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FRM Part II · FRM Exam Part II · Beyond Exceedance-Based Backtesting of Value-at-Risk Models

A bank's two VaR models both pass the Kupiec unconditional coverage test at 99%, each with 2 or 3 exceedances in 250 days. A validator wants to decide which is better. Which approach is most appropriate under a scoring-function framework?

The validator should compare average scores from a consistent scoring function and test whether the difference is statistically significant. Coverage tests only check pass or fail, while scores use loss magnitude and penalise both breaches and excess conservatism, enabling a meaningful ranking.

  1. ACompare their average scores from a consistent scoring function and test whether the difference is statistically significantCorrect
  2. BSelect the model with the higher average VaR, since it is safer
  3. CSelect the model with fewer exceedances regardless of loss size
  4. DChoose the model whose VaR is less volatile over time

Explanation

Passing coverage tests does not discriminate between models. A consistent scoring function evaluated on losses lets the validator rank models, and a significance test on the score difference checks that the ranking is not noise. Higher VaR is penalised for conservatism, and exceedance count ignores magnitude.

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