Order Book Queue Hawkes Markovian Modeling

SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page 1-25, March 2024.
Abstract. This article presents a Hawkes process model with Markovian baseline intensities for high-frequency order book data modeling. We classified intraday order book trading events into a range of categories based on their order types and the price change after their arrivals. In order to capture the stimulating effects between multiple types of order book events, we use a multivariate Hawkes process to model the self-exciting and mutually exciting event arrivals. We also integrate Markovian baseline intensities into the event arrival dynamic, by including the impacts of order book liquidity state and time factor on the baseline intensity. A regression-based nonparametric estimation procedure is adopted to estimate the model parameters in our Hawkes+Markovian model. To eliminate redundant model parameters, LASSO regularization is incorporated into the estimation procedure. Besides, a model selection method based on Akaike information criteria is applied to evaluate the effect of each part of the proposed model. An implementation example based on real limit order book data is provided. Through the example we studied the empirical shapes of Hawkes excitement functions, the effects of liquidity as well as time factors, the LASSO variable selection, and the explanation power of Hawkes and Markovian elements to the dynamics of order book.