Order Book Queue Hawkes-Markovian Modeling

TL;DR

This paper introduces a novel Hawkes-Markovian model for high-frequency order book data that captures event interactions and liquidity states, using non-parametric estimation and regularization techniques.

Contribution

It combines Hawkes processes with Markovian baseline intensities to better model order book event dynamics, incorporating liquidity and time effects.

Findings

Empirical analysis of real LOB data reveals characteristic excitement functions.

Liquidity state and time factors significantly influence event intensities.

LASSO regularization effectively identifies key model components.

Abstract

This article presents a Hawkes process model with Markovian baseline intensities for high-frequency order book data modeling. We classify intraday order book trading events into a range of categories based on their order types and the price changes after their arrivals. To capture the stimulating effects between multiple types of order book events, we use the multivariate Hawkes process to model the self- and mutually-exciting event arrivals. We also integrate a Markovian baseline intensity into the event arrival dynamic, by including the impacts of order book liquidity state and time factor to the baseline intensity. A regression-based non-parametric estimation procedure is adopted to estimate the model parameters in our Hawkes+Markovian model. To eliminate redundant model parameters, LASSO regularization is incorporated in the estimation procedure. Besides, 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 LOB data is provided. Through the example, we study the empirical shapes of Hawkes excitement functions, the effects of liquidity state as well as time factors, the LASSO variable selection, and the explanatory power of Hawkes and Markovian elements to the dynamics of the order book.