Research on Parameter Estimation for Operational Risk Measurement based on Small Sampling Data

To ensure the parameter estimation quality based on small sampling data, Bayesian inference theory was applied. Taking experts' experience and opinion as the prior distributions of parameters, the way to assess the frequency distribution and severity distribution was developed from a Bayesian perspective. Poisson distribution was chosen as the loss frequency distribution, and Gamma Distribution was set as the prior distribution. Extreme Value Theory(EVT)was applied in loss severity modeling, and GPD was used to fit the loss distribution. Both the location parameter and scale were assumed to have the prior Gamma distribution separately. Methodology for estimating parameters of the loss distribution was extended from Maximum Likelihoods Estimation(MLE) to Markov Chain Monte Carlo(MCMC)method. Results reveal that compared with the MLE method, MCMC method, which is based on Bayesian Inference, provides more effective and stable estimation for parameters in circumstances of small sampling dada.