Modeling Bid and Ask Price Dynamics with an Extended Hawkes Process and Its Empirical Applications for High-Frequency Stock Market Data

Abstract

This study proposes a versatile model for the dynamics of the best bid and ask prices using an extended Hawkes process. The model incorporates the zero intensities of the spread-narrowing processes at the minimum bid–ask spread, spread-dependent intensities, possible negative excitement, and nonnegative intensities. We apply the model to high-frequency best bid and ask price data from U.S. stock markets. The empirical findings demonstrate a spread-narrowing tendency, excitations of the intensities caused by previous events, the impact of flash crashes, characteristic trends in fast trading over time, and the different features of market participants in the various exchanges.

Modelling Price and Variance Jump Clustering Using the Marked Hawkes Process

“…There are many recent studies containing financial applications. Aı ¨t-Sahalia, Cacho-Diaz, and Laeven (2015) apply a multivariate HP to study jumps in international markets (see also Gresnigt, Kole, and Franses, 2016;Lee and Seo, 2022). Lee and Seo (2017) apply an MMHP to take both the impact of marked values and periodicity into account.…”