Joint modeling of clustered operational-loss severities and event frequency

Develop and evaluate a joint model of clustered DeFi operational-loss severities and event frequency, together with a detailed analysis of the independence assumption between severity and frequency in the loss-distribution approach.

Background

The paper models monthly event frequency with a negative-binomial distribution and treats loss severity and event frequency as independent, following standard banking loss-distribution practice. However, the observed monthly event counts are strongly over-dispersed, indicating that operational-risk events may cluster rather than arrive independently.

Because clustered events may be associated with correlated or unusually severe losses, the independence assumption could affect annual aggregate-loss estimates and the resulting 99.9% value-at-risk capital buffers. The paper identifies a joint model of clustered severities and frequency, along with a more detailed assessment of the independence assumption, as unresolved future work.

References

Severity and frequency are treated as independent, following standard banking-LDA practice \citep{Chernobai2008,Cope2009}. A detailed analysis of this assumption and a potential joint model of clustered severities is left to future work.

— Pricing the DeFi Tail: Do Protocols or Depositors Price Operational Risk?  (2609.00911 - Bundi, 1 Sep 2026) in Section 3, “Methodology: The Loss-Distribution Approach,” subsection “Frequency”