ConstantLiquidityVolatility.java
package org.drip.sample.almgren2003;
import org.drip.execution.dynamics.*;
import org.drip.execution.impact.ParticipationRateLinear;
import org.drip.execution.nonadaptive.ContinuousConstantTradingEnhanced;
import org.drip.execution.optimum.EfficientTradingTrajectoryContinuous;
import org.drip.execution.profiletime.UniformParticipationRateLinear;
import org.drip.function.definition.R1ToR1;
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>ConstantLiquidityVolatility</i> demonstrates the Dependence of the Optimal Trading Trajectory as a
* Function of Constant Trading Enhanced Volatilities. 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 ConstantLiquidityVolatility {
private static final void AlphaRun (
final double dblAlpha,
final double dblT,
final int iNumInterval)
throws Exception
{
double dblEta = 5.e-06;
double dblSigma = 1.;
double dblLambda = 1.e-05;
double dblX = 100000.;
ArithmeticPriceEvolutionParameters apep = ArithmeticPriceEvolutionParametersBuilder.TradingEnhancedVolatility (
dblSigma,
new UniformParticipationRateLinear (ParticipationRateLinear.SlopeOnly (dblEta)),
new UniformParticipationRateLinear (
new ParticipationRateLinear (
dblAlpha,
0.
)
)
);
ContinuousConstantTradingEnhanced ccte = ContinuousConstantTradingEnhanced.Standard (
dblX,
dblT,
apep,
dblLambda
);
EfficientTradingTrajectoryContinuous ettc = (EfficientTradingTrajectoryContinuous) ccte.generate();
R1ToR1 r1ToR1Holdings = ettc.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]);
}
String strDump = "\t|" + FormatUtil.FormatDouble (dblAlpha, 1, 1, 1.) + " =>";
for (int i = 0; i < adblExecutionTime.length; ++i)
strDump = strDump + FormatUtil.FormatDouble (adblHoldings[i] / dblX, 2, 1, 100.) + "% ";
strDump = strDump + FormatUtil.FormatDouble (ettc.transactionCostExpectation(), 5, 0, 1.) + " | ";
strDump = strDump + FormatUtil.FormatDouble (ettc.transactionCostVariance(), 5, 0, 1.e-06) + " | ";
strDump = strDump + FormatUtil.FormatDouble (ettc.characteristicTime(), 1, 3, 1.) + " ||";
System.out.println (strDump);
}
public static final void main (
final String[] astrArgs)
throws Exception
{
EnvManager.InitEnv (
"",
true
);
double dblT = 5.;
int iNumInterval = 10;
double[] adblAlpha = new double[] {
0.0,
0.1,
0.2,
0.3,
0.4,
0.5,
0.6,
0.7,
0.8,
0.9,
1.0,
1.1,
1.2,
1.3,
1.4,
1.5,
1.6,
1.7,
1.8,
1.9,
2.0
};
System.out.println();
System.out.println ("\t|--------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t| ALMGREN (2003) CONSTANT TEMPORARY IMPACT VOLATILITY - OFFSET DEPENDENCE ||");
System.out.println ("\t|--------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t| L -> R: ||");
System.out.println ("\t| Alpha Level ||");
System.out.println ("\t| Outstanding Trajectory (%) ||");
System.out.println ("\t| Transaction Cost Expectation ||");
System.out.println ("\t| Transaction Cost Variance (X 10^-06) ||");
System.out.println ("\t| Characteristic Time (Days) ||");
System.out.println ("\t|--------------------------------------------------------------------------------------------------------------||");
String strTimeNode = "\t| ";
for (int i = 0; i <= iNumInterval; ++i)
strTimeNode = strTimeNode + FormatUtil.FormatDouble (dblT * i / iNumInterval, 1, 2, 1.) + " ";
System.out.println (strTimeNode);
System.out.println ("\t|--------------------------------------------------------------------------------------------------------------||");
for (double dblAlpha : adblAlpha)
AlphaRun (
dblAlpha,
dblT,
iNumInterval
);
System.out.println ("\t|--------------------------------------------------------------------------------------------------------------||");
EnvManager.TerminateEnv();
}
}