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

31 Pages Posted: 5 Jun 2015

See all articles by Fabien Guilbaud

Fabien Guilbaud

Université Paris VII Denis Diderot

Huyên Pham

Université Paris VII Denis Diderot

Date Written: July 2015

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 chooses to post either market orders or limit orders, which are represented, respectively, by impulse controls and regular controls. We discuss the consequences of the two main features of this microstructure: first, the limit orders are only partially executed, and therefore she has no control on the executed quantity. Second, the high‐frequency trader faces the overtrading risk, which is the risk of large variations in her inventory. The consequences of this risk are investigated in the context of optimal liquidation. The optimal trading problem is studied by stochastic control and dynamic programming methods, and we provide the associated numerical resolution procedure and prove its convergence. We propose dimension reduction techniques in several cases of practical interest. We also detail a high‐frequency trading strategy in the case where a (predictive) directional information on the price is available. Each of the resulting strategies is illustrated by numerical tests.

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

Suggested Citation

Guilbaud, Fabien and Pham, Huyen, Optimal High‐Frequency Trading in a Pro Rata Microstructure with Predictive Information (July 2015). Mathematical Finance, Vol. 25, Issue 3, pp. 545-575, 2015. Available at SSRN: https://ssrn.com/abstract=2614737 or http://dx.doi.org/10.1111/mafi.12042

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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