OptimalTrajectoryMeasures.java
package org.drip.sample.principal;
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.principal.Almgren2003Estimator;
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) 2018 Lakshmi Krishnamurthy
* Copyright (C) 2017 Lakshmi Krishnamurthy
* Copyright (C) 2016 Lakshmi Krishnamurthy
*
* This file is part of DRIP, a free-software/open-source library for buy/side financial/trading model
* libraries targeting analysts and developers
* https://lakshmidrip.github.io/DRIP/
*
* DRIP is composed of four main libraries:
*
* - DRIP Fixed Income - https://lakshmidrip.github.io/DRIP-Fixed-Income/
* - DRIP Asset Allocation - https://lakshmidrip.github.io/DRIP-Asset-Allocation/
* - DRIP Numerical Optimizer - https://lakshmidrip.github.io/DRIP-Numerical-Optimizer/
* - DRIP Statistical Learning - https://lakshmidrip.github.io/DRIP-Statistical-Learning/
*
* - DRIP Fixed Income: Library for Instrument/Trading Conventions, Treasury Futures/Options,
* Funding/Forward/Overnight Curves, Multi-Curve Construction/Valuation, Collateral Valuation and XVA
* Metric Generation, Calibration and Hedge Attributions, Statistical Curve Construction, Bond RV
* Metrics, Stochastic Evolution and Option Pricing, Interest Rate Dynamics and Option Pricing, LMM
* Extensions/Calibrations/Greeks, Algorithmic Differentiation, and Asset Backed Models and Analytics.
*
* - DRIP Asset Allocation: Library for model libraries for MPT framework, Black Litterman Strategy
* Incorporator, Holdings Constraint, and Transaction Costs.
*
* - DRIP Numerical Optimizer: Library for Numerical Optimization and Spline Functionality.
*
* - DRIP Statistical Learning: Library for Statistical Evaluation and Machine Learning.
*
* 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.
*/
/**
* OptimalTrajectoryMeasures demonstrates the Trade Scheduling using the Equity Market Impact Functions
* determined empirically by Almgren, Thum, Hauptmann, and Li (2005), using the Parameterization of Almgren
* (2003) for IBM. It generates the Transaction Cost/Principal Discount Measures from the Run The References
* are:
*
* - Almgren, R., and N. Chriss (1999): Value under Liquidation, Risk 12 (12).
*
* - Almgren, R., and N. Chriss (2000): Optimal Execution of Portfolio Transactions, Journal of Risk 3 (2)
* 5-39.
*
* - Almgren, R. (2003): Optimal Execution with Nonlinear Impact Functions and Trading-Enhanced Risk,
* Applied Mathematical Finance 10 (1) 1-18.
*
* - Almgren, R., and N. Chriss (2003): Bidding Principles, Risk 97-102.
*
* - Almgren, R., C. Thum, E. Hauptmann, and H. Li (2005): Equity Market Impact, Risk 18 (7) 57-62.
*
* @author Lakshmi Krishnamurthy
*/
public class OptimalTrajectoryMeasures {
public static final void main (
final String[] astrArgs)
throws Exception
{
EnvManager.InitEnv ("");
double dblS0 = 50.;
double dblX = 100000.;
double dblVolatility = 1.;
double dblDailyVolume = 1000000.;
double dblDailyVolumeExecutionFactor = 0.1;
double dblPermanentImpactFactor = 0.;
double dblTemporaryImpactFactor = 0.01;
double dblT = 5.;
int iNumInterval = 20;
double dblLambda = 1.e-06;
double dblK = 1.;
double dblPrincipalDiscount = 0.15;
PriceMarketImpactPower pmip = new PriceMarketImpactPower (
new AssetTransactionSettings (
dblS0,
dblDailyVolume,
0.
),
dblPermanentImpactFactor,
dblTemporaryImpactFactor,
dblDailyVolumeExecutionFactor,
dblK
);
LinearPermanentExpectationParameters lpep = ArithmeticPriceEvolutionParametersBuilder.Almgren2003 (
new ArithmeticPriceDynamicsSettings (
0.,
new FlatUnivariate (dblVolatility),
0.
