A statistical model is a possible representation (not necessarily complex) of a situation of the real world. Models are useful to give a good knowledge of the principal elements of the examined situation and so to make previsions or to control such a situation. In the banking sector, models, techniques and regulations have been developed for evaluating Market and Credit risks, for linking together risks, capital and profit opportunity. The regulations and vigilance standards on the capital have been developed from the Basel Committee founded at the end of 1974 by the G10. The standards for the capital’s measurement system were defined in 1988 with the “Capital Accord” (BIS, 1988); nowadays, it is supported from over 150 countries around the world. In January 2001 the Basel Committee published the document “The New Basel Capital Accord” (BIS, 2001), which is a consultative document to define the new regulation for the bank capital requirement. Such a document has been revisited many times (see BIS, 2005). With the new accord there is the necessity of appraising and managing, beyond the financial risks, also the category of the operational risks (OR) already responsible of losses and bankruptcies (Cruz (Ed.), 2004; Alexander (Ed.), 2003; Cruz, 2002).
The operational risk (OR), according to the new Basel accord, is due to detrimental events caused by the inadequacy or the failure of internal processes and systems, human errors and external events, for instance natural calamity (BIS, 2005).
The evaluation of a suitable risk profile is important, because banks with the same levels of market and credit risk can have a different OR profile. The operational risk, in fact, is an intrinsic characteristic of the bank, of the performed activities and of the place in which the institution is located (Cruz (Ed.), 2004).
Due to the peculiarity of OR, the difficulties that are peculiar to its modelling are the following:
The OR set is heterogeneous and strongly dependent of the context where it is valued.
Some events, which are referable to the OR, produce damages that are hardly evaluable.
Some OR events are very rare. Probably the single bank has never faced such events, and in this case the institution needs also external data.
For some events the past history is not a good indication of the future.
Lack of reliable historical data.
Associated problems with events’ estimate that have high frequency and low impact (HFLI) and vice versa with low frequency and high impact (LFHI).
Besides, the greatest problems arise from the organization of the database (DB) for the construction and validation of the models, (Cruz (Ed.), 2004; Alexander (Ed.), 2003).
The Basel Committee with the new accord recommends the use of three methods for the valuation of the value at risk (VaR) characterized by increasing complexity: base (BIA), standard (STA) and advanced (AMA), (BIS, 2005; Cornalba & Giudici 2004).
Such approaches are subjected to criticisms due to the difficulties to evaluate operational risk and for the way in which they influence the capital (necessary to cover OR) in function of the institution amplitude (Cruz (Ed.), 2004; Alexander (Ed.), 2003).Top
The AMA approach is more complex, but it makes the calculation of the value at risk (VaR) more sensitive to the risk profile and generally smaller than the approach calculated with BIA and STA. Every bank can use its advanced internal model if it satisfies the qualitative and quantitative standards defined by the new accord (BIS, 2005; BIS, 2003).
The AMA methods are bottom-up type and this because the VaR calculation is achieved considering the losses obtained by dividing the bank’s activities in eight business lines (BL) and seven event types (ET or risk category). In this manner there will be at least 56 different kind of losses, one for each intersection BL/ET.