Modeling Operational Risk with Truncated Samples

Operational risk for a bank is the risk arising from execution of their business functions. The increasing sophistication of derivative securities enables banks to mitigate many risks associated with lending and investment activities, leaving operational risk as a growing portion of their overall risk portfolios. Regulations require banks set aside capital to cover operational losses, called regulatory capital. We discuss the loss distribution approach for estimating regulatory capital according to the advanced modeling approach discussed in Basel II. For a given business line and event type, our approach applies simple statistical and visual tools for choosing a loss severity distribution from a list of candidate parametric distributions. Candidate distribution parameters are estimated from operational loss data that are truncated below at a known minimum reporting threshold using the maximum likelihood method. This truncated approach assumes that unobservable losses below the reporting threshold follow the same distribution as observable losses. Evaluating estimated loss severity distributions at this minimum reporting threshold produces estimates of the proportion of losses that are unobserved, which we call implied probability. We use implied probability estimates in addition to AIC, QQ-plots, and Quantile Score when selecting candidate loss severity distributions and discuss some of the challenges associated with this process. We then simulate operational losses and use our advanced modeling approach to estimate regulatory capital.