.dynamics.*;
import org.drip.execution.impact.ParticipationRateLinear;
import org.drip.execution.nonadaptive.ContinuousAlmgrenChriss;
import org.drip.execution.optimum.EfficientTradingTrajectoryContinuous;
import org.drip.execution.parameters.*;
import org.drip.execution.profiletime.UniformParticipationRateLinear;
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>StaticContinuousOptimalTrajectory</i> demonstrates the Generation and Usage of Continuous Version of
* the Discrete Trading Trajectory generated by the Almgren and Chriss (2000) Scheme under the Criterion of
* No-Drift. The References are:
*
* <br><br>
* <ul>
* <li>
* Almgren, R. F., and N. Chriss (2000): Optimal Execution of Portfolio Transactions <i>Journal of
* Risk</i> <b>3 (2)</b> 5-39
* </li>
* <li>
* Almgren, R. F. (2009): Optimal Trading in a Dynamic Market
* https://www.math.nyu.edu/financial_mathematics/content/02_financial/2009-2.pdf
* </li>
* <li>
* Almgren, R. F. (2012): Optimal Trading with Stochastic Liquidity and Volatility <i>SIAM Journal
* of Financial Mathematics</i> <b>3 (1)</b> 163-181
* </li>
* <li>
* Geman, H., D. B. Madan, and M. Yor (2001): Time Changes for Levy Processes <i>Mathematical
* Finance</i> <b>11 (1)</b> 79-96
* </li>
* <li>
* Walia, N. (2006): Optimal Trading: Dynamic Stock Liquidation Strategies <b>Princeton
* University</b>
* </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/almgren2009/README.md">Almgren (2009) Optimal Adaptive HJB</a></li>
* </ul>
* <br><br>
*
* @author Lakshmi Krishnamurthy
*/
public class StaticContinuousOptimalTrajectory {
public static void main (
final String[] astrArgs)
throws Exception
{
EnvManager.InitEnv (
"",
true
);
double dblS0 = 50.;
double dblX = 1000000.;
double dblT = 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;
int iN = 20;
double dblTime = 0.;
double dblTimeWidth = dblT / iN;
ArithmeticPriceDynamicsSettings apds = ArithmeticPriceDynamicsSettings.FromAnnualReturnsSettings (
dblAnnualReturns,
dblAnnualVolatility,
0.,
dblS0
);
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)
);
ContinuousAlmgrenChriss cac = ContinuousAlmgrenChriss.Standard (
dblX,
dblT,
lpep,
dblLambdaU
);
EfficientTradingTrajectoryContinuous ettc = (EfficientTradingTrajectoryContinuous) cac.generate();
R1ToR1 r1ToR1Holdings = ettc.holdings();
R1ToR1 r1ToR1TradeRate = ettc.tradeRate();
R1ToR1 r1ToR1TransactionCostVariance = ettc.transactionCostVarianceFunction();
R1ToR1 r1ToR1TransactionCostExpectation = ettc.transactionCostExpectationFunction();
System.out.println ();
System.out.println ("\t|-------------------------------------------||");
System.out.println ("\t| STATIC CONTINUOUS OPTIMAL TRAJECTORY ||");
System.out.println ("\t|-------------------------------------------||");
System.out.println ("\t| L -> R: ||");
System.out.println ("\t| - Time ||");
System.out.println ("\t| - Holdings ||");
System.out.println ("\t| - Trade Rate ||");
System.out.println ("\t| - Transaction Cost Expectation ||");
System.out.println ("\t| - Transaction Cost Volatility ||");
System.out.println ("\t|-------------------------------------------||");
for (int i = 1; i <= iN; ++i) {
dblTime = dblTime + dblTimeWidth;
System.out.println (
"\t|" +
FormatUtil.FormatDouble (dblTime, 1, 2, 1.) + " => " +
FormatUtil.FormatDouble (r1ToR1Holdings.evaluate (dblTime) / dblX, 1, 3, 1.) + " | " +
FormatUtil.FormatDouble (r1ToR1TradeRate.evaluate (dblTime) * dblTimeWidth / dblX, 1, 3, 1.) + " | " +
FormatUtil.FormatDouble (r1ToR1TransactionCostExpectation.evaluate (dblTime) / dblX, 1, 3, 1.) + " | " +
FormatUtil.FormatDouble (Math.sqrt (r1ToR1TransactionCostVariance.evaluate (dblTime)) / dblX, 1, 3, 1.) + " ||"
);
}
System.out.println ("\t|-------------------------------------------||");
EnvManager.TerminateEnv();
}
}