Abstract
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.
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