Operational Risk Bias Quanti fication and Correction

Identifying the Maximum Domain of Attraction (MDA) of a given (severity) distribution in Operational Risk is not an easy task with a significant impact on the Value at Risk (VaR). One could resort to the result of Pickands (1975) and select a suitably high threshold to model the excesses so that the Generalized Pareto Distribution (GPD) approximation holds and the shape parameter estimate belong to the correct MDA. On the other hand moving the threshold to the right leaves us with only a limited number of observations which in turn increases the statistical error of the (shape) parameter estimate resulting in an upward bias in the Value at Risk (VaR) calculation. We propose here a methodology to measure and correct this bias thus reducing this tradeoff. We finally present results showing the goodness of this correction