  We derive a continuous time model for the joint evolution of the mid price
and the bid-ask spread from a multiscale analysis of the whole limit order book
(LOB) dynamics. We model the LOB as a multiclass queueing system and perform
our asymptotic analysis using stylized features observed empirically. We argue
that in the asymptotic regime supported by empirical observations the mid price
and bid-ask-spread can be described using only certain parameters of the book
(not the whole book itself). Our limit process is characterized by reflecting
behavior and state-dependent jumps. Our analysis allows to explain certain
characteristics observed in practice such as: the connection between power-law
decaying tails in the volumes of the order book and the returns, as well as
statistical properties of the long-run spread distribution.
