Statistics of Extreme Risks

Abstract

When we model returns using a GARCH process with normally distributed innovations, we have already taken into account the second stylised fact. The the random returns automatically have a leptokurtic distribution and larger losses occur more frequently than under the assumption that the returns are normally distributed. If one is interested in the 95%-VaR of liquid assets, this approach produces the most useful results. For extreme risk quantiles such as the 99%-VaR and for riskier types of investments, the risk is often underestimated when the innovations are assumed to be normally distributed, since a higher probability of particularly be extreme losses than a GARCH process εt with normally distributed Z _t can be produced.