Asymptotic results for over-dispersed operational risk by using the asymptotic expansion method

In this paper, the author considers a new Loss-distribution-approach model, in which the over-dispersed operational risks are modeled by the compound negative binomial process. In the single dimensional case, asymptotic expansion for the quantile of compound negative binomial process is explored for computing the capital charge of a bank for operational risk. Moreover, when the dependence structure between different risk cells is modeled by the Frank copula, this approach is extended to the multi-dimensional setting. A practical example is given to demonstrate the effectiveness of approximation results.