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

Daily losses show volatility clustering, so extreme losses tend to occur in bunches. A risk manager wants to apply peaks-over-threshold EVT to these data. Which approach best addresses the problem?

Filter the returns with a conditional volatility model such as GARCH and apply EVT to the standardized residuals, which are closer to iid. The tail estimate can then be scaled by current volatility. Applying EVT to raw clustered losses violates the independence assumption.

  1. AApply the GPD directly to raw losses, since clustering has no effect on the iid assumption
  2. BFilter the data with a volatility model such as GARCH, then apply EVT to the standardized residualsCorrect
  3. CDrop all observations from high-volatility periods
  4. DReplace the GPD with a normal distribution for exceedances

Explanation

Basic EVT assumes approximately iid observations, which clustering violates. Fitting a conditional volatility model and applying EVT to the roughly