FRM Part II · FRM Exam Part II · Parametric Approaches (II): Extreme Value
Using the peaks-over-threshold method with a threshold u = 2.0%, a fitted generalized Pareto distribution has β = 0.60 and ξ = 0.20. The EVT-based 99% VaR is 3.00%. What is the corresponding 99% expected shortfall?
The expected shortfall is 4.00%. Under the generalized Pareto tail, ES equals VaR plus β minus ξ times u, all divided by one minus ξ. That is (3.00 + 0.60 − 0.40) divided by 0.80, which equals 4.00%.
- A4.00%Correct
- B4.50%
- C3.75%
- D2.67%
Explanation
ES = (VaR + β − ξu)/(1 − ξ) = (3.00 + 0.60 − 0.40)/0.80 = 3.20/0.80 = 4.00%. Omitting the −ξu adjustment gives 4.50%. Dividing VaR by (1−ξ) alone gives 3.75%. Dividing by (1+ξ) gives 2.67%, which is also wrong.
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