Skip to content

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

A risk manager notes that estimated GEV parameters for monthly maximum losses change materially when the block length is changed from one month to one quarter. Which explanation is most consistent with extreme value theory?

Longer blocks shift the location and scale parameters, since maxima of larger blocks are larger and more dispersed, but the tail index should stay roughly constant because it reflects the underlying distribution's tail. Material changes in the tail index point to estimation noise or a poor approximation.

  1. AThe tail index ξ should be identical in every case, so the changes indicate an error in the theory, not in the data
  2. BOnly the location and scale parameters should change with block length, while the tail index ξ should remain approximately the same if the GEV approximation holdsCorrect
  3. CThe tail index must double when block length triples, because maxima scale linearly with time
  4. DGEV parameters are independent of block size, so any change reflects only sampling noise in the mean return

Explanation

Under extreme value theory, the tail index characterizes the tail of the underlying distribution and is invariant to block length, whereas location and scale grow with block size. Large shifts in ξ suggest small-sample noise or poor approximation, but the stable-ξ expectation is the key idea.

Did you get it right without looking?

One question tells you little. A timed set on Parametric Approaches (II): Extreme Value shows your real accuracy, how long you take and where you lose marks.

Practise Parametric Approaches (II): Extreme ValueFree diagnostic mock

More Parametric Approaches (II): Extreme Value questions