  Accurate modeling of operational risk is important for a bank and the finance
industry as a whole to prepare for potentially catastrophic losses. One
approach to modeling operational is the loss distribution approach, which
requires a bank to group operational losses into risk categories and select a
loss frequency and severity distribution for each category. This approach
estimates the annual operational loss distribution, and a bank must set aside
capital, called regulatory capital, equal to the 0.999 quantile of this
estimated distribution. In practice, this approach may produce unstable
regulatory capital calculations from year-to-year as selected loss severity
distribution families change. This paper presents truncation probability
estimates for loss severity data and a consistent quantile scoring function on
annual loss data as useful severity distribution selection criteria that may
lead to more stable regulatory capital. Additionally, the Sinh-arcSinh
distribution is another flexible candidate family for modeling loss severities
that can be easily estimated using the maximum likelihood approach. Finally, we
recommend that loss frequencies below the minimum reporting threshold be
collected so that loss severity data can be treated as censored data.
