Abstract: Internal fraud is the most important loss type of Chinese commercial banks and has caused a lot of losses. Since the nature of operational risk, loss data is deficiency, in order to do more accurate and robust calculation with little data, this paper uses the Bayesian posterior forecasting distribution to calculate the parameters. Since the chosen of location parameter is important to the evaluation, we set the location varying with linear trend to get more robust parameters estimation. The loss frequency is Poisson distribution, and we set the prior Gamma distribution, while the loss severity is Generalized Pareto distribution, and we set the prior distribution mixture Gamma distribution, then we get the posterior predictive distributions of loss frequency and loss severity, with Monte Carlo simulation we get the combined distributions. Compared to the classical method of Poisson-GPD, The results are better and we get much stable parameters and much lower capital charge for internal fraud. And Bayesian analysis is helpful to calculate accurately the parameters with small sample.

Key words: operational risk, internal fraud, Bayesian posterior forecasting distribution, general Pareto distribution, linear trend for location parameter