LinearTemporaryImpact.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>LinearTemporaryImpact</i> computes and holds the Optimal Trajectory using the Linear Temporary Impact
* Function for the given set of Inputs. It provides a Default Unconstrained Trajectory Implementation. 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 LinearTemporaryImpact {
private double _dblSpotTime = java.lang.Double.NaN;
private double _dblFinishTime = java.lang.Double.NaN;
private double _dblSpotHoldings = java.lang.Double.NaN;
private double _dblGrossPriceChange = java.lang.Double.NaN;
private double _dblTransactionCostGain = java.lang.Double.NaN;
private double _dblStaticTransactionCost = java.lang.Double.NaN;
private double _dblInstantaneousTradeRate = java.lang.Double.NaN;
private org.drip.execution.bayesian.PriorConditionalCombiner _pcc = null;
private org.drip.execution.impact.TransactionFunctionLinear _tflTemporary = null;
private org.drip.execution.optimum.EfficientTradingTrajectoryContinuous _ectt = null;
/**
* Generate an Unconstrained LinearTemporaryImpact 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 Unconstrained LinearTemporaryImpact Instance
*/
public static final LinearTemporaryImpact Unconstrained (
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 dblHorizon = dblFinishTime - dblSpotTime;
org.drip.measure.gaussian.R1UnivariateNormal r1unPosterior = pcc.posteriorDriftDistribution
(dblGrossPriceChange);
if (null == r1unPosterior) return null;
final double dblScaledDrift = 0.25 * r1unPosterior.mean() / tflTemporary.slope();
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 (0. >= dblHorizon) return 0.;
if (!org.drip.numerical.common.NumberUtil.IsValid (dblTau))
throw new java.lang.Exception
("LinearTemporaryImpact::Holdings::evaluate => Invalid Inputs");
if (dblTau <= dblSpotTime) return dblSpotHoldings;
if (dblTau >= dblFinishTime) return 0.;
return (dblFinishTime - dblTau) * (dblSpotHoldings / (dblFinishTime - dblSpotTime) -
dblScaledDrift * (dblTau - dblSpotTime));
}
};
try {
return new LinearTemporaryImpact (dblSpotTime, dblFinishTime, dblSpotHoldings, pcc,
dblGrossPriceChange, tflTemporary, dblFinishTime - dblSpotTime, r1ToR1Holdings, 0 >=
dblHorizon ? 0. : dblSpotHoldings / dblHorizon + dblScaledDrift * dblHorizon);
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
protected LinearTemporaryImpact (
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 double dblCharacteristicTime,
final org.drip.function.definition.R1ToR1 r1ToR1Holdings,
final double dblInstantaneousTradeRate)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (_dblSpotTime = dblSpotTime) ||
!org.drip.numerical.common.NumberUtil.IsValid (_dblFinishTime = dblFinishTime) ||
!org.drip.numerical.common.NumberUtil.IsValid (_dblSpotHoldings = dblSpotHoldings) || null ==
(_pcc = pcc) || !org.drip.numerical.common.NumberUtil.IsValid (_dblGrossPriceChange =
dblGrossPriceChange) || null == (_tflTemporary = tflTemporary) || null ==
r1ToR1Holdings || !org.drip.numerical.common.NumberUtil.IsValid
(_dblInstantaneousTradeRate = dblInstantaneousTradeRate))
throw new java.lang.Exception ("LinearTemporaryImpact Constructor => Invalid Inputs");
final double dblLiquidityCoefficient = _tflTemporary.slope();
double dblDriftEstimate = _pcc.posteriorDriftDistribution (_dblGrossPriceChange).mean();
final double dblExecutionTime = _dblFinishTime - _dblSpotTime;
_dblStaticTransactionCost = _dblSpotHoldings * _dblSpotHoldings * dblLiquidityCoefficient /
dblExecutionTime + 0.5 * _dblSpotHoldings * dblDriftEstimate * dblExecutionTime -
dblExecutionTime * dblExecutionTime * dblExecutionTime * dblDriftEstimate * dblDriftEstimate
/ (48. * dblLiquidityCoefficient);
double dblDriftConfidence = _pcc.prior().confidence();
final double dblPriceVolatility = _pcc.conditional().priceVolatility();
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;
}
};
final double dblRho = dblPriceVolatility * dblPriceVolatility / (dblDriftConfidence *
dblDriftConfidence * dblExecutionTime);
