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

When choosing the threshold u in a POT analysis, which statement best describes the central trade-off?

A very high threshold leaves too few exceedances, so the GPD parameter estimates have high variance, while a low threshold includes data that are not truly tail observations, so the GPD approximation is biased. Practitioners must balance bias against variance when choosing the threshold.

  1. AA very high threshold leaves few exceedances and gives high variance in parameter estimates, while a low threshold risks bias because the GPD approximation may not holdCorrect
  2. BA high threshold increases bias because the GPD is exact only for the center of the distribution
  3. CA low threshold reduces both bias and variance because more observations are used
  4. DThe threshold has no effect on the estimates if maximum likelihood is used

Explanation

The theorem is asymptotic in the threshold: a low u brings in non-tail data and biases the GPD fit, while a high u leaves few excesses, so estimates of xi and beta are imprecise. This is the bias-variance trade-off.

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