Event definition and the branching ratio: Hawkes estimates of price-change clustering in the consolidated quote feed

Abstract

Hawkes models of price changes in the consolidated US quote feed find a sub-millisecond kernel component and a branching ratio near criticality. We show that in large-tick stocks the first is the feed's construction: half of NBBO changes are locks or depleted quotes, resolved within a millisecond, which the model reads as excitation. Defining the event as a mid-price level persisting for one millisecond removes the component. Raw fits put three times the clean kernel mass within one second, which a simulation reproduces. Since the total branching ratio trades off against the baseline, we report kernel mass on a fixed window.