Journal of Operational Risk

Measuring tail operational risk in univariate and multivariate models with extreme losses

Yang Yang, Yishan Gong and Jiajun Liu

  • The authors consider operational risk models with weakly tail dependent, heavy-tailed loss severities and general loss frequency processes.
  • Based on capital approximation within the Basel II/III regulatory capital accords, the Loss Distribution Approach is used to analyse operational risks.
  • Some limit behaviors for the Value-at-Risk and Conditional Tail Expectation of aggregate operational risks are derived.

This paper considers some univariate and multivariate operational risk models, in which the loss severities are modeled by some weakly tail dependent and heavy-tailed positive random variables, and the loss frequency processes are some general counting processes. We derive some limit behaviors for the value-at-risk and conditional tail expectation of aggregate operational risks in such models. The methodology is based on capital approximation within the Basel II/III framework (the so-called loss distribution approach). We also conduct some simulation studies to check the accuracy of our approximations and the (in)sensitivity due to different dependence structures or to the heavy-tailedness of the severities.

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