A Semi-Parametric Approach to Estimating the Operational Risk and Expected Shortfall

This paper proposes some improvements to advanced measurement approach (AMA) to modelling operational losses and applies this approach to US business losses. The AMA involves, among others, modelling a loss severity distribution and estimating its Expected Loss and the 99.9% operational value-at-risk (OpVaR). These measures form a basis for computing the levels of regulatory and economic capitals to cover risks arising from losses. With our improvements to peak-over-threshold (POT) method, the parameters of the generalised Pareto distribution fitted to tail losses were estimated consistently and efficiently. From these parameter estimates, Expected Loss and OpVaR were also correctly estimated. Additionally, this paper estimated a coherent risk measure known as Expected Shortfall as an alternative to OpVaR. Applying the improved POT method to four business-lines and three event-types operational losses, we found that estimates of OpVaR can be much lower than those of Expected Shortfall. The results indicate that the heavier the tail of a loss distribution the larger the difference between OpVaR and Expected Shortfall, implying that the latter would provide the right level of capital to cover risks than would the former, particularly during crises