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The definition of operational risk per Basel II includes which of the following:
1. Risk of loss resulting from inadequate or failed internal processes, people and systems or from external events
2. Legal risk
3. Strategic risk
4. Reputational risk
Extreme value theory focuses on the extreme and rare events, and in the case of VaR calculations, it is focused on the right tail of the loss distribution. In very simple and non-technical terms, EVT says the following:
1. Pull a number of large iid random samples from the population,
2. For each sample, find the maximum,
3. Then the distribution of these maximum values will follow a Generalized Extreme Value distribution.
(In some ways, it is parallel to the central limit theorem which says that the the mean of a large number of random samples pulled from any population follows a normal distribution, regardless of the distribution of the underlying population.)
Generalized Extreme Value (GEV) distributions have three parameters: (shape parameter), (location parameter) and (scale parameter). Based upon the value of , a GEV distribution may either be a Frechet, Weibull or a Gumbel. These are the only three types of extreme value distributions.