A generalized birth-death stochastic model for high-frequency order book dynamics

He Huang, Alec N. Kercheval

We use a generalized birth-death stochastic process to model the high-frequency dynamics of the limit order book, and illustrate it using parameters estimated f rom Level II data for a stock on the London Stock Exchange. A new feature of th is model is that limit orders are allowed to arrive in multiple sizes, an important empirical feature of the order book. We can compute various quantities of interest without resorting to simulation, conditional on the state of the order book, such as the probability that the next move of the mid-price will be upward, or the probability, as a function of order size, that a limit ask order will be executed before a downward move in the mid-price. This generalizes a successful model of Cont, Stoikov, and Talreja by means of a new technical approach to computing the distribution of first passage times.