  The bid-ask spread, which is defined by the difference between the best
selling price and the best buying price in a Limit Order Book at a given time,
is a crucial factor in the analysis of financial securities. In this study, we
propose a "State-dependent Spread Hawkes model" (SDSH) that accounts for
various spread jump sizes and incorporates the impact of the current spread
state on its intensity functions. We apply this model to the high-frequency
data from the Cac40 Euronext market and capture several statistical properties,
such as the spread distributions, inter-event time distributions, and spread
autocorrelation functions. We illustrate the ability of the SDSH model to
forecast spread values at short-term horizons.
