Exploiting Spillovers to forecast Crashes

We develop Hawkes models in which events are triggered through self as well as cross-excitation. We examine whether incorporating cross-excitation improves the forecasts of extremes in asset returns compared to only self-excitation. The models are applied to US stocks, bonds and dollar exchange rates. In-sample, a Lagrange Multiplier test indicates the existence of cross-excitation for these series. Out-of-sample, we find that the models that include spillover effects forecast crashes and the Value-at-Risk significantly more accurately than the models without.