Bid-ask spread dynamics: large upward jump with geometric catastrophes

Abstract

We propose a simple continuous-time stochastic model for capturing the dynamics of a limit order book in the presence of liquidity fluctuations, manifested by gaps in filled price levels within the OB. Inspired by Farmer et al. (2004), we define a model for the dynamics of spread that incorporates liquidity fluctuations and undertake a comprehensive theoretical  study of the model's properties, providing rigorous proofs of several key asymptotic theorems. Furthermore, we show how large deviations manifest in the spread under this regime.