I have an event that takes place over a period of a few days, and I want to estimate the effect it has on market volatility using intraday data with one minute frequency. The problem is, that e.g. GARCH, EGARCH and GJR are not able to account for the asymmetry in the distribution of the observations because there are several observations that lay well outside normal distribution (e.g. many of the stocks have 20+ 5 sigma returns during the sample period, majority of these during the event window).
Since I am interested in the effect that the aforementioned event has on volatility, I am trying to understand how to deal with these outliers. They obviously carry relevant information, and thus including dummy variables to account for every outlier would seem impractical and not very reasonable? My initial intuition for solving the problem was running whatever ARCH model gives the best fit and include dummy for the event period, but now I am starting to question whether this is the right method with the data I am working with after all.
All advice and references to articles I might've missed are greatly appreciated.