Risk estimation for short-term financial data through pooling of stable fits

We suggest a new, parsimonious, method to fit financial data with a stable distribution. As a result of a stable fitting via maximum likelihood estimation (MLE), we find that some assets have similar values as stability indices, independently of the time interval considered. This fact can be exploited to pool the assets in groups and to choose a parameter α as an ex ante stability index, valid for every asset in the pool sector. With this fixed parameter, MLE is used again to obtain the other stable parameters. We discuss an innovative risk measure, based on the Expected Shortfall, which exploits the above procedure. We show that it gives a good estimation of risk even when only short time series are available. Finally, we introduce the notion of Risk Class, which allows us to classify assets according to their risk exposition and to compare different methods for the computation of the Expected Shortfall.