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

TL;DR

This paper develops a continuous-time model for the joint evolution of mid prices and bid-ask spreads in limit order books, linking empirical features with a queueing system framework.

Contribution

It introduces a novel continuous-time model derived from multiscale analysis of limit order book dynamics, capturing key empirical features with simplified parameters.

Findings

Explains the connection between order volume tails and return distributions.

Describes the spread distribution's long-term statistical properties.

Models mid price and spread with reflecting behavior and state-dependent jumps.

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.