A Credibility Framework for Extreme Value-at-Risk

Value-at-risk estimates derived from extreme value data by fitting fat-tailed distributions can be so large that their validity is open to question. In this paper, an objective criterion, and a framework from which it was developed, are presented in order to decide whether or not a fitted distribution is inappropriate for the purpose of value-at-risk calculation. That criterion is based on established extreme value theory (principally the Pickands-Balkema-deHaan Theorem), which is used to calculate a sequence of reference value-at-risk estimates using Generalised Pareto distributions. Those estimates are used to develop a closed-form formula for calculating a theoretical 'maximum' value-at-risk. The method is validated by generating 100 random data sets and testing them against the framework for varying input parameter values. Approximately 75% of those cases passed the validation test.