Measuring the Over-dispersed Data in Operational Risk with the Negative Binomial Process

In this paper, the negative binomial process is used to account for the over-dispersion in operational risk data. We estimate operational risk by means of the non-convex and convex risk measure, such as Value at Risk and Expected Shortfall, and provide a simple approximation to operational risk in a single risk cell. Moreover this approach is extended to the multivariate case, where the dependence structure between different risk cells is modeled by the Frank copula. In the final, we discuss almost all the limit cases when the dependence parameter differs. A practical example is presented to demonstrate the efficiency of approximation results.