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This paper proposes improvements to advanced measurement approach (AMA) to estimating operational risks, and applies the improved methods to US business losses categorised into five business lines and three event types operational losses. The AMA involves, among others, modelling a loss severity distribution and estimating 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 efficiently by nonparametric 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 findings 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 difference 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

A semiparametric method is developed for estimating the dependence parameter and the joint distribution of the error term in the multivariate linear regression model. The nonpara- metric part of the method treats the marginal distributions of the error term as unknown, and estimates them by suitable empirical distribution functions. Then a pseudolikelihood is maximized to estimate the dependence parameter. It is shown that this estimator is as- ymptotically normal, and a consistent estimator of its large sample variance is given. A simulation study shows that the proposed semiparametric estimator is better than the para- metric methods available when the error distribution is unknown, which is almost always the case in practice. It turns out that there is no loss of asymptotic e±ciency due to the estimation of the regression parameters. An empirical example on portfolio management is used to illustrate the method. This is an extension of earlier work by Oakes (1994) and Genest et al. (1995) for the case when the observations are independent and identically distributed, and Oakes and Ritz (2000) for the multivariate regression model.

This paper investigates whether or not there are significant changes in the dependence between the Thai equity market and six Asian markets - namely, Singaporean, Malaysian, Hong Kong, Korean, Indonesian and Taiwanese markets - due to 1997-July financial crisis. If so, this may be an indication that the underlying bivariate joint distributions capturing the dependence between the Thai market and these six markets have changed. We employ the chi-plot proposed by Fisher and Switzer (2001) and the Kendall plot proposed by Genest and Boies (2003) to examine the dependence in these six markets for the pre- and post-1997 financial crisis periods. We find that marginal distributions of all seven markets have notably changed due to this financial crisis, and that the functional forms of the underlying joint distributions generating the dependence in the Korean, Indonesian and Taiwan markets have also changed for the post-crisis period. It appears that the same parametric copula can capture the dependence in the Singapore, Malaysia and Hong Kong markets for both pre- and post-crisis periods, and that only the tail indices of bivariate distributions between the Thai and these three markets have changed. It is interesting to observe that the same conclusions can be drawn using both chi- and Kendall plots.