Skip to content

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

A bank has 2,000 daily loss observations. Using peaks-over-threshold, the analyst sets a threshold u equal to the 95th percentile of losses, so 100 observations exceed it. Which statement about choosing the threshold is correct?

Raising the threshold improves the validity of the GPD approximation and reduces bias, but it leaves fewer exceedances and increases the variance of the estimates. Lowering it does the opposite, so threshold choice is a bias-variance trade-off.

  1. ARaising the threshold lowers bias from the asymptotic approximation but leaves fewer exceedances, raising estimator varianceCorrect
  2. BLowering the threshold always reduces both bias and variance because more data are used
  3. CThe threshold has no effect on the estimates if the GPD is correctly specified for the whole sample
  4. DThe threshold should be set at the sample mean so that the exceedances are centered

Explanation

There is a bias-variance trade-off. A high threshold makes the GPD approximation more accurate (less bias) but leaves few exceedances, so parameter estimates are noisy. A low threshold uses more data (lower variance) but the GPD fits less well (more bias). Both claims of a free lunch are wrong.

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