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

A risk manager has estimated a 99.9% one-day VaR from a GPD fitted to exceedances. Which practical concern is MOST relevant to the reliability of this estimate?

The most relevant concern is that the estimate extrapolates well beyond most observed data and is therefore very sensitive to the fitted shape parameter and the threshold. Clustering violates iid assumptions and short backtests have little power at 99.9%, so the other statements are wrong.

  1. AThe estimate extrapolates far beyond most of the data, so it is highly sensitive to the shape parameter and to the threshold choiceCorrect
  2. BThe GPD requires losses to be normally distributed below the threshold
  3. CThe estimate is unaffected by serial dependence such as volatility clustering
  4. DThe estimate can be validated reliably with a few months of backtesting exceptions

Explanation

At extreme confidence levels the estimate rests on few exceedances and on extrapolation, so small changes in the shape parameter or threshold change VaR substantially. EVT assumes roughly iid exceedances, so clustering does matter. Backtesting a 99.9% VaR has very low power over short periods.

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