Order Book Dynamics with Liquidity Fluctuations: Asymptotic Analysis of Highly Competitive Regime

We introduce a class of Markov models to describe the bid-ask price dynamics in the presence of liquidity fluctuations. In a highly competitive regime, the spread evolution belongs to a class of Markov processes known as a population process with uniform catastrophes. Our mathematical analysis focuses on establishing the law of large numbers, the central limit theorem, and large deviations for this catastrophe-based model. Large deviation theory allows us to illustrate how huge deviations in the spread and prices can occur in the model. Moreover, our research highlights how these local trends and volatility are influenced by the typical values of the bid-ask spread. We calibrated the model parameters using available high-frequency data and conducted Monte Carlo numerical simulations to demonstrate its ability to reasonably replicate key phenomena in the presence of liquidity fluctuations.