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

A risk team notes that its 99.9% VaR from a normal model is far below that from an EVT model fitted to the same loss history, which has a positive tail index. Which explanation is most consistent with this difference?

The normal model has thin tails and so understates the likelihood of extreme losses, while the EVT model with a positive tail index captures heavy tails. At very high confidence levels such as 99.9%, this makes the EVT VaR considerably larger.

  1. AThe normal model has thin tails and understates the probability of extreme losses that the EVT model capturesCorrect
  2. BThe EVT model ignores the tail, so it overstates losses
  3. CThe normal model is more conservative at extreme quantiles because it uses all observations
  4. DBoth models must give identical VaR beyond the 99% confidence level

Explanation

A positive tail index implies a heavy, power-law tail. The normal distribution decays much faster, so at very high confidence levels it gives a smaller quantile. EVT is built specifically around the tail, not ignoring it, and the two models diverge increasingly at extreme confidence levels.

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