Can volatility models explain extreme events?

Abstract

This paper revisits several existing volatility models by the light of extremal dependence, that is, serial dependence in extreme returns. First, we investigate the extremal properties of different high-frequency-based volatility processes and show that only a subset of them can generate dependence in the extremes. Second, we corroborate the empirical evidence on extremal dependence in financial returns, showing that extreme returns present strong and persistent correlation and that extreme negative returns are much more correlated than positive ones. Finally, a large empirical analysis suggests that only models exhibiting extremal dependence and endowed with a leverage component can appropriately explain extreme events.