ContinuousPowerImpact.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>ContinuousPowerImpact</i> contains the Temporary Impact Power Law Trading Trajectory generated by the
* Almgren and Chriss (2003) Scheme under the Criterion of No-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. 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. (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/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 ContinuousPowerImpact extends org.drip.execution.nonadaptive.StaticOptimalSchemeContinuous {
/**
* Create the Standard ContinuousPowerImpact Instance
*
* @param dblStartHoldings Trajectory Start Holdings
* @param dblFinishTime Trajectory Finish Time
* @param lpep Almgren 2003 Linear Permanent Expectation Market Impact Parameters
* @param dblRiskAversion The Risk Aversion Parameter
*
* @return The ContinuousPowerImpact Instance
*/
public static final ContinuousPowerImpact Standard (
final double dblStartHoldings,
final double dblFinishTime,
final org.drip.execution.dynamics.LinearPermanentExpectationParameters lpep,
final double dblRiskAversion)
{
try {
return new ContinuousPowerImpact (new org.drip.execution.strategy.OrderSpecification
(dblStartHoldings, dblFinishTime), lpep, new
org.drip.execution.risk.MeanVarianceObjectiveUtility (dblRiskAversion));
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
private ContinuousPowerImpact (
final org.drip.execution.strategy.OrderSpecification os,
final org.drip.execution.dynamics.LinearPermanentExpectationParameters lpep,
final org.drip.execution.risk.MeanVarianceObjectiveUtility mvou)
throws java.lang.Exception
{
super (os, lpep, mvou);
}
@Override public org.drip.execution.optimum.EfficientTradingTrajectory generate()
{
org.drip.execution.dynamics.LinearPermanentExpectationParameters lpep =
(org.drip.execution.dynamics.LinearPermanentExpectationParameters) priceEvolutionParameters();
final org.drip.execution.impact.TransactionFunction tfTemporaryExpectation =
lpep.temporaryExpectation().epochImpactFunction();
if (!(tfTemporaryExpectation instanceof org.drip.execution.impact.TransactionFunctionPower))
return null;
double dblEpochVolatility = java.lang.Double.NaN;
final org.drip.execution.impact.TransactionFunctionPower tfpTemporaryExpectation =
(org.drip.execution.impact.TransactionFunctionPower) tfTemporaryExpectation;
double dblLambda = ((org.drip.execution.risk.MeanVarianceObjectiveUtility)
objectiveUtility()).riskAversion();
try {
dblEpochVolatility = lpep.arithmeticPriceDynamicsSettings().epochVolatility();
} catch (java.lang.Exception e) {
e.printStackTrace();
return null;
}
final double dblSigma = dblEpochVolatility;
org.drip.execution.strategy.OrderSpecification os = orderSpecification();
double dblGamma = ((org.drip.execution.impact.TransactionFunctionLinear)
lpep.linearPermanentExpectation().epochImpactFunction()).slope();
final double dblK = tfpTemporaryExpectation.exponent();
final double dblExecutionTime = os.maxExecutionTime();
double dblEta = tfpTemporaryExpectation.constant();
final double dblX = os.size();
final double dblTStar = java.lang.Math.pow (dblK * dblEta * java.lang.Math.pow (dblX, dblK - 1.) /
(dblLambda * dblSigma * dblSigma), 1. / (dblK + 1.));
double dblTMax = dblK > 1. ? (dblK + 1.) / (dblK - 1.) * dblTStar : java.lang.Double.NaN;
double dblE = 0.5 * dblGamma * dblX * dblX + (dblK + 1.) / (3. * dblK + 1.) * dblEta *
java.lang.Math.pow (dblX / dblTStar, dblK + 1.) * dblTStar;
double dblV = (dblK + 1.) / (3. * dblK + 1.) * dblSigma * dblSigma * dblTStar * dblX * dblX;
double dblHyperboloidBoundaryValue = java.lang.Math.pow ((dblK + 1.) / (3. * dblK + 1.), dblK + 1.) *
dblEta * java.lang.Math.pow (dblSigma, 2. * dblK) * java.lang.Math.pow (dblX, 3. * dblK + 1.);
final org.drip.function.definition.R1ToR1 r1ToR1Holdings = new org.drip.function.definition.R1ToR1
(null) {
@Override public double evaluate (
final double dblT)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblT))
throw new java.lang.Exception
("ContinuousPowerImpact::generate::evaluate => Invalid Inputs");
if (1. > dblK)
return dblX * java.lang.Math.pow (1. + ((1. - dblK) * dblT) / ((1. + dblK) * dblTStar),
-1. * (1. + dblK) / (1. - dblK));
if (1. == dblK) return dblX * java.lang.Math.pow (java.lang.Math.E, -1. * dblT/ dblTStar);
double dblHoldings = dblX * java.lang.Math.pow (1. - ((dblK - 1.) * dblT) / ((dblK + 1.) *
dblTStar), (dblK + 1.) / (dblK + 1.));
return 0. > dblX * dblHoldings ? 0. : dblHoldings;
}
};
final org.drip.function.definition.R1ToR1 r1ToR1TradeRateSquared = new
org.drip.function.definition.R1ToR1 (null) {
@Override public double evaluate (
final double dblTime)
throws java.lang.Exception
{
double dblTradeRate = r1ToR1Holdings.derivative (dblTime, 1);
double dblTemporaryImpactCoefficient = tfpTemporaryExpectation.evaluate (dblTradeRate);
return dblTemporaryImpactCoefficient * dblTemporaryImpactCoefficient * dblTradeRate *
dblTradeRate;
}
};
org.drip.function.definition.R1ToR1 r1ToR1TransactionCostExpectation = new
org.drip.function.definition.R1ToR1 (null) {
@Override public double evaluate (
final double dblTime)
throws java.lang.Exception
{
return r1ToR1TradeRateSquared.integrate (dblTime, dblExecutionTime);
}
};
final org.drip.function.definition.R1ToR1 r1ToR1HoldingsSquared = new
org.drip.function.definition.R1ToR1 (null) {
@Override public double evaluate (
final double dblTime)
throws java.lang.Exception
{
double dblHoldings = r1ToR1Holdings.evaluate (dblTime);
return dblHoldings * dblHoldings;
}
};
org.drip.function.definition.R1ToR1 r1ToR1TransactionCostVariance = new
org.drip.function.definition.R1ToR1 (null) {
@Override public double evaluate (
final double dblTime)
throws java.lang.Exception
{
return dblSigma * dblSigma * r1ToR1HoldingsSquared.integrate (dblTime, dblExecutionTime);
}
};
return org.drip.execution.optimum.PowerImpactContinuous.Standard (dblExecutionTime, dblE,
dblV, dblTStar, dblTMax, dblHyperboloidBoundaryValue, dblEta * (dblX / dblExecutionTime) /
(dblEpochVolatility * java.lang.Math.sqrt (dblExecutionTime)), r1ToR1Holdings,
r1ToR1TransactionCostExpectation, r1ToR1TransactionCostVariance);
}
}