ConstrainedLinearTemporaryImpact.java
package org.drip.execution.cost;
/*
* -*- 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>ConstrainedLinearTemporaryImpact</i> computes and holds the Optimal Trajectory under Trading Rate Sign
* Constraints using Linear Temporary Impact Function for the given set of Inputs. The References are:
*
* <br><br>
* <ul>
* <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>
* Almgren, R., and N. Chriss (2000): Optimal Execution of Portfolio Transactions <i>Journal of
* Risk</i> <b>3 (2)</b> 5-39
* </li>
* <li>
* Brunnermeier, L. K., and L. H. Pedersen (2005): Predatory Trading <i>Journal of Finance</i> <b>60
* (4)</b> 1825-1863
* </li>
* <li>
* Almgren, R., and J. Lorenz (2006): Bayesian Adaptive Trading with a Daily Cycle <i>Journal of
* Trading</i> <b>1 (4)</b> 38-46
* </li>
* <li>
* Kissell, R., and R. Malamut (2007): Algorithmic Decision Making Framework <i>Journal of
* Trading</i> <b>1 (1)</b> 12-21
* </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/cost/README.md">Linear Temporary Market Impact Cost</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class ConstrainedLinearTemporaryImpact extends org.drip.execution.cost.LinearTemporaryImpact {
private double _dblCriticalDrift = java.lang.Double.NaN;
private double _dblTradeStartTime = java.lang.Double.NaN;
private double _dblTradeFinishTime = java.lang.Double.NaN;
/**
* Generate a ConstrainedLinearTemporaryImpact Instance
*
* @param dblSpotTime Spot Time
* @param dblFinishTime Finish Time
* @param dblSpotHoldings Spot Holdings
* @param pcc The Prior/Conditional Combiner
* @param dblGrossPriceChange The Gross Price Change
* @param tflTemporary The Temporary Linear Impact Function
*
* @return The ConstrainedLinearTemporaryImpact Instance
*/
public static final ConstrainedLinearTemporaryImpact Standard (
final double dblSpotTime,
final double dblFinishTime,
final double dblSpotHoldings,
final org.drip.execution.bayesian.PriorConditionalCombiner pcc,
final double dblGrossPriceChange,
final org.drip.execution.impact.TransactionFunctionLinear tflTemporary)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblSpotTime) ||
!org.drip.numerical.common.NumberUtil.IsValid (dblFinishTime) ||
!org.drip.numerical.common.NumberUtil.IsValid (dblSpotHoldings) || null == pcc || null ==
tflTemporary)
return null;
final double dblLiquidityCoefficient = tflTemporary.slope();
org.drip.measure.gaussian.R1UnivariateNormal r1unPosterior = pcc.posteriorDriftDistribution
(dblGrossPriceChange);
if (null == r1unPosterior) return null;
final double dblDriftEstimate = r1unPosterior.mean();
double dblTradeStartTime = dblSpotTime;
double dblTradeFinishTime = dblFinishTime;
double dblHorizon = dblFinishTime - dblSpotTime;
double dblInstantaneousTradeRate = java.lang.Double.NaN;
double dblCriticalDrift = 4. * dblLiquidityCoefficient * dblSpotHoldings / (dblHorizon * dblHorizon);
if (dblDriftEstimate > dblCriticalDrift) {
dblTradeStartTime = dblSpotTime;
dblInstantaneousTradeRate = java.lang.Math.sqrt (dblDriftEstimate * dblSpotHoldings /
dblLiquidityCoefficient);
dblTradeFinishTime = dblSpotTime + java.lang.Math.sqrt (4. * dblLiquidityCoefficient *
dblSpotHoldings / dblDriftEstimate);
} else if (dblDriftEstimate < -1. * dblCriticalDrift) {
dblTradeFinishTime = dblFinishTime - java.lang.Math.sqrt (-4. * dblLiquidityCoefficient *
dblSpotHoldings / dblDriftEstimate);
dblInstantaneousTradeRate = 0.;
dblTradeFinishTime = dblFinishTime;
} else
dblInstantaneousTradeRate = dblSpotHoldings / dblHorizon + dblDriftEstimate * dblHorizon /
dblLiquidityCoefficient;
final double dblt = dblTradeStartTime;
final double dblT = dblTradeFinishTime;
org.drip.function.definition.R1ToR1 r1ToR1Holdings = new org.drip.function.definition.R1ToR1 (null) {
@Override public double evaluate (
final double dblTau)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblTau))
throw new java.lang.Exception
("ConstrainedLinearTemporaryImpact::Holdings::evaluate => Invalid Inputs");
if (dblTau <= dblt) return dblSpotHoldings;
if (dblTau >= dblT) return 0.;
return (dblT - dblTau) * (dblSpotHoldings / (dblT - dblt) - 0.25 * dblDriftEstimate * (dblTau
- dblt) / dblLiquidityCoefficient);
}
};
try {
return new ConstrainedLinearTemporaryImpact (dblSpotTime, dblFinishTime, dblSpotHoldings, pcc,
dblGrossPriceChange, tflTemporary, r1ToR1Holdings, dblInstantaneousTradeRate,
dblCriticalDrift, dblTradeStartTime, dblTradeFinishTime);
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
protected ConstrainedLinearTemporaryImpact (
final double dblSpotTime,
final double dblFinishTime,
final double dblSpotHoldings,
final org.drip.execution.bayesian.PriorConditionalCombiner pcc,
final double dblGrossPriceChange,
final org.drip.execution.impact.TransactionFunctionLinear tflTemporary,
final org.drip.function.definition.R1ToR1 r1ToR1Holdings,
final double dblInstantaneousTradeRate,
final double dblCriticalDrift,
final double dblTradeStartTime,
final double dblTradeFinishTime)
throws java.lang.Exception
{
super (dblSpotTime, dblFinishTime, dblSpotHoldings, pcc, dblGrossPriceChange, tflTemporary,
dblTradeFinishTime - dblTradeStartTime, r1ToR1Holdings, dblInstantaneousTradeRate);
if (!org.drip.numerical.common.NumberUtil.IsValid (_dblCriticalDrift = dblCriticalDrift) ||
!org.drip.numerical.common.NumberUtil.IsValid (_dblTradeStartTime = dblTradeStartTime) ||
!org.drip.numerical.common.NumberUtil.IsValid (_dblTradeFinishTime = dblTradeFinishTime))
throw new java.lang.Exception ("ConstrainedLinearTemporaryImpact Constructor => Invalid Inputs");
}
/**
* Retrieve the Critical Drift
*
* @return The Critical Drift
*/
public double criticalDrift()
{
return _dblCriticalDrift;
}
/**
* Retrieve the Trade Start Time
*
* @return The Trade Start Time
*/
public double tradeStartTime()
{
return _dblTradeStartTime;
}
/**
* Retrieve the Trade Finish Time
*
* @return The Trade Finish Time
*/
public double tradeFinishTime()
{
return _dblTradeFinishTime;
}
}