Abstract

http://ssrn.com/abstract=2185452
 
 

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Optimal Limit Order Execution in a Simple Model for Market Microstructure Dynamics


Yuri Burlakov


Chicago Trading Company, LLC

Michael Kamal


Chicago Trading Company, LLC

Michele Salvadore


Banca IMI; Chicago Trading Company, LLC

October 24, 2012


Abstract:     
Market participants that have a task to acquire a certain position in a listed security at a predetermined price on behalf of a third party with no time urgency, i.e. to fill a perpetual limit order, can optimize the profitability of their trading strategy in order to accomplish this task. We study the statistical properties of the profit distribution of a particular market-making strategy: one which increments the inventory as the underlying price approaches the limit order price S0 and locks in profits by gradually liquidating the inventory as the market drifts away from S0. We do so by adopting a simple model of market microstructure in which an unobservable continuous stochastic process, the microprice, drives the dynamics of limit and market orders. In this model, the arrival of market orders and updates of the limit order book are determined by the microprice crossing a discrete set of n equidistant levels between the price ticks. Assuming normal dynamics for the microprice and adopting a standard mean-variance framework, we are able to derive a closed-form solution for the optimal inventory profile which is remarkably simple: the cumulative amount held when the market price is Si is inversely proportional to Si-S0, the distance in price terms from the limit order price. Finally, we show that n represents a sort of micro-volatility of the market that is entirely independent of the diffusive volatility of the microprice and is a measure of the intensity of the bid-ask bounce.

Number of Pages in PDF File: 37

Keywords: market microstructure, high-frequency trading, optimal execution, limit order book, upcrossing, price of immediacy, tick data, electronic order-driven markets

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Date posted: December 5, 2012 ; Last revised: April 27, 2013

Suggested Citation

Burlakov, Yuri and Kamal, Michael and Salvadore, Michele, Optimal Limit Order Execution in a Simple Model for Market Microstructure Dynamics (October 24, 2012). Available at SSRN: http://ssrn.com/abstract=2185452 or http://dx.doi.org/10.2139/ssrn.2185452

Contact Information

Yuri Burlakov
Chicago Trading Company, LLC ( email )
440 South LaSalle, 4th Floor
Chicago, IL 60605
United States
Michael Kamal
Chicago Trading Company, LLC ( email )
440 South LaSalle, 4th Floor
Chicago, IL 60605
United States
Michele Salvadore (Contact Author)
Banca IMI ( email )
Largo Mattioli, 3
Milano, MI 20121
Italy
Chicago Trading Company, LLC ( email )
440 South LaSalle, 4th Floor
Chicago, IL 60605
United States
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