Optimal High-Frequency Trading in a Pro-Rata Microstructure with Predictive Information

26 Pages Posted: 16 Apr 2012 Last revised: 7 May 2012

See all articles by Fabien Guilbaud

Fabien Guilbaud

Université Paris VII Denis Diderot

Huyên Pham

Université Paris VII Denis Diderot

Date Written: April 16, 2012

Abstract

We propose a framework to study optimal trading policies in a one-tick pro-rata limit order book, as typically arises in short-term interest rate futures contracts. The high-frequency trader has the choice to trade via market orders or limit orders, which are represented respectively by impulse controls and continuous controls. We model and discuss the consequences of the two main features of this particular microstructure: first, the limit orders sent by the high frequency trader are only partially executed, and therefore she has no control on the executed quantity. For this purpose, we model cumulative executed volumes by compound Poisson processes. Second, the high frequency trader faces the overtrading risk, which is the risk of brutal variations in her inventory. The consequences of this risk are investigated in the context of optimal liquidation.

We study the regular/impulse control problem using dynamic programming methods, which leads to a characterization of the value function in terms of an integro quasi-variational inequality. We then provide the associated numerical resolution procedure, and convergence of this computational scheme is proved. Next, we examine several situations where we can one one hand simplify the numerical procedure by reducing the number of state variables, and on the other hand focus on specific cases of practical interest. We examine both a market making problem and a best execution problem in the case where the mid-price process is a martingale. We also detail a high frequency trading strategy in the case where a (predictive) directional information on the mid-price is available. Each of the resulting strategies are illustrated by numerical tests.

Keywords: Market making, limit order book, pro-rata microstructure, inventory risk, marked point process, stochastic control

JEL Classification: G11

Suggested Citation

Guilbaud, Fabien and Pham, Huyen, Optimal High-Frequency Trading in a Pro-Rata Microstructure with Predictive Information (April 16, 2012). Available at SSRN: https://ssrn.com/abstract=2040867 or http://dx.doi.org/10.2139/ssrn.2040867

Fabien Guilbaud (Contact Author)

Université Paris VII Denis Diderot ( email )

2, place Jussieu
Paris, 75005
France

Huyen Pham

Université Paris VII Denis Diderot ( email )

Batiment Sophie Germain 5 rue Thomas Mann
Paris, 75205
France

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