Scale-, time- and asset-dependence of Hawkes process estimates on high frequency price changes

Classification of flash crashes using the Hawkes(p,q)framework

“…On the basis of our exemplary selection of events, we find that the events in equity and bond futures are both to be classified to be of endogenous nature, whereas only few of the foreign exchange crashes are found to fall in the endogenous category and many are in fact triggered exogenously. The fact that flash crashes in foreign exchange more often appear to be of exogenous nature is in line with the fact that, at time scales up to a few days, we generally find higher levels of endogeneity in equity futures than foreign exchange markets (Wehrli et al 2020), which are naturally more exposed to shocks from international news and macroeconomic releases. In some cases, the abnormal price moves furthermore seem to be a simple consequence of a large transaction instantaneously exhausting available liquidity.…”

“…This is also corroborated by the fact that trade intensity spikes significantly, whereas quoting intensity as measured by ‡ We have indeed found evidence for such a diurnal overnight rise in the branching ratio also in other currency pairs, see e.g. Wehrli et al (2020).…”

“…exogenous influences (Filimonov and Sornette 2012, Hardiman et al 2013, Filimonov et al 2014, Hardiman and Bouchaud 2014, Filimonov and Sornette 2015b)-a task that we call 'solving the endo-exo problem' (Wheatley et al 2019, Wehrli et al 2020). In the standard Hawkes model, the parameter η-being defined most naturally in the language of branching processes (Harris 1963, Daley andVere-Jones 2008) as the average number of offspring of first generation triggered per observed point-characterizes also the degree of self-excitation inherent to the dynamics of the system.…”

“…We note that some of these issues with data quality could be remedied by working with aggregated point processes in the form of integer-valued time series models, where the spurious microstructure induced by timestamp inaccuracies are naturally aggregated out. The integer-valued autoregressive (INAR) process representation of the Hawkes process for example and its estimation using EM algorithms, as developed in Wehrli et al (2020), can be extended to time-varying branching ratios like we use here in a straightforward manner. This however goes beyond the scope of this paper and is left for future work.…”

“…In the context of fluctuations in high frequency financial prices, Filimonov and Sornette (2012) have opened the road toward the full utilization of the dynamics of the branching ratio in order to diagnose different regimes and to possibly forecast impending crises associated with the approach to criticality, which is determined by η = 1. Here, we leverage recent methodological developments in Wheatley et al (2019) and Wehrli et al (2020) and extend the framework proposed therein to allow estimation of the full dynamics of η(t) in a structural manner.…”