8 DETERMINATION OF THE CAPITAL CHARGE FOR OPERATIONAL RISKstraight line with positive gradient above a certain value, this indicates a
heavy-tailed distribution.
The visual inspection of MEF is sometimes tricky as no (or several)
“break(s)” can be observed. Several authors have suggested methods to
identify the optimal threshold (see, for example, Drees and Kaufmann,
1998; Dupuis, 1999; Matthys and Beirlant, 2003) but no single approach
has become widely accepted. A possible solution is proposed in Chapelle,
Crama, Hübner and Peters (2005) with an algorithmic procedure that builds
on ideas from Huisman, Koedijk, Kool and Palm (2001) and shares some
similarities with a procedure used by Longin and Solnik (2001) in a different
context. The Appendix summarizes the various steps of this algorithm.
1.3 THE COLLECTION THRESHOLD
1.3.1 Selection of a threshold
A sound loss data collection process is key to operational risk management
and measurement as statistical inference based on historical internal loss
dataandmonitoring/reporting activities both heavily rely on the quality of
the collected data. Coherence and completeness of collected data amongst
business units is therefore crucial.
Selecting the most adequate collection threshold is obviously bank-
specific, as each bank will examine the tradeoff between increasing the
number of observations in its internal database and the associated increase
in costs.
In addition to cost issues, reporting very low losses is likely to be viewed
as a waste of time by the employees. When this is the case, adhesion of
the employees is hard to obtain and the reliability of the collection process
can be questioned. On the measurement side, this results in an incomplete
database and the accuracy of the capital charge estimation is not ensured.
In contrast, however, fixing a very high threshold creates a truncation bias
that can lead to an over-estimation of the severity (see Frachot, Moudoulaud
and Roncalli, 2003).
To determine an adequate threshold, some banks rely on indications
given by Basel II, which recommends setting the collection threshold at
10,000 EUR.^6 For banks that are members of a data collection consortium,
the decision is sometimes driven by the rules of the consortium:
The Italian initiative DIPO led by the ABI (the Italian Bankers’ Associa-
tion) requires banks to provide all their operational risk losses above a
threshold fixed at 5,000 EUR.
ORX is a private consortium comprising large internationally active
banks. It has fixed the reporting threshold at 20,000 EUR.