Exploiting Spillovers to Forecast Crashes

We develop Hawkes models in which events are triggered through self-excitation 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. We predict the probability of crashes in the series and the value at risk (VaR) over a period that includes the financial crisis of 2008 using a moving window. A Lagrange multiplier test suggests the presence of cross-excitation for these series. Out-of-sample, we find that the models that include spillover effects forecast crashes and the VaR significantly more accurately than the models without these effects.