Order Book Dynamics In The Presence Of Liquidity Fluctuations

We propose a stochastic model for a limit order book with liquidity fluctuations. Our model shows how severe intermittencies in the liquidity affect the order book dynamics. The law of large numbers (LLN), central limit theorem (CLT) and large deviations (LD) are proved for our model. Our results allow us to satisfactorily explain the volatility and local trends in the prices, relevant empirical characteristics that are observed in this type of markets. Furthermore, it shows us how these local trends and volatility are determined by the typical values of the bid-ask spread. In addition, we use our model to show how large deviations occur in the spread and prices, such as those observed in flash crashes.