Skip to content

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

An analyst applies the block maxima approach to 20 years of daily loss data for an equity index. She chooses blocks of one year each. Which consequence of this design choice is most accurate?

Annual blocks over 20 years yield only 20 maxima, so the GEV is fitted to a very small sample and its parameters are imprecise. Longer blocks improve the asymptotic approximation but reduce data, which is the bias-variance tradeoff in choosing block size.

  1. AShe obtains 20 block maxima, so the sample for GEV estimation is small and parameter estimates will be impreciseCorrect
  2. BShe obtains about 5,000 observations, so estimates are highly precise
  3. CShe must use the peaks-over-threshold method, since block maxima cannot use annual blocks
  4. DShe will have the bias removed because longer blocks make the maxima exactly Gumbel distributed

Explanation

With 20 years and annual blocks there are only 20 maxima. Longer blocks improve the GEV approximation (less bias) but reduce the sample, raising estimation variance. This bias-variance tradeoff is central to block size choice.

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