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

A risk manager fits a generalized Pareto distribution to exceedances over a threshold and notices that the estimated tail index and the resulting 99.9% VaR change sharply when the threshold is moved from the 95th to the 97th percentile of losses. Which interpretation is most appropriate?

The sensitivity reflects the bias-variance trade-off in selecting the threshold. Low thresholds increase bias, high thresholds leave few exceedances and increase variance. The analyst should examine stability across thresholds and report the uncertainty instead of relying on a single choice.

  1. AThe result shows the data are normally distributed in the tail
  2. BThe estimate reflects the bias-variance trade-off in threshold choice, so the sensitivity should be examined and reported rather than ignoredCorrect
  3. CThe higher threshold must be correct because it is always more accurate
  4. DSensitivity is a sign the peaks-over-threshold method cannot be used with any dataset

Explanation

A low threshold brings more data (lower variance) but risks bias because the GPD approximation is poorer; a high threshold reduces bias but leaves few exceedances and noisy estimates. Sensitivity should be assessed, for example through stability plots. A higher threshold is not automatically better.

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