ContinuousLowUrgencyAsymptote.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>ContinuousLowUrgencyAsymptote</i> contains the Low Urgency Asymptote of the Static Continuous 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): <i>Optimal Trading: Dynamic Stock Liquidation Strategies</i> Princeton
University
* </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 ContinuousLowUrgencyAsymptote extends
org.drip.execution.nonadaptive.StaticOptimalSchemeContinuous {
/**
* Create the Standard ContinuousLowUrgencyAsymptote Instance
*
* @param dblStartHoldings Trajectory Start Holdings
* @param dblFinishTime Trajectory Finish Time
* @param lpep The Linear Impact Expectation Parameters
* @param dblRiskAversion The Risk Aversion Parameter
*
* @return The ContinuousLowUrgencyAsymptote Instance
*/
public static final ContinuousLowUrgencyAsymptote Standard (
final double dblStartHoldings,
final double dblFinishTime,
final org.drip.execution.dynamics.LinearPermanentExpectationParameters lpep,
final double dblRiskAversion)
{
try {
return new ContinuousLowUrgencyAsymptote (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 ContinuousLowUrgencyAsymptote (
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();
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;
}
final double dblSigma = dblEpochVolatility;
final double dblEta = tflTemporaryExpectation.slope();
final double dblLambda = ((org.drip.execution.risk.MeanVarianceObjectiveUtility)
objectiveUtility()).riskAversion();
final double dblKappa = java.lang.Math.sqrt (dblLambda * dblSigma * dblSigma / dblEta);
org.drip.execution.strategy.OrderSpecification os = orderSpecification();
final double dblT = os.maxExecutionTime();
final double dblX = os.size();
final org.drip.function.definition.R1ToR1 r1ToR1Holdings = new org.drip.function.definition.R1ToR1
(null) {
@Override public double evaluate (
final double dblTime)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblTime))
throw new java.lang.Exception
("ContinuousLowUrgencyAsymptote::Holdings::evaluate => Invalid Inputs");
return java.lang.Math.sinh (dblKappa * (dblT - dblTime)) / java.lang.Math.sinh (dblKappa *
dblT) * dblX;
}
};
org.drip.function.definition.R1ToR1 r1ToR1TradeRate = new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double dblTime)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblTime))
throw new java.lang.Exception
("ContinuousLowUrgencyAsymptote::TradeRate::evaluate => Invalid Inputs");
return dblT == dblTime ? 0. : r1ToR1Holdings.evaluate (dblTime) / (dblT - dblTime);
}
};
org.drip.function.definition.R1ToR1 r1ToR1TransactionCostExpectation = new
org.drip.function.definition.R1ToR1 (null) {
@Override public double evaluate (
final double dblTime)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblTime))
throw new java.lang.Exception
("ContinuousLowUrgencyAsymptote::TransactionCostExpectation::evaluate => Invalid Inputs");
double dblRemainingTime = dblT - dblTime;
if (0. >= dblRemainingTime) return 0.;
double dblHoldings = r1ToR1Holdings.evaluate (dblTime);
return dblEta * dblHoldings * dblHoldings / dblRemainingTime + (dblLambda * dblSigma *
dblSigma * dblHoldings * dblHoldings * dblRemainingTime / 3.);
}
};
final org.drip.function.definition.R1ToR1 r1ToR1TransactionCostVarianceRate = new
org.drip.function.definition.R1ToR1 (null) {
@Override public double evaluate (
final double dblTime)
throws java.lang.Exception
{
double dblHoldings = r1ToR1Holdings.evaluate (dblTime);
return dblSigma * dblSigma * 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 r1ToR1TransactionCostVarianceRate.integrate (dblTime, dblT);
}
};
try {
return new org.drip.execution.optimum.EfficientTradingTrajectoryContinuous (dblT, dblEta *
dblKappa * dblX * dblX / java.lang.Math.tanh (dblKappa * dblT),
r1ToR1TransactionCostExpectation.evaluate (0.), 1. / dblKappa, dblEta * dblX / (dblT *
dblEpochVolatility * java.lang.Math.sqrt (dblT)), r1ToR1Holdings, r1ToR1TradeRate,
r1ToR1TransactionCostExpectation, r1ToR1TransactionCostVariance);
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
}