Extreme Volatilities, Financial Crises and L-Moment Estimations of Tail Indexes

Abstract

Following Bali and Weinbaum (2005) and Maillet et al. (2008), we present several estimates of volatilities computed with high- and low-frequency data and complement their results using additional measures of risk and several alternative methods for tail-index estimation. The aim is here to confirm previous results regarding the slope of the tail of various risk measure distributions, in order to define the high watermarks of market risks. We also produce synthetic general results concerning the method of estimation of the tail- indexes related to expressions of the L-moments. Based on estimates of tail indexes, backed-out from the high frequency 30' sampled CAC40 French stock Index series on the period 1997-2006, using Non-parametric Generalized Hill, Maximum Likelihood and various kinds of L-moment Methods for the estimation of both a Generalized Extreme Value density and a Generalized Pareto Distribution, we confirm that a heavy-tail density specification of the Log-volatility is not necessary.