Addressing Impact of Truncation and Parameter Uncertainty on Operational Risk Estimates

Typically, operational risk losses are reported above some threshold. This paper studies the impact of ignoring data truncation on the 0.999 quantile of the annual loss distribution for operational risk for a broad range of distribution parameters and truncation levels. Loss frequency and severity are modelled by the Poisson and Lognormal distributions respectively. Two cases of ignoring data truncation are studied: the quot;naive modelquot; - fitting a Lognormal distribution with support on a positive semi-infinite interval, and quot;shifted modelquot; - fitting a Lognormal distribution shifted to the truncation level. For all practical cases, the quot;naive modelquot; leads to underestimation (that can be severe) of the 0.999 quantile. The quot;shifted modelquot; overestimates the 0.999 quantile except some cases of small underestimation for large truncation levels. Conservative estimation of capital charge is usually acceptable and the use of the quot;shifted modelquot; can be justified while the quot;naive modelquot; should not be allowed. However, if parameter uncertainty is taken into account (in practice it is often ignored), the quot;shifted modelquot; can lead to considerable underestimation of capital charge. This is demonstrated with a practical example