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

An analyst has 1,000 daily loss observations (in % of portfolio value). Fifty losses exceed the threshold u = 2.0%. A GPD fitted to the exceedances gives shape ξ = 0.2 and scale β = 0.5. Using the POT formula VaR = u + (β/ξ)[(n/Nu × (1 − α))^(−ξ) − 1], what is the 99% VaR?

The 99% VaR is about 2.95%. The tail probability scaled by n/Nu is 0.2, raised to the power −0.2 gives 1.3797, less one is 0.3797, times β/ξ of 2.5 is 0.949, and adding the 2.0% threshold gives 2.95%.

  1. AApproximately 2.95%Correct
  2. BApproximately 5.45%
  3. CApproximately 5.78%
  4. DApproximately 1.31%

Explanation

n/Nu × (1 − α) = 20 × 0.01 = 0.2. Then 0.2^(−0.2) = e^(0.2 × 1.6094) ≈ 1.3797, minus 1 gives 0.3797. Multiplying by β/ξ = 2.5 gives 0.949, so VaR = 2.0 + 0.949 ≈ 2.95%. Omitting the −1 gives 5.45%, which is wrong because the term in brackets must be reduced by 1. Using the sign-flipped exponent gives 1.31%.

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