On the role of volatility for modelling risk exposure

We show in this paper that volatility measures can be misleading indicators of risk if returns do not follow a Gaussian distribution. A more reliable measure of risk is the probability distribution of the return on an asset. Estimators for these measures are usually challenging and need of nonparametric and semi-parametric techniques. The aim of this paper is twofold. First, it proposes the use of semi-parametric estimators of the distribution function of the return on an asset based on extreme value theory for computing Value-at-Risk; and second, it discusses the validity of different volatility models in this semi-parametric framework. The conclusion is that different volatility models can yield different valid risk measures if coupled with the appropriate distribution function. Hence the puzzle in the choice of volatility measures. This is shown in an empirical exercise for data of financial indexes from USA, UK, Germany, Japan and Spain.