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

With the fitted POT model (n = 1,000, N_u = 50, u = 3%, ξ = 0.5, β = 1), a risk committee asks for the 99.9% VaR rather than the 99% VaR of 5.47%. Which value is correct?

The 99.9% VaR is about 15.14%. The tail ratio is 20 × 0.001 = 0.02, its −0.5 power is 7.071, subtracting 1 and multiplying by 2 gives 12.14, and adding the 3% threshold yields 15.14%. This is much larger than normal scaling would suggest.

  1. A7.27%
  2. B12.14%
  3. C17.14%
  4. D15.14%Correct

Explanation

n/N_u × (1 − p) = 20 × 0.001 = 0.02. 0.02^(−0.5) = 7.0711, minus 1 = 6.0711, times β/ξ = 2 gives 12.142. Adding u = 3 gives 15.14%. Omitting u gives 12.14%, forgetting the −1 gives 17.14%, and scaling the normal quantile ratio gives 7.27%, which ignores the heavy tail.

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