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

A bank has 1,000 daily loss observations, of which 50 exceed the threshold u = 2.0 (in USD millions). A GPD is fitted to the excesses with ξ = 0.20 and β = 0.80. Using the POT VaR formula VaR = u + (β/ξ)[(n/Nu × (1 − c))^(−ξ) − 1], what is the 99% VaR, to the nearest 0.01?

The 99% VaR is about 3.52 million. The ratio n/Nu is 20, times 0.01 gives 0.20; raised to the power −0.2 it equals 1.3797. Subtracting 1 and multiplying by β/ξ of 4 gives 1.519, and adding the threshold of 2.0 gives 3.52.

  1. A3.07
  2. B3.52Correct
  3. C4.00
  4. D2.74

Explanation

n/Nu = 1000/50 = 20, and 1 − c = 0.01, so the product is 0.20. Then 0.20^(−0.2) = e^(0.2 × 1.6094) = e^0.32189 = 1.3797. Subtract 1 to get 0.3797, multiply by β/ξ = 4 to get 1.519, and add u = 2.0 for 3.52. A common mistake is to use 1 − c without scaling by n/Nu, giving 0.01^(−0.2)=2.512, which yields 2 + 4×1.512 = 8.05, not an option.

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