Abstract: Due to the inherent characteristics of operational loss and the data collection problem, the internal data is always insufficient and hardly to get correct and robust estimation. External data is the most recommended supplement data to internal data, but it has inherent biases, and there should be inevitable result deviation if directly mixed with internal data. How to combine external data with internal data is a hard problem and needs discussion. Since the operational data of Chinese commercial banks is scarce, the selection of candidate factors for factor method subjectively, the Bayesian method with strong subjective and the quantile methods assumptions strictly, these application all are limited to Chinese commercial banks. The factors are just splitred as the common component and the idiosyncratic component, and the loss affected by the common factors are equal. Using Macarthur's homogeneity measure, the homogeneity of the internal data and external data is estimated, which enables us to get the idiosyncratic factor of internal and external data. Then the external data is modified using scaling model and combined with the internal data. Since common model can't fit the operational risk well, while the extreme theory model can just modify the tail distribution well, the two-phase mixture model is used to fit the whole operational risk severity distribution. The threshold is set as a parameter is used to be estimated. Considering the continuity constraint at the threshold, it is found that the distribution with log-normal as the body and the generalized Pareto distribution as the tail fits well to the mixture data. With the frequency simulated, the annual loss distribution is gotten. The external data comes from the 10 years collection of our team and the internal data from the bank. The result shows that the external data should be modified before combined to internal data. The threshold selection is more stable and the result more reliable of the mixed data and mixture models. The external data modified method we used has no assumption to distribution similarity, and it gives a reference to the mixture data literature.

Key words: operational risk, mixing data, common component, idiosyncratic component, parametric mixture models