Introduction to the Extreme Value Theory applied to operational risk

This paper aims to present the main lines of the Extreme Value Theory applied to the operational risk. The idea is to present a methodology which allows to identify a threshold by type of risk, and to feign the losses below the threshold with the classical laws, and the losses above with a Generalized Pareto Distribution (GPD). The adequacy of the data to the law GPD allows to consider an extreme quantile, as minimal strategy, sensitive to the size of samples, and to plan random costs whose probability of occurrence is very low, but the choice of the threshold beyond of which the observation will be judged extreme, is a point to be handled with precaution, even if we propose a technique to quantify this threshold. Furthermore, the costs of extreme losses do not lend themselves to modeling; by definition this type of costs is rare, and the forecasts or the estimations must be often established with a big distrust, and outside the available data. The models must be used in a supple way, without believing completely to the limit. The adoption of this method could allow the risk managers to observe the extreme events with a certain objectivity, to check the hierarchical organization of the classes of operational risks, and in the other hand, establish reserves to face these risks.