Package org.drip.execution.athl

Class PermanentImpactQuasiArbitrage

java.lang.Object

org.drip.function.definition.R1ToR1

org.drip.execution.impact.TransactionFunction

org.drip.execution.impact.TransactionFunctionPower

org.drip.execution.athl.PermanentImpactQuasiArbitrage

public class PermanentImpactQuasiArbitrage
extends TransactionFunctionPower

PermanentImpactQuasiArbitrage 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). It provides the following Functions:

• PermanentImpactQuasiArbitrage Constructor
• Retrieve the Liquidity Factor
• Retrieve the Asset Flow Parameters
• Regularize the Input Function using the specified Trade Inputs
• Modulate/Scale the Impact Output
• Retrieve the Constant Market Impact Parameter
• Retrieve the Power Law Exponent Market Impact Parameter
• Evaluate the Impact for the given Normalized Holdings
• Calculate the Ordered Derivative

The References are:

• Almgren, R., and N. Chriss (2000): Optimal Execution of Portfolio Transactions Journal of Risk 3 (2) 5-39
• Almgren, R. (2003): Optimal Execution with Nonlinear Impact Functions and Trading-Enhanced Risk Applied Mathematical Finance 10 (1) 1-18
• Almgren, R., and N. Chriss (2003): Bidding Principles Risk 97-102
• Almgren, R., C. Thum, E. Hauptmann, and H. Li (2005): Equity Market Impact Risk 18 (7) 57-62
• Huberman, G., and W. Stanzl (2004): Price Manipulation and Quasi-arbitrage Econometrics 72 (4) 1247-1275

Module	Computational Core Module
Library	Numerical Optimizer Library
Project	Optimal Impact/Capture Based Trading Trajectories - Deterministic, Stochastic, Static, and Dynamic
Package	Almgren-Thum-Hauptmann-Li Calibration

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
PermanentImpactQuasiArbitrage(AssetFlowSettings assetFlowSettings)	PermanentImpactQuasiArbitrage Constructor

Method Summary

Modifier and Type	Method	Description
AssetFlowSettings	assetFlowSettings()	Retrieve the Asset Flow Parameters
double	constant()	Retrieve the Constant Market Impact Parameter
double	derivative(double normalizedX, int order)	Calculate the Ordered Derivative
double	evaluate(double normalizedX)	Evaluate the Impact for the given Normalized Holdings
double	exponent()	Retrieve the Power Law Exponent Market Impact Parameter
double	liquidityFactor()	Retrieve the Liquidity Factor
double	modulate(double tradeInterval)	Modulate/Scale the Impact Output
double	regularize(double tradeInterval)	Regularize the Input Function using the specified Trade Inputs

Methods inherited from class org.drip.execution.impact.TransactionFunction

crossHoldingsDerivative, evaluate, leftHoldingsDerivative, rightHoldingsDerivative

Methods inherited from class org.drip.function.definition.R1ToR1

antiDerivative, conditionNumber, differential, differential, integrate, maxima, maxima, minima, minima, poleResidue

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

PermanentImpactQuasiArbitrage

public PermanentImpactQuasiArbitrage(AssetFlowSettings assetFlowSettings)
                              throws java.lang.Exception

PermanentImpactQuasiArbitrage Constructor

Parameters:

assetFlowSettings - Asset Flow Parameters

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Method Details

liquidityFactor

public double liquidityFactor()

Retrieve the Liquidity Factor

Returns:

The Liquidity Factor

assetFlowSettings

public AssetFlowSettings assetFlowSettings()

Retrieve the Asset Flow Parameters

Returns:

The Asset Flow Parameters

regularize

public double regularize(double tradeInterval)
                  throws java.lang.Exception

Regularize the Input Function using the specified Trade Inputs

Specified by:

regularize in class TransactionFunction

Parameters:

tradeInterval - The Trade Interval

Returns:

The Regularize Input

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

modulate

public double modulate(double tradeInterval)
                throws java.lang.Exception

Modulate/Scale the Impact Output

Specified by:

modulate in class TransactionFunction

Parameters:

tradeInterval - The Trade Interval

Returns:

The Modulated Output

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

constant

public double constant()

Retrieve the Constant Market Impact Parameter

Specified by:

constant in class TransactionFunctionPower

Returns:

The Constant Market Impact Parameter

exponent

public double exponent()

Retrieve the Power Law Exponent Market Impact Parameter

Specified by:

exponent in class TransactionFunctionPower

Returns:

The Power Law Exponent Market Impact Parameter

evaluate

public double evaluate(double normalizedX)
                throws java.lang.Exception

Evaluate the Impact for the given Normalized Holdings

Specified by:

evaluate in class R1ToR1

Parameters:

normalizedX - Normalized Holdings

Returns:

The calculated Impact

Throws:

java.lang.Exception - Thrown if evaluation cannot be done

derivative

public double derivative(double normalizedX,
int order)
                  throws java.lang.Exception

Calculate the Ordered Derivative

Overrides:

derivative in class R1ToR1

Parameters:

normalizedX - Normalized Holdings

order - Order of the derivative to be computed

Returns:

The Ordered Derivative

Throws:

java.lang.Exception - Thrown if Inputs are Invalid