  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 "naive model" - fitting a Lognormal
distribution with support on a positive semi-infinite interval, and "shifted
model" - fitting a Lognormal distribution shifted to the truncation level. For
all practical cases, the "naive model" leads to underestimation (that can be
severe) of the 0.999 quantile. The "shifted model" 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 "shifted model" can be justified while the "naive model" should not
be allowed. However, if parameter uncertainty is taken into account (in
practice it is often ignored), the "shifted model" can lead to considerable
underestimation of capital charge. This is demonstrated with a practical
example.
