On the selection of loss severity distributions to model operational risk

Daniel Hadley, Harry Joe and Natalia Nolde

Abstract

The accurate modeling of operational risk is important for banks and the finance industry as a whole to prepare for potentially catastrophic losses. One modeling approach 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. The annual operational loss distribution is estimated as a compound sum of losses from all risk categories, and a bank must set aside capital, called regulatory capital (RC), equal to the 99.9% quantile of this estimated distribution. In practice, this approach may produce unstable RC from year to year as the selected loss severity distribution family changes. 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 stabilize RC. In addition, the sinh–arcsinh distribution is another flexible candidate family for modeling loss severities that is 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.