On the Selection of Loss Severity Distributions to Model Operational Risk

22 Pages Posted: 13 Sep 2019

See all articles by Daniel Hadley

Daniel Hadley

University of British Columbia (UBC)

Harry Joe

University of British Columbia - Department of Statistics

Natalia Nolde

Statistics Department

Date Written: September 11, 2019

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.

Keywords: operational risk, advanced measurement approach (AMA), loss distribution approach (LDA), regulatory capital (RC)

Suggested Citation

Hadley, Daniel and Joe, Harry and Nolde, Natalia, On the Selection of Loss Severity Distributions to Model Operational Risk (September 11, 2019). Journal of Operational Risk, Forthcoming. Available at SSRN: https://ssrn.com/abstract=3451242

Daniel Hadley (Contact Author)

University of British Columbia (UBC) ( email )

2329 West Mall
Vancouver, British Columbia BC V6T 1Z4
Canada

Harry Joe

University of British Columbia - Department of Statistics ( email )

2329 West Mall
Vancouver, British Columbia BC V6T 1Z2
Canada
(604) 822 2829 (Phone)

Natalia Nolde

Statistics Department ( email )

2329 West Mall
Vancouver, British Columbia BC V6T 1Z4
Canada

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