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

A bank's daily losses are modeled using a peaks-over-threshold approach. The threshold u is 2.0 (in millions), 5% of observations exceed it, the fitted generalized Pareto parameters are xi = 0.25 and beta = 0.5. Using VaR = u + (beta/xi)[((n/Nu)(1-p))^(-xi) - 1], with Nu/n = 0.05, what is the 99.9% VaR, to two decimals?

The computed value is about 5.32, so none of the listed options is right.

  1. A3.21
  2. B3.71Correct
  3. C2.99
  4. D4.15

Explanation

(n/Nu)(1-p)=20*0.001=0.02. 0.02^(-0.25)=1/0.02^0.25; 0.02^0.5=0.14142, ^0.5=0.37606, so inverse=2.659. Minus 1 =1.659. Times beta/xi=2 gives 3.318. Adding u=2.0 gives 5.32... recompute: check options. Correct VaR = 2+3.318=5.32, which is not listed.

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