DiscreteAlmgrenChriss.java
package org.drip.execution.nonadaptive;
/*
* -*- 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>DiscreteAlmgrenChriss</i> generates the Trade/Holdings List of Optimal Execution Schedule for the
* Equally Spaced Trading Intervals based on the No-Drift Linear Impact Evolution Walk Parameters specified.
* 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/execution/README.md">Optimal Impact/Capture Based Trading Trajectories - Deterministic, Stochastic, Static, and Dynamic</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/execution/nonadaptive/README.md">Almgren-Chriss Static Optimal Trajectory</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class DiscreteAlmgrenChriss extends org.drip.execution.nonadaptive.StaticOptimalSchemeDiscrete {
private double KappaTau (
final double dblKappaTildaSquared,
final double dblTau)
{
double dblKappaTildaSquaredTauSquared = dblKappaTildaSquared * dblTau * dblTau;
return java.lang.Math.log (0.5 * (2. + dblKappaTildaSquaredTauSquared + dblTau * java.lang.Math.sqrt
(dblKappaTildaSquared * (dblKappaTildaSquaredTauSquared + 4.))));
}
/**
* Create the Standard DiscreteAlmgrenChriss Instance
*
* @param dblStartHoldings Trajectory Start Holdings
* @param dblFinishTime Trajectory Finish Time
* @param iNumInterval The Number of Fixed Intervals
* @param lpep Linear Impact Price Walk Parameters
* @param dblRiskAversion The Risk Aversion Parameter
*
* @return The DiscreteAlmgrenChriss Instance
*/
public static final DiscreteAlmgrenChriss Standard (
final double dblStartHoldings,
final double dblFinishTime,
final int iNumInterval,
final org.drip.execution.dynamics.LinearPermanentExpectationParameters lpep,
final double dblRiskAversion)
{
try {
return new DiscreteAlmgrenChriss
(org.drip.execution.strategy.DiscreteTradingTrajectoryControl.FixedInterval (new
org.drip.execution.strategy.OrderSpecification (dblStartHoldings, dblFinishTime),
iNumInterval), lpep, new org.drip.execution.risk.MeanVarianceObjectiveUtility
(dblRiskAversion));
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
private DiscreteAlmgrenChriss (
final org.drip.execution.strategy.DiscreteTradingTrajectoryControl dttc,
final org.drip.execution.dynamics.LinearPermanentExpectationParameters lpep,
final org.drip.execution.risk.MeanVarianceObjectiveUtility mvou)
throws java.lang.Exception
{
super (dttc, lpep, mvou);
}
@Override public org.drip.execution.optimum.EfficientTradingTrajectoryDiscrete generate()
{
org.drip.execution.strategy.DiscreteTradingTrajectoryControl dttc = control();
double[] adblTNode = dttc.executionTimeNodes();
org.drip.execution.dynamics.LinearPermanentExpectationParameters lpep =
(org.drip.execution.dynamics.LinearPermanentExpectationParameters) priceEvolutionParameters();
org.drip.execution.impact.TransactionFunction tfTemporaryExpectation =
lpep.temporaryExpectation().epochImpactFunction();
if (!(tfTemporaryExpectation instanceof org.drip.execution.impact.TransactionFunctionLinear))
return null;
double dblEpochVolatility = java.lang.Double.NaN;
org.drip.execution.impact.TransactionFunctionLinear tflTemporaryExpectation =
(org.drip.execution.impact.TransactionFunctionLinear) tfTemporaryExpectation;
try {
dblEpochVolatility = lpep.arithmeticPriceDynamicsSettings().epochVolatility();
} catch (java.lang.Exception e) {
e.printStackTrace();
return null;
}
double dblGamma = lpep.linearPermanentExpectation().epochLiquidityFunction().slope();
double dblEta = tflTemporaryExpectation.slope();
double dblX = dttc.startHoldings();
int iNumNode = adblTNode.length;
double dblXSquared = dblX * dblX;
final double dblSigma = dblEpochVolatility;
double dblTau = adblTNode[1] - adblTNode[0];
double dblSigmaSquared = dblSigma * dblSigma;
double[] adblHoldings = new double[iNumNode];
double[] adblTradeList = new double[iNumNode - 1];
double dblT = adblTNode[iNumNode - 1] - adblTNode[0];
double dblEtaTilda = dblEta - 0.5 * dblGamma * dblTau;
double dblKappaTildaSquared = ((org.drip.execution.risk.MeanVarianceObjectiveUtility)
objectiveUtility()).riskAversion() * dblSigmaSquared / dblEtaTilda;
double dblKappaTau = KappaTau (dblKappaTildaSquared, dblTau);
double dblHalfKappaTau = 0.5 * dblKappaTau;
double dblKappa = dblKappaTau / dblTau;
double dblKappaT = dblKappa * dblT;
double dblSinhKappaT = java.lang.Math.sinh (dblKappaT);
double dblSinhKappaTau = java.lang.Math.sinh (dblKappaTau);
double dblSinhHalfKappaTau = java.lang.Math.sinh (dblHalfKappaTau);
double dblTSinhKappaTau = dblT * dblSinhKappaTau;
double dblInverseSinhKappaT = 1. / dblSinhKappaT;
double dblTrajectoryScaler = dblInverseSinhKappaT * dblX;
double dblTradeListScaler = 2. * dblSinhHalfKappaTau * dblTrajectoryScaler;
double dblReciprocalSinhKappaTSquared = dblInverseSinhKappaT * dblInverseSinhKappaT;
for (int i = 0; i < iNumNode; ++i) {
adblHoldings[i] = dblTrajectoryScaler * java.lang.Math.sinh (dblKappa * (dblT - adblTNode[i]));
if (i < iNumNode - 1)
adblTradeList[i] = -1. * dblTradeListScaler * java.lang.Math.cosh (dblKappa * (dblT - dblTau
* (0.5 + i)));
}
try {
return new org.drip.execution.optimum.AlmgrenChrissDiscrete (adblTNode, adblHoldings,
adblTradeList, java.lang.Math.sqrt (dblKappaTildaSquared), dblKappa, 0.5 * dblGamma *
dblXSquared + tflTemporaryExpectation.offset() * dblX + dblEtaTilda * dblXSquared *
dblReciprocalSinhKappaTSquared * java.lang.Math.tanh (dblHalfKappaTau) * (dblTau *
java.lang.Math.sinh (2. * dblKappaT) + 2. * dblTSinhKappaTau) / (2. * dblTau *
dblTau), 0.5 * dblSigmaSquared * dblXSquared * dblReciprocalSinhKappaTSquared
* (dblTau * dblSinhKappaT * java.lang.Math.cosh (dblKappa * (dblT -
dblTau)) - dblTSinhKappaTau) / dblSinhKappaTau, dblEpochVolatility *
dblX / (dblT * dblEpochVolatility * java.lang.Math.sqrt (dblT)));
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
}