20 DETERMINATION OF THE CAPITAL CHARGE FOR OPERATIONAL RISK- Consistentmeans that for largen, the estimates converge to the true value of the
parameters,Unbiasedmeans that for all sample sizes the parameter of interest is
calculated correctly,Efficientmeans that the ML estimate is the estimate with the
smallest variance whileSufficientindicates that is uses all the information in the
observations. - Note that, for the Poisson distribution,χ^2 converges exactly to the chi-square dis-
tributions withk−1 degrees of freedom. See for instance section 6.6.2 of Law and
Kelton (2000) for a discussion on this test. - SeeAppendixAofKlugmanetal.(1998)forawiderrangeofcontinuousdistributions.
- See BCBS, 2004, § 673.
- This approach is not Basel II compliant as it assumes independence between the
various loss event types of a given business line. While this should be carefully kept
in mind, it does not have an impact of the results of the present study and allows us
increasing the size of samples under consideration. - Themeansquareerrorsassociatedwiththeoptimumthresholdsare0.0588and0.0402
for BL1 and BL2, respectively. - In the MLE estimation, the location parameter is fixed to the optimized value
obtained with the algorithm. - We assume that the bank under consideration in this study accounts for expected
losses in its tariff policy. Regulatory capital charge is the difference between unex-
pected loss (the 0.999th quantile of the aggregate loss distribution) and expected loss
(the mean of the aggregate loss distribution). - We choose the MSE criterion because it explicitly accounts for both the bias and
inefficiency effects (see Theil, 1971).
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