Advances in Risk Management

YVES CRAMA, GEORGES HÜBNER AND JEAN-PHILIPPE PETERS 17

Table 1.6Estimated frequency and severity distributions

Business Line 1

Collection threshold 0.25 1 5 10 20 50
No. obs. 1,666 979 427 324 190 95

Frequency Poisson Poisson Poisson Poisson Poisson Poisson
Body Weibull Weibull Log-Normal Weibull Pareto Pareto

Parameter #1 3.056 2.447 1.658 14.249 20 50
Parameter #2 0.147 0.174 1.768 0.048 0.797 0.776

% of extremes 1.6% 2.7% 6.1% 8.0% 13.7% 27.4%
GPD – location 375 375 375 375 375 375
GPD – shape 1.041 1.041 1.041 1.041 1.041 1.041

GPD – scale 1677 1677 1677 1677 1677 1677

Business Line 2

Collection threshold 0.25 1 5 10 20 50
No. obs. 7,841 3,754 1,348 901 593 359

Severity Poisson Poisson Poisson Poisson Poisson Poisson
Body Weibull Pareto Pareto Pareto Pareto Pareto

Parameter #1 11.852 1 5 10 20 50
Parameter #2 0.047 0.551 0.514 0.492 0.402 0.375

% of extremes 0.6% 1.2% 3.3% 4.9% 7.4% 12.3%
GPD – location 450 450 450 450 450 450
GPD – shape 0.750 0.750 0.750 0.750 0.750 0.750

GPD – scale 601 601 601 601 601 601

not been previously documented in the operational risk management
literature.
First, the level of the collection threshold has little impact on regulatory
capital charge estimations. The own funds needed to cover operational risk
are indeed stable in both business lines. For BL1, it ranges from 1.26 million
to 1.43 million depending on the threshold. The variation range is narrower
for BL2 as capital charge fluctuates between 0.78 and 0.85 million.
Second, this result is mainly due to the way the tail is modeled. As we
rely on EVT to model the very high losses, the collection threshold has no
or little impact on the fatness of the tail for the severity distribution.
Finally, the choice of the collection threshold should thus not be guided
by capital requirements concerns but rather by a “pro/cons” analysis of the
practical implementation issues (costs, required systems, resources...) as
regulatory arbitrage seems not to be applicable in this case.