THRESHOLD PARAMETER OF THE EXPECTED LOSSES

The objective of extreme value analysis is to quantify the probabilistic behavior of unusually large losses using only extreme values above some high threshold rather than using all of the data which gives better fit to tail distribution in comparison to traditional methods with assumption of normality. In our case we estimate market risk using daily returns of the CROBEX index at the Zagreb Stock Exchange. Therefore, it's necessary to define the excess distribution above some threshold, i.e. Generalized Pareto Distribution (GPD) is used as much more reliable than the normal distribution due to the fact that gives the accent on the extreme values. Parameters of GPD distribution will be estimated using maximum likelihood method (MLE). The contribution of this paper is to specify threshold which is large enough so that GPD approximation valid but low enough so that a sufficient number of observations are available for a precise fit.