Almgren2003Estimator.java
package org.drip.execution.principal;
/*
* -*- 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>Almgren2003Estimator</i> generates the Gross Profit Distribution and the Information Ratio for a given
* Level of Principal Discount for an Optimal Trajectory that is generated using the Almgren (2003) Scheme.
* 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>
* Almgren, R., C. Thum, E. Hauptmann, and H. Li (2005): Equity Market Impact <i>Risk</i> <b>18 (7)</b>
* 57-62
* </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/principal/README.md">Information Ratio Based Principal Trades</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class Almgren2003Estimator extends org.drip.execution.principal.GrossProfitEstimator {
private org.drip.execution.dynamics.LinearPermanentExpectationParameters _lpep = null;
/**
* Almgren2003Estimator Constructor
*
* @param pic The Power Continuous Market Impact Trajectory
* @param lpep The Linear Permanent Expectation Paremeter
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public Almgren2003Estimator (
final org.drip.execution.optimum.PowerImpactContinuous pic,
final org.drip.execution.dynamics.LinearPermanentExpectationParameters lpep)
throws java.lang.Exception
{
super (pic);
if (null == (_lpep = lpep))
throw new java.lang.Exception ("Almgren2003Estimator Constructor => Invalid Inputs");
}
/**
* Generate the Horizon that results in the Optimal Information Ratio
*
* @param dblD The Principal Discount "D"
*
* @return The Horizon that results in the Optimal Information Ratio
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public double optimalInformationRatioHorizon (
final double dblD)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblD))
throw new java.lang.Exception
("Almgren2003Estimator::optimalInformationRatioHorizon => Invalid Inputs");
org.drip.execution.impact.TransactionFunctionPower tfpTemporaryExpectation =
(org.drip.execution.impact.TransactionFunctionPower)
_lpep.temporaryExpectation().epochImpactFunction();
double dblGamma = ((org.drip.execution.impact.TransactionFunctionLinear)
_lpep.linearPermanentExpectation().epochImpactFunction()).slope();
double dblEta = tfpTemporaryExpectation.constant();
double dblK = tfpTemporaryExpectation.exponent();
double dblX = efficientTrajectory().tradeSize();
return dblX * java.lang.Math.pow (dblEta * (dblK + 1.) * (dblK + 1.) / (3. * dblK + 1.) / (dblD - 0.5
* dblGamma * dblX), 1. / dblK);
}
/**
* Compute the Optimal Information Ratio
*
* @param dblD The Principal Discount "D"
*
* @return The Optimal Information Ratio
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public double optimalInformationRatio (
final double dblD)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblD))
throw new java.lang.Exception
("Almgren2003Estimator::optimalInformationRatio => Invalid Inputs");
org.drip.execution.impact.TransactionFunctionPower tfpTemporaryExpectation =
(org.drip.execution.impact.TransactionFunctionPower)
_lpep.temporaryExpectation().epochImpactFunction();
double dblSigma = _lpep.arithmeticPriceDynamicsSettings().epochVolatility();
double dblGamma = ((org.drip.execution.impact.TransactionFunctionLinear)
_lpep.linearPermanentExpectation().epochImpactFunction()).slope();
double dblEta = tfpTemporaryExpectation.constant();
double dblK = tfpTemporaryExpectation.exponent();
double dblX = efficientTrajectory().tradeSize();
return java.lang.Math.pow (3. * dblK + 1. , (1. * dblK + 2.) / (2. * dblK)) /
java.lang.Math.pow (1. * dblK + 1. , (3. * dblK + 4.) / (2. * dblK)) *
java.lang.Math.pow (dblD - 0.5 * dblGamma * dblX, (1. * dblK + 1.) / (1. * dblK)) /
java.lang.Math.pow (dblEta , (0. * dblK + 1.) / (1. * dblK)) /
(dblX * dblSigma);
}
/**
* Compute the Principal Discount Hurdle given the Information Ratio
*
* @param dblI The Optimal Information Ratio "I"
*
* @return The Principal Discount Hurdle
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public double principalDiscountHurdle (
final double dblI)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblI))
throw new java.lang.Exception
("Almgren2003Estimator::principalDiscountHurdle => Invalid Inputs");
org.drip.execution.impact.TransactionFunctionPower tfpTemporaryExpectation =
(org.drip.execution.impact.TransactionFunctionPower)
_lpep.temporaryExpectation().epochImpactFunction();
double dblEta = tfpTemporaryExpectation.constant();
double dblGamma = ((org.drip.execution.impact.TransactionFunctionLinear)
_lpep.linearPermanentExpectation().epochImpactFunction()).slope();
double dblSigma = _lpep.arithmeticPriceDynamicsSettings().epochVolatility();
double dblK = tfpTemporaryExpectation.exponent();
double dblX = efficientTrajectory().tradeSize();
return java.lang.Math.pow (
0.5 * dblGamma * dblX +
java.lang.Math.pow (1. * dblK + 1. , (3. * dblK + 4.) / (2. * dblK)) /
java.lang.Math.pow (3. * dblK + 1. , (1. * dblK + 2.) / (2. * dblK)) *
java.lang.Math.pow (dblEta , (0. * dblK + 1.) / (1. * dblK)) *
(dblX * dblSigma * dblI),
dblK / (dblK + 1.)
);
}
/**
* Generate the Constant/Exponent Dependencies on the Market Parameters for the Optimal Execution Horizon
* / Information Ratio
*
* @return The Optimal Execution Horizon/Information Ratio Dependency
*/
public org.drip.execution.principal.HorizonInformationRatioDependence optimalMeasures()
{
org.drip.execution.impact.TransactionFunctionPower tfpTemporaryExpectation =
(org.drip.execution.impact.TransactionFunctionPower)
_lpep.temporaryExpectation().epochImpactFunction();
double dblK = tfpTemporaryExpectation.exponent();
try {
return new org.drip.execution.principal.HorizonInformationRatioDependence (
new org.drip.execution.principal.OptimalMeasureDependence (
java.lang.Math.pow ((dblK + 1.) * (dblK + 1.) / (3. * dblK + 1.), 1. / dblK),
1. / dblK,
1.,
0.,
-1. / dblK
),
new org.drip.execution.principal.OptimalMeasureDependence (
java.lang.Math.pow (3. * dblK + 1., (1. * dblK + 2.) / (2. * dblK)) /
java.lang.Math.pow (1. * dblK + 1., (3. * dblK + 4.) / (2. * dblK)),
-1. / dblK,
-1.,
-1.,
(dblK + 1.) / dblK
)
);
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
}