Advances in Risk Management

16 DETERMINATION OF THE CAPITAL CHARGE FOR OPERATIONAL RISK

Table 1.5 Summary results for BL1 and BL2 (collection

threshold=0.25)

Business line 1 Business line 2

Frequency Poisson (1666) Poisson (7841)

“Body” Weibull Weibull

Parameter #1 3.056 11.852

Parameter #2 0.147 0.047

“Tail” GPD GPD

Location parameter 375 450

Shape parameter 1.041 0.750

Scale parameter 1677 601

Expected loss 282,429 179,893

Unexpected loss 1,596,046 990,471

Regulatory capital charge^10 1,313,617 810,578

observed losses, respectively. The higher value for Business Line 1 is not
surprising as BL1 is characterized by a higher proportion of severe losses.
This is reflected in the aggregate loss distribution with a fatter tail and,
consequently, proportionally heavier capital requirements.

1.4.3 Sensitivity analysis

Next, we move on to the analysis of the impact of the collection threshold
on the regulatory capital charge. We thus apply the approach of section 1.4.2
to both business lines when considering 6 collection thresholds: 0.25, 1, 5,
10, 20 and 50. In all cases, using a single distribution to fit the entire severity
distribution appears to perform badly when it comes to model its extreme
right part. As a consequence, we use EVT in all 12 cases. Results are provided
in Table 1.6.
With all this information, Monte Carlo simulations are performed and
10,000 years of losses are simulated. The resulting 10,000 aggregate losses
form the aggregate loss distribution from which the capital charge is derived.
Table 1.7 summarizes the main results, while Figure 1.5 provides a visual
overview of the fluctuation of the capital charge depending on the collection
threshold.

1.5 CONCLUSION

This chapter has provided three kinds on evidence on the impact of
the choice of the collection threshold for operational losses that have