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We derive a continuous time model for the joint evolution of the mid priceand 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 performour asymptotic analysis using stylized features observed empirically. We arguethat in the asymptotic regime supported by empirical observations the mid priceand bid-ask-spread can be described using only certain parameters of the book(not the whole book itself). Our limit process is characterized by reflectingbehavior and state-dependent jumps. Our analysis allows to explain certaincharacteristics observed in practice such as: the connection between power-lawdecaying tails in the volumes of the order book and the returns, as well asstatistical properties of the long-run spread distribution.

Continuous-time Modeling of Bid-Ask Spread and Price Dynamics in Limit Order Books