2 DETERMINATION OF THE CAPITAL CHARGE FOR OPERATIONAL RISKBasel II leaves the choice between three approaches for quantifying the
regulatory capital for operational risk. Both the Basic Indicator Approach
(BIA)and theStandardizedApproach(SA)define the operationalrisk capital
of a business line as a fraction of its gross income, thus explicitly assuming
that operational risk is related to size. Under the Advanced Measurement
Approach (AMA), banks can develop their own model for assessing the reg-
ulatory capital that covers their operational risk exposure over a one-year
period within a confidence interval of 99.9 percent (henceforth Operational
Value at Risk, or OpVaR). They must apply this model for each of the
eight Business Lines and for each of the seven Loss Event Types defined
in the Revised Framework. By default, capital charges associated to all 56
combinations are added to compute the regulatory capital requirement for
operational risk.^1
Although operational risk has been the focus of much attention in
the manufacturing industry for several decades, most financial institu-
tions have had a tendency to neglect this heterogeneous family of risks
which, except for fraud, are often perceived as diffuse and peripheral.
For the same reasons, until recently, very few banks had set up system-
atic procedures for the collection of data relative to operational losses. As a
consequence of Basel II, however, many banks are now in the process of set-
ting up a sound and homogeneous loss data collection system for all types
of risks.
A question that often arises when implementing a loss data collection
process is the determination of the collection threshold. Recordingallthe
operational loss events is indeed impossible, or at least wasteful, as the cost
(in terms both of systems and time) of the process would be much too high in
regard to its potential benefits. Therefore, banks are led to fixing a minimum
collection threshold under which losses are not collected.
While the literature on operational risk modeling is booming (see for
example, Frachot, Georges and Roncalli (2001), Cruz (2002), Alexander
(2003), Fontnouvelle, Jordan and Rosengren (2003), Fontnouvelle, Rosen-
gren and Jordan (2004), Moscadelli (2004), or Chapelle, Crama, Hübner and
Peters (2005)), few studies have paid specific attention to the choice of the
collection threshold for operational risk modeling and to its impact on the
capital charge.
This chapter examines the tradeoff between the cost of collecting data
from a very low money value and the loss of information induced by a
higher threshold. It is organized as follows. In section 1.2, we introduce the
LDA method to model operational risk losses. Next, we discuss the loss
data collection process, the related choice of the collection threshold and its
impact on estimated parameters. Section 1.4 uses real life data to examine
the impact of the collection threshold on the value of the capital charge for
operational risk. Section 1.5 contains some conclusions.