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

A risk manager uses the GEV distribution for block maxima of daily losses with location μ = 2.0%, scale σ = 1.0% and shape ξ = 0 (Gumbel). Blocks are 20 trading days. The cumulative distribution is F(x) = exp(-exp(-(x-μ)/σ)). What is the loss x such that the block maximum exceeds it with probability 1%? (Use ln(-ln 0.99) = -4.600.)

The 99th percentile of the Gumbel block maximum is μ plus σ times 4.600, which gives 2.0% + 4.6% = 6.6%. This is the loss exceeded by the 20-day block maximum with 1% probability.

  1. A4.0%
  2. B6.6%Correct
  3. C2.0%
  4. D9.2%

Explanation

Set F(x)=0.99: -(x-μ)/σ = ln(-ln 0.99) = -4.600, so x = 2.0% + 1.0% × 4.600 = 6.6%. The 4.0% option wrongly drops the factor and uses 2 times σ; 9.2% doubles the 4.6 term.

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