Change point methods in extreme value theory with applications in finance

Studying the distribution of a random variable, the tail behaviour might change at some point. This tail behaviour can be described by absolute or relative excesses of the data over a high threshold, given that the random variable exceeds the threshold. The limit distribution of the absolute excesses is given by a Generalized Pareto Distribution with parameters ° and &/190;: When °, called the extreme value index, is positive, the relative excesses can be described in the limit by a Pareto distribution with parameter °:. In this seminar we concentrate on testing whether a change of the extreme value index ° and/or &/190; occurs. To this end appropriate test statistics are introduced based on the likelihood approach of CsÄorg}o and Horv¶ath (1997) for independent data. The asymptotic properties of these test statistics are studied in this extreme value context in order to propose adequate critical values. Finally a practical test procedure is given and applied in simulations. We illustrate the procedures with real life examples from the stock market, geosciences and reinsurance.
This research is based on joint work with Goedele Dierckx, Economic University of Brussels.