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FRM Part II · FRM Exam Part II · Parametric Approaches (II): Extreme Value

A risk analyst at a trading firm notes that a normal distribution fitted to daily returns badly underestimates the frequency of very large losses. Which statement best describes the motivation for applying extreme value theory (EVT) to this problem?

EVT is motivated by the need to model tail losses directly. Using limiting distributions for extremes, it fits only the tail rather than forcing a single distribution, such as the normal, to describe both centre and tails, which typically understates the frequency of very large losses.

  1. AEVT models only the tail observations directly, rather than forcing one distribution to fit both the centre and the tailsCorrect
  2. BEVT improves the fit of the centre of the distribution by using all observations equally
  3. CEVT removes the need to assume anything about the independence of observations
  4. DEVT guarantees that VaR at any confidence level will be lower than under the normal model

Explanation

EVT focuses on the tail of the distribution and estimates it using limiting results for extremes, instead of fitting a single distribution dominated by the bulk of the data. It does not improve the centre fit, it does not remove all assumptions (standard EVT typically assumes iid or approximately so), and it often produces higher, not lower, extreme VaR for fat-tailed data.

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