Truncated lognormals as a power-law mimic in operational risk

Carolyn Moclair

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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.
Truncating a lognormal distribution far on the right tail produces a behavior on the right tail of the distribution that can be considered a 'power-law mimicry'.
This article shows both analytically and empirically on a real operational risk dataset this power-law mimicry property of truncated lognormals.

Abstract

ABSTRACT

Real operational loss data in some cases exhibits power laws on a wide part of the tail distributions, with sharp deviations far to the right, suggesting they decrease to zero faster at infinity. Taking into account such deviations when modeling operational risk leads to large differences in value-at-risk estimates, stemming from different asymptotic distributions of extreme events. We make use of the power-law mimicry properties of the 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.

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