Skip to content

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

An analyst re-estimates a POT-based VaR model and raises the threshold u so that only 10 of 1,000 observations remain as exceedances, compared with 100 previously. What is the most likely consequence?

Raising the threshold lowers the bias of the GPD approximation because the excesses are more truly extreme, but with only 10 exceedances left the shape and scale estimates become much less precise. This is the classic bias-variance trade-off in threshold selection.

  1. ABias from the GPD approximation rises, while parameter estimation variance falls
  2. BBoth bias and estimation variance fall because the tail is purer
  3. CBias in the GPD approximation falls, but the parameter estimates become less preciseCorrect
  4. DNeither bias nor variance changes, since VaR depends only on p

Explanation

A higher threshold makes the GPD a better asymptotic approximation of the excesses, so bias falls. However, only 10 exceedances remain to estimate ξ and β, so estimation variance rises. This is the standard bias-variance trade-off in choosing the threshold.

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