org.drip.function.definition.R1ToR1 r1ToR1Quadrature = new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double dblDelta)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblDelta))
throw new java.lang.Exception
("LinearTemporaryImpact::r1ToR1Quadrature::evaluate => Invalid Inputs");
double dblRemainingTime = 1. - dblDelta;
double dblDimensionlessTime = dblDelta + dblRho;
return dblRemainingTime * dblRemainingTime * dblRemainingTime / (dblDimensionlessTime *
dblDimensionlessTime);
}
};
_dblTransactionCostGain = dblPriceVolatility * dblPriceVolatility * dblExecutionTime *
dblExecutionTime / (48. * linearTemporaryImpact().slope()) * r1ToR1Quadrature.integrate (0., 1.);
org.drip.function.definition.R1ToR1 r1ToR1TradeRate = new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double dblS)
throws java.lang.Exception
{
return r1ToR1Holdings.derivative (dblS, 1);
}
};
final org.drip.function.definition.R1ToR1 r1ToR1TransactionCostExpectationRate = new
org.drip.function.definition.R1ToR1 (null) {
@Override public double evaluate (
final double dblTime)
throws java.lang.Exception
{
double dblTradeRate = r1ToR1Holdings.derivative (dblTime, 1);
return dblLiquidityCoefficient * dblLiquidityCoefficient * 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 r1ToR1TransactionCostExpectationRate.integrate (dblTime, dblExecutionTime);
}
};
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 dblPriceVolatility * dblPriceVolatility * 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, dblExecutionTime);
}
};
_ectt = new org.drip.execution.optimum.EfficientTradingTrajectoryContinuous (dblExecutionTime,
_dblStaticTransactionCost + _dblTransactionCostGain, dblPriceVolatility * dblPriceVolatility *
r1ToR1HoldingsSquared.integrate (_dblSpotTime, _dblFinishTime), dblCharacteristicTime,
dblLiquidityCoefficient * _dblSpotHoldings / (dblExecutionTime * dblLiquidityCoefficient
* java.lang.Math.sqrt (dblExecutionTime)), r1ToR1Holdings, r1ToR1TradeRate,
r1ToR1TransactionCostExpectation, r1ToR1TransactionCostVariance);
}
/**
* Retrieve the Spot Time
*
* @return The Spot Time
*/
public double spotTime()
{
return _dblSpotTime;
}
/**
* Retrieve the Finish Time
*
* @return The Finish Time
*/
public double finishTime()
{
return _dblFinishTime;
}
/**
* Retrieve the Spot Holdings
*
* @return The Spot Holdings
*/
public double spotHoldings()
{
return _dblSpotHoldings;
}
/**
* Retrieve the Prior/Conditional Distributions Combiner
*
* @return The Prior/Conditional Distributions Combiner
*/
public org.drip.execution.bayesian.PriorConditionalCombiner combiner()
{
return _pcc;
}
/**
* Retrieve the Gross Price Change
*
* @return The Gross Price Change
*/
public double grossPriceChange()
{
return _dblGrossPriceChange;
}
/**
* Retrieve the Drift Expectation Estimate
*
* @return The Drift Expectation Estimate
*/
public double driftExpectationEstimate()
{
return _pcc.posteriorDriftDistribution (_dblGrossPriceChange).mean();
}
/**
* Retrieve the Drift Volatility Estimate
*
* @return The Drift Volatility Estimate
*/
public double driftVolatilityEstimate()
{
return java.lang.Math.sqrt (_pcc.posteriorDriftDistribution (_dblGrossPriceChange).variance());
}
/**
* Retrieve the Linear Temporary Market Impact Function
*
* @return The Linear Temporary Market Impact Function
*/
public org.drip.execution.impact.TransactionFunctionLinear linearTemporaryImpact()
{
return _tflTemporary;
}
/**
* Retrieve the Holdings Trajectory
*
* @return The Holdings Trajectory
*/
public org.drip.execution.optimum.EfficientTradingTrajectoryContinuous trajectory()
{
return _ectt;
}
/**
* Retrieve the Instantaneous Trade Rate
*
* @return The Instantaneous Trade Rate
*/
public double instantaneousTradeRate()
{
return _dblInstantaneousTradeRate;
}
/**
* Estimate of the Static Transaction Cost
*
* @return The Static Transaction Cost Estimate
*/
public double staticTransactionCost()
{
return _dblStaticTransactionCost;
}
/**
* Estimate the Transaction Cost Gain available from the Bayesian Drift
*
* @return The Transaction Cost Gain available from the Bayesian Drift
*/
public double transactionCostGain()
{
return _dblTransactionCostGain;
}
}