A Bayesian approach to estimate the Marginal loss distributions in Operational Risk management.

One of the main problems in risk management is the lack of loss data, which affects the parameter estimates of the marginal distributions of the losses. This drawback suggests the employment of Bayesian methods and simulation tools as a natural solution to this problem. The use of Bayesian methods allows us to integrate the scarce and inaccurate quantitative information collected by a bank with prior information brought by experts. With the present work, we present an original Bayesian approach for modelling operational risk and for calculating the capital required to cover the estimated risks. Besides this methodological innovation we propose a computational scheme, based on MCMC, able to implement what proposed theoretically. We show the advantages in terms of reduction of capital charge according to different choices of the marginal loss distributions.