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

A risk manager at a bank notices that a normal-distribution VaR model repeatedly underestimates losses on days of severe market stress. She proposes extreme value theory (EVT). Which statement best captures the main motivation for using EVT in this setting?

EVT is motivated by the need to model the tail directly. Conventional distributions are fitted mainly to central observations and can badly misstate extreme losses, whereas EVT uses limiting results for extremes. It still requires choosing a threshold or block size and offers no guarantee against exceedances.

  1. AEVT models only the tail of the loss distribution directly, rather than fitting the whole distribution and relying on the centre of the dataCorrect
  2. BEVT guarantees that the estimated tail quantile will never be exceeded in the future
  3. CEVT removes the need to choose any threshold or block size
  4. DEVT assumes losses are normally distributed beyond a chosen cut-off

Explanation

Standard fits are dominated by the bulk of observations and often describe the tails poorly. EVT focuses on the tail itself, using limiting results for extremes. It does not guarantee no exceedances, it requires a block size or threshold choice, and it does not assume normality in the tail.

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