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FRM Part I · FRM Exam Part I · Operational Risk

When fitting severity distributions to operational loss data, analysts often use a heavy-tailed distribution such as the generalized Pareto above a high threshold (peaks-over-threshold). What is the main reason?

Heavy-tailed models like the generalized Pareto above a threshold are used because rare, very large losses dominate high-percentile capital, and a distribution fitted to the bulk of the data usually fits the tail poorly. Extreme value theory models the tail directly.

  1. AExtreme losses drive capital at high percentiles, and the body of the data does not describe the tail wellCorrect
  2. BIt guarantees that the frequency distribution becomes normal
  3. CIt removes the need to collect external loss data or scenarios
  4. DIt ensures that aggregate losses across cells are perfectly uncorrelated

Explanation

Operational losses are skewed with rare large events that dominate capital at the 99.9% level, so extreme value theory models the tail separately from the body. It does not affect frequency, replace data needs (tail data are scarce, so external data and scenarios remain important), or determine dependence.

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