Skip to content

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

A risk manager fits a generalized Pareto distribution to losses above a threshold and is deciding how to set the threshold. Which statement best describes the trade-off involved?

A low threshold brings in non-tail observations and biases the tail estimates, while a high threshold leaves few exceedances and raises estimator variance. The threshold choice therefore balances bias against variance. Saying a higher threshold lowers variance reverses this relationship.

  1. AA higher threshold lowers the variance of the tail parameter estimates but increases bias because fewer observations are used
  2. BA lower threshold increases the bias of the tail estimates because it admits observations that are not in the tail, while a higher threshold increases estimator variance because fewer exceedances remainCorrect
  3. CA lower threshold reduces both bias and variance because more data are used
  4. DThe threshold has no effect on estimates once the GPD is fitted by maximum likelihood

Explanation

Choosing the threshold is a bias-variance trade-off. Too low a threshold includes central observations that the GPD does not describe, causing bias. Too high a threshold leaves few exceedances, causing noisy estimates. The first option reverses the roles of bias and variance.

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