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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.
Hernández et al. (Tue,) studied this question.
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