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The bid-ask spread, which is defined by the difference between the bestselling 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, wepropose a "State-dependent Spread Hawkes model" (SDSH) that accounts forvarious spread jump sizes and incorporates the impact of the current spreadstate on its intensity functions. We apply this model to the high-frequencydata from the Cac40 Euronext market and capture several statistical properties,such as the spread distributions, inter-event time distributions, and spreadautocorrelation functions. We illustrate the ability of the SDSH model toforecast spread values at short-term horizons.

The self-exciting nature of the bid-ask spread dynamics