The structural modelling of operational risk via the Bayesian inference

combining loss data with expert opinions

Pavel V. Shevchenko, Mario V. Wüthrich

Research output: Contribution to journalArticle


Typically, operational risk losses are reported above some threshold. This paper studies the impact of ignoring data truncation on the 0.999 quantile of the annual loss distribution for operational risk for a broad range of distribution parameters and truncation levels. Loss frequency and severity are modelled by the Poisson and Lognormal distributions respectively. Two cases of ignoring data truncation are studied: the “naive model” - fitting a Lognormal distribution with support on a positive semi-infinite interval, and “shifted model” - fitting a Lognormal distribution shifted to the truncation level. For all practical cases, the “naive model” leads to underestimation (that can be severe) of the 0.999 quantile. The “shifted model” overestimates the 0.999 quantile except some cases of small underestimation for large truncation levels. Conservative estimation of capital charge is usually acceptable and the use of the “shifted model” can be justified while the “naive model” should not be allowed. However, if parameter uncertainty is taken into account (in practice it is often ignored), the “shifted model” can lead to considerable underestimation of capital charge. This is demonstrated with a practical example.
Original languageEnglish
Pages (from-to)3-26
Number of pages24
JournalJournal of Operational Risk
Issue number3
Publication statusPublished - 2006
Externally publishedYes


  • operational risk
  • loss distribution approach
  • Bayesian inference
  • Basel II
  • Advanced Measurement Approaches
  • compound process
  • quantitative risk management

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