Truncated Lognormals as a Power Law Mimicry in Operational Risk

Abstract

Real operational loss data exhibit in some cases power laws on a wide part of the tail distributions, with sharp deviations far on the right suggesting they decrease to zero faster at infinity. Taking into account such deviations when modelling operational risk leads to great differences in VaR estimates, stemming from different asymptotic distribution of extreme events. We make use of the power law mimicry properties of Truncated Lognormal distribution and show how they fit operational risk data considerably well in these cases. For the few exceptions we show how a mixture of Truncated Lognormals can pass the goodness of fit test.