Aftershock prediction for high-frequency financial markets' dynamics

The occurrence of aftershocks following a major financial crash mani- fests the critical dynamical response of financial markets. Aftershocks put additional stress on markets, with conceivable dramatic consequences. Such a phenomenon has been shown to be common to most financial assets, both at high and low fre- quency. Its present-day description relies on an empirical characterization proposed by Omori at the end of 1800 for seismic earthquakes. We point out the limited pre- dictive power in this phenomenological approach and present a stochastic model, based on the scaling symmetry of financial assets, which is potentially capable to predict aftershocks occurrence, given the main shock magnitude. Comparisons with S&P high-frequency data confirm this predictive potential.