Quantile distance estimation for operational risk: a practical application

ABSTRACT Within the loss distribution approach framework, the required capital is the 99.9% value-at-risk of the annual loss distribution, which is based on the fit of the severity and frequency distributions using internal data. The severity estimation is the most difficult to undertake because of the specificity of operational risk data, which sometimes makes common techniques, such as maximum likelihood and the generalized method of moments, unreliable. This paper adapts an alternative method called quantile distance estimation - which is based on the minimization of a distance between empirical and theoretical quantiles - to operational risk modeling in the loss distribution approach framework. We calibrate the different parameters that enable this approach to be used for operational risk and then perform a study comparing it with the common estimation methods that use real data sets from the industry. We show that quantile distance estimation compares favorably with the other methods in an operational risk context.