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 [D. Farmer, L. Gillemot, F. Lillo, S. Mike and A. Sen, Quant. Finance 4 (2004) 383–397.], 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.
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