| Abstract | The quantification of operational risk has to deal with various concerns regarding data. One of the main questions is the bias in the data on the operational losses amounts recorded even if it's compiled internally. We show that it's possible, based on mild assumptions on the internal procedures put in place to manage operational losses, to estimate the parameters for the losses amounts, taking in consideration the bias that, not being considered, generates a twofold error in the estimators for the mean loss amount and the total loss amount, the former being overvalued and the last undervalued. We consider that the probability that a loss is reported and ends up recorded for analysis, increases with the size of the loss, what causes the bias in the database but, at the same time, we don't consider the existence of a threshold, above which, all losses are recorded. Hence, no loss has probability one of being recorded, in what we defend is a realist framework. We deduce the general formulae, present simulations for common theoretical distributions, estimate the impact for not considering the bias factor when estimating the value at risk and estimate the true total operational losses the bank incurred. |
