Modeling Order Book Dynamics Using Queues and Point Processes

The objective of this dissertation is to study the queuing and point process models that try to capture as many features as possible of the high-frequency data of a limit order book. First, 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 from Level II data for a stock on the London Stock Exchange. A new feature of this 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. Furthermore, univariate-bivariate Hawkes' processes are developed and calibrated to capture the ``clustering'' and "mutually exciting'' features of the order arrivals in a limit order book. Although due to technical reasons, probabilities of interest such as those of prices going up for the next move are not shown for this model, a Monte Carlo simulation algorithm of point processes called emph{thinning algorithm} is successfully modified to derive the cumulative distribution functions of some first-passage times in the order book.