A New Methodology for Modelling Operational Risk using Skew t Copula and Bayesian Inference

We present a general methodology based on skew t copulas and Bayesian inference for modelling extreme multivariate dependent losses and the regulatory capital for operational risk. Current approaches fail to model both asymmetric dependence and accurate extreme upper tail dependence (e.g. 99.9% percentile), which is critical information for risk managers. This paper addresses this gap. The method is applied to SAS® Operational Risk Global Data to model operational risk at big U.S. banks. We compare the impact of established multivariate copulas and the multivariate skew t copula for estimating total regulatory capital. We find significance evidence of tail dependence in the extreme tails (i.e. 99.9% percentile) of the loss distributions, heterogeneous pairwise dependence and asymmetric dependence. We show that the skew t copula can be used effectively in high dimensions and yields asymmetric and in principle more accurate measures of upper tail dependence. Our methodology suggests a conservative estimation of capital charge compared with less flexible methods and overall provides a smaller capital charge, a reduction of up to 24% with respect to the standard Basel model