On binomial order avalanches

This paper introduces a discrete limit order book model where new orders are placed with a fixed displacement from the mid-price. Further, the trade event occurs whenever the mid-price hits the price level on which there is some volume. Therefore, the dynamics of the limit order book model leads to two trading mechanisms, namely Type I trade and Type II trade. A Type I trade takes place whenever the price maximum increases, while a Type II trade occurs if the price drops by $\mu$ or more and then increases by $\mu$ again. Our focus is mainly on the distribution of order avalanches length, and by an avalanche length we consider a series of order executions where the length of periods with no trade event cannot exceed $\varepsilon$.