),
new UniformParticipationRateLinear ((ParticipationRateLinear) pmip.permanentTransactionFunction()),
new UniformParticipationRate ((ParticipationRatePower) pmip.temporaryTransactionFunction())
);
ContinuousPowerImpact cpi = ContinuousPowerImpact.Standard (
dblX,
dblT,
lpep,
dblLambda
);
PowerImpactContinuous pic = (PowerImpactContinuous) cpi.generate();
R1ToR1 r1ToR1Holdings = pic.holdings();
double[] adblHoldings = new double[iNumInterval];
double[] adblExecutionTime = new double[iNumInterval];
for (int i = 1; i <= iNumInterval; ++i) {
adblExecutionTime[i - 1] = dblT * i / iNumInterval;
adblHoldings[i - 1] = r1ToR1Holdings.evaluate (adblExecutionTime[i - 1]);
}
Almgren2003Estimator a2003e = new Almgren2003Estimator (
pic,
lpep
);
System.out.println();
System.out.println ("\t|----------------------------------||");
System.out.println ("\t| IBM ATHL 2005 Optimal Trajectory ||");
System.out.println ("\t|----------------------------------||");
System.out.println ("\t| L -> R: ||");
System.out.println ("\t| - Execution Time Node ||");
System.out.println ("\t| - Holdings Remaining ||");
System.out.println ("\t| - Trade List Amount ||");
System.out.println ("\t| - Holdings (%) ||");
System.out.println ("\t|----------------------------------||");
for (int i = 1; i < adblExecutionTime.length; ++i)
System.out.println (
"\t| " +
FormatUtil.FormatDouble (adblExecutionTime[i], 1, 2, 1.) + " | " +
FormatUtil.FormatDouble (adblHoldings[i], 5, 0, 1.) + " | " +
FormatUtil.FormatDouble (adblHoldings[i] - adblHoldings[i - 1], 5, 0, 1.) + " | " +
FormatUtil.FormatDouble (adblHoldings[i] / dblX, 2, 1, 100.) + "% ||"
);
System.out.println ("\t|----------------------------------||");
System.out.println();
System.out.println ("\t|-----------------------------------------------------------------------||");
System.out.println ("\t| IBM ATHL 2005 Optimal Trajectory Transaction Cost Measures ||");
System.out.println ("\t|-----------------------------------------------------------------------||");
System.out.println (
"\t| Transaction Cost Expectation ( X 10^-03) : " +
FormatUtil.FormatDouble (pic.transactionCostExpectation(), 5, 2, 1.e-03) + " ||"
);
System.out.println (
"\t| Transaction Cost Variance ( X 10^-06) : " +
FormatUtil.FormatDouble (pic.transactionCostVariance(), 5, 2, 1.e-06) + " ||"
);
System.out.println (
"\t| Characteristic Time : " +
FormatUtil.FormatDouble (pic.characteristicTime(), 5, 2, 1.) + " ||"
);
System.out.println (
"\t| Efficient Frontier Hyperboloid Boundary Value ( X 10^-12) : " +
FormatUtil.FormatDouble (pic.hyperboloidBoundaryValue(), 5, 2, 1.e-12) + " ||"
);
System.out.println (
"\t| Break-even Principal Discount (cents per unit) : " +
FormatUtil.FormatDouble (a2003e.breakevenPrincipalDiscount(), 5, 2, 100.) + " ||"
);
System.out.println (
"\t| Gross Profit Expectation : " +
FormatUtil.FormatDouble (a2003e.principalMeasure (dblPrincipalDiscount).mean(), 5, 2, 1.) + " ||"
);
System.out.println (
"\t| Gross Profit Variance ( X 10^-06) : " +
FormatUtil.FormatDouble (a2003e.principalMeasure (dblPrincipalDiscount).variance(), 5, 2, 1.e-06) + " ||"
);
System.out.println (
"\t| Gross Returns Expectation : " +
FormatUtil.FormatDouble (a2003e.horizonPrincipalMeasure (dblPrincipalDiscount).mean(), 5, 2, 1.) + " ||"
);
System.out.println (
"\t| Gross Returns Variance ( X 10^-06) : " +
FormatUtil.FormatDouble (a2003e.horizonPrincipalMeasure (dblPrincipalDiscount).variance(), 5, 2, 1.e-06) + " ||"
);
System.out.println (
"\t| Information Ratio ( X 10^+03) : " +
FormatUtil.FormatDouble (a2003e.informationRatio (dblPrincipalDiscount), 5, 2, 1.e+03) + " ||"
);
System.out.println (
"\t| Optimal Information Ratio ( X 10^+03) : " +
FormatUtil.FormatDouble (a2003e.optimalInformationRatio (dblPrincipalDiscount), 5, 2, 1.e+03) + " ||"
);
System.out.println (
"\t| Optimal Information Ratio Horizon : " +
FormatUtil.FormatDouble (a2003e.optimalInformationRatioHorizon (dblPrincipalDiscount), 5, 2, 1.) + " ||"
);
System.out.println ("\t|-----------------------------------------------------------------------||");
}
}