Non-parametric Estimation of Operational Risk and Expected Shortfall

This paper proposes improvements to advanced measurement approach (AMA) to estimating operational risks, and applies the improved methods to US business losses categorised into ve business lines and three event types operational losses. The AMA involves, among others, modelling a loss severity distribution and es- timating the Expected Loss and the 99.9% operational value-at-risk (OpVaR). These measures form a basis for calculating the levels of regulatory and economic capitals required to cover risks arising from operational losses. In this paper, Expected Loss and OpVaR are estimated consistently and e ciently by nonpara- metric methods, which use the large (tail) losses as primary inputs. In addition, the 95% intervals for the underlying true OpVaR are estimated by the weighted empirical likelihood method. As an alternate measure to OpVaR, the Expected Shortfall - a coherent risk- is also estimated. The empirical ndings show that the interval estimates are asymmetric, with very large upper bounds, highlighting the extent of uncertainties associated with the 99.9% OpVaR point estimates. The Expected Shortfalls are invariably greater than the corresponding OpVaRs. The heavier the loss severity distribution the greater the di erence between OpVaR and Expected Shortfall, from which we infer that the latter would provide the right level of capital to cover risks than would the former, particularly during crises