Investor Fears and Risk Premia for Rare Events

Abstract

This paper uses the method developed by Bollerslev and Todorov (2011b) to estimate risk premia for extreme events for the US and the German stock markets. The method extracts jump tail measures from high-frequency futures price datav and from options data. In a second step, jump tail distributions are approximated using the extreme value theory. Applying the method to German data yields very similar results to the ones shown for the US data. The risk premia for rare events constitute a considerable part of the total equity and variance risk premia for both markets. When using the results to build an investor fear index for the US and Germany, I find that the correlation of the fear index for the US with the VIX is 89.5% and that of the fear index for Germany with the VDAX is 90.6%. However, the fear index carries additional information of higher moments.

Keywords: Crisis indicator, extreme value theory, implied moments

JEL Classification: C13, G10, G12