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

A risk team has 10 years of daily loss data (about 2,500 observations) and wants a 99.9% VaR estimate. They compare a historical simulation estimate with an EVT peaks-over-threshold estimate. Which statement is most accurate regarding the trade-off in choosing the threshold for the EVT approach?

Raising the threshold improves the validity of the generalised Pareto approximation, lowering bias, but leaves fewer exceedances and so increases the variance of estimated parameters. A low threshold gives more data but more bias. This bias-variance trade-off is the central difficulty in peaks-over-threshold estimation.

  1. AA very high threshold lowers bias but leaves few exceedances, raising the variance of the parameter estimatesCorrect
  2. BA very high threshold raises bias and lowers variance because more exceedances are retained
  3. CA very low threshold lowers bias because the generalised Pareto approximation is then most accurate
  4. DThe threshold choice affects only the scale parameter, not the shape parameter

Explanation

The generalised Pareto approximation is valid only far in the tail, so a high threshold reduces bias. But fewer observations exceed it, so estimates become noisy (higher variance). A low threshold does the opposite: more data but the approximation may be poor, adding bias. Threshold choice affects both parameters.

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