  Market making is one of the most important aspects of algorithmic trading,
and it has been studied quite extensively from a theoretical point of view. The
practical implementation of so-called "optimal strategies" however suffers from
the failure of most order book models to faithfully reproduce the behaviour of
real market participants.
  This paper is twofold. First, some important statistical properties of order
driven markets are identified, advocating against the use of purely Markovian
order book models. Then, market making strategies are designed and their
performances are compared, based on simulation as well as backtesting. We find
that incorporating some simple non-Markovian features in the limit order book
greatly improves the performances of market making strategies in a realistic
context.
