PermanentImpactQuasiArbitrage.java
package org.drip.execution.athl;
/*
* -*- 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>PermanentImpactQuasiArbitrage</i> implements the Linear Permanent Market Impact with Coefficients that
* have been determined empirically by Almgren, Thum, Hauptmann, and Li (2005), independent of the no Quasi-
* Arbitrage Criterion identified by Huberman and Stanzl (2004). The References are:
*
* <br><br>
* <ul>
* <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>
* <li>
* Huberman, G., and W. Stanzl (2004): Price Manipulation and Quasi-arbitrage <i>Econometrics</i>
* <b>72 (4)</b> 1247-1275
* </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/athl/README.md">Almgren-Thum-Hauptmann-Li Calibration</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class PermanentImpactQuasiArbitrage extends org.drip.execution.impact.TransactionFunctionPower {
private double _dblLiquidityFactor = java.lang.Double.NaN;
private org.drip.execution.parameters.AssetFlowSettings _afp = null;
/**
* PermanentImpactQuasiArbitrage Constructor
*
* @param afp The Asset Flow Parameters
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public PermanentImpactQuasiArbitrage (
final org.drip.execution.parameters.AssetFlowSettings afp)
throws java.lang.Exception
{
if (null == (_afp = afp))
throw new java.lang.Exception ("PermanentImpactQuasiArbitrage Constructor => Invalid Inputs");
_dblLiquidityFactor = java.lang.Math.pow (afp.inverseTurnover(),
org.drip.execution.athl.CalibrationEmpirics.PERMANENT_IMPACT_INVERSE_TURNOVER_EXPONENT);
}
/**
* Retrieve the Liquidity Factor
*
* @return The Liquidity Factor
*/
public double liquidityFactor()
{
return _dblLiquidityFactor;
}
/**
* Retrieve the Asset Flow Parameters
*
* @return The Asset Flow Parameters
*/
public org.drip.execution.parameters.AssetFlowSettings assetFlowParameters()
{
return _afp;
}
@Override public double regularize (
final double dblTradeInterval)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblTradeInterval) || 0 >= dblTradeInterval)
throw new java.lang.Exception ("PermanentImpactQuasiArbitrage::regularize => Invalid Inputs");
return 1. / (_afp.averageDailyVolume() * dblTradeInterval);
}
@Override public double modulate (
final double dblTradeInterval)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblTradeInterval) || 0 >= dblTradeInterval)
throw new java.lang.Exception ("PermanentImpactQuasiArbitrage::modulate => Invalid Inputs");
return dblTradeInterval * _afp.dailyVolatility();
}
@Override public double constant()
{
return org.drip.execution.athl.CalibrationEmpirics.PERMANENT_IMPACT_COEFFICIENT *
_dblLiquidityFactor;
}
@Override public double exponent()
{
return org.drip.execution.athl.CalibrationEmpirics.PERMANENT_IMPACT_EXPONENT_ATHL2005;
}
@Override public double evaluate (
final double dblNormalizedX)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblNormalizedX))
throw new java.lang.Exception ("PermanentImpactQuasiArbitrage::evaluate => Invalid Inputs");
double dblAlpha = org.drip.execution.athl.CalibrationEmpirics.PERMANENT_IMPACT_EXPONENT_ATHL2005;
double dblGamma = org.drip.execution.athl.CalibrationEmpirics.PERMANENT_IMPACT_COEFFICIENT;
return 0.5 * dblGamma * (dblNormalizedX < 0. ? -1. : 1.) * java.lang.Math.pow (java.lang.Math.abs
(dblNormalizedX), dblAlpha) * _dblLiquidityFactor;
}
@Override public double derivative (
final double dblNormalizedX,
final int iOrder)
throws java.lang.Exception
{
if (0 >= iOrder || !org.drip.numerical.common.NumberUtil.IsValid (dblNormalizedX))
throw new java.lang.Exception ("PermanentImpactQuasiArbitrage::derivative => Invalid Inputs");
double dblCoefficient = 1.;
double dblAlpha = org.drip.execution.athl.CalibrationEmpirics.PERMANENT_IMPACT_EXPONENT_ATHL2005;
double dblGamma = org.drip.execution.athl.CalibrationEmpirics.PERMANENT_IMPACT_COEFFICIENT;
for (int i = 0; i < iOrder; ++i)
dblCoefficient = dblCoefficient * (dblAlpha - i);
return 0.5 * dblGamma * (dblNormalizedX < 0. ? -1. : 1.) * dblCoefficient * java.lang.Math.pow
(java.lang.Math.abs (dblNormalizedX), dblAlpha - iOrder) * _dblLiquidityFactor;
}
}