It has been suggested that marked point processes might be good candidates for the
modelling of financial high-frequency data. A special class of point processes, Hawkes
processes, has been the subject of various investigations in the financial community.
In this paper, we propose to enhance a basic zero-intelligence order book simulator
with arrival times of limit and market orders following mutually (asymmetrically)
exciting Hawkes processes. Modelling is based on empirical observations on time intervals
between orders that we verify on several markets (equity, bond futures, index futures).
We show that this simple feature enables a much more realistic treatment of the bid-ask
spread of the simulated order book.