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

A risk analyst at a bank wants to estimate the 99.9% VaR of daily trading losses using only the extreme tail observations rather than fitting a distribution to the full sample. What is the main motivation for using extreme value theory (EVT) in this situation?

EVT is motivated by the need to model rare, extreme losses. It concentrates on the tail and applies a limiting distribution derived from theory, allowing extrapolation beyond observed data, whereas fitting the central part of a distribution gives poor information about extreme quantiles such as 99.9%.

  1. AEVT provides a tail model for rare extreme events where the central part of the distribution gives little informationCorrect
  2. BEVT guarantees that VaR estimates will equal the historical simulation estimate
  3. CEVT removes the need to make any assumptions about the shape of the tail
  4. DEVT assumes returns are normally distributed so tail estimates are more reliable

Explanation

Standard methods fit the bulk of the data, which says little about extremes beyond the sample. EVT focuses only on the tail and uses a theoretically justified limiting distribution to extrapolate to rare events. It does not assume normality, and it does make tail-shape assumptions (a GEV or GPD form).

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