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UBC Theses and Dissertations

Modeling operational risk using the truncation approach Hadley, Daniel P.


Banks that use the advanced measurement approach to model operational risk may struggle to develop an internal process that produces stable regulatory capital over time. Large decreases in regulatory capital are scrutinized by regulators while large increases may force banks to set aside more assets than necessary. A major source of this instability arises from the loss severity selection process, especially when the selected distribution families for severity risk categories change year-to-year. In this report, we examine the process of selecting severity distributions from a candidate distribution list within the guidelines of the advanced measurement approach, propose useful tools to aid in selecting an appropriate severity distribution, and analyze the effect of selection criteria on regulatory capital. The log sinh-arcsinh distribution family is added to a list of common candidate severity distributions used by industry. This 4-parameter family solves issues introduced by the 4-parameter g-and-h distribution without sacrificing flexibility and shows promise in outperforming 2-parameter families, reducing the frequency of severity distribution families changing year-to-year. Distribution parameters are estimated using the maximum likelihood approach from loss data truncated at a known minimum reporting threshold. Our severity distribution selection process combines truncation probability estimates with Akaike Information Criterion (AIC), Bayesian Information Criterion, modified Anderson-Darling, QQ-plots, and predictive measures such as the quantile scoring function and out-of-sample AIC, and we discuss some of the challenges associated with this process. We then simulate operational losses and calculate regulatory capital, comparing the effect on regulatory capital of selecting loss severity distributions using AIC versus quantile score. A combination of these two criteria is recommended when selecting loss severity distributions.

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