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

A risk manager estimates the 99.9% one-day VaR by fitting a GPD to losses. Which practical issue most directly limits confidence in the extreme-quantile estimate?

The main limitation is extrapolation into the far tail based on very few exceedances. The estimate depends heavily on the fitted tail shape and threshold, so sampling error is large and model uncertainty is material, even though EVT provides a principled way to extrapolate.

  1. AExtrapolating far beyond the observed data, which leaves the estimate dependent on few tail observations and on the assumed tail modelCorrect
  2. BThe GPD requires losses to be symmetric around zero
  3. CUsing exceedances rather than the full sample always increases the sample size
  4. DEVT cannot be applied to financial returns because they are independent

Explanation

Extreme quantiles lie near or beyond the largest observations, so estimates rely on a handful of exceedances and on the assumed tail form; standard errors are large. GPD fits only the tail and does not need symmetry. Exceedance approaches use fewer, not more, observations. Returns are not independent, which is itself a complication.

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