Integration of Qualitative and Quantitative Operational Risk Data: A Bayesian Approach

The aim of this chapter is to provide a Bayesian model that allows us to manage operational risk and measure internally the capital requirement, compliant with the Advanced Measurement Approaches (AMA) recommended by Basel Committee on Banking Supervision (Basel II) for internationally active banks (see, eg, Basel Committee on Banking Supervision, 2003). In general, the objective is to estimate a loss distribution and to derive functions of interest from it (such as the value-at-risk, or VAR). More precisely, losses in operational risk are realisations of a convolution between a counting process (frequency) and a number of continuous ones (severities). For a review of statistical models used in operational risk management see, eg, Cruz (2002) and Cornalba and Giudici (2004). A general problem for such models is the lack of appropriate historical databases, which makes difficult to apply statistical inference techniques to “squeeze” in a correct manner information to check the tail of loss distribution. Bayesian networks offer a solution to this problem, combining in a coherent way qualitative and quantitative data, as well as risk indicators and external databases. Indeed such an approach seems to well reflect the requirements of the AMA to measuring operational risk. Consider the following quotation from the 2001 working paper on the regulatory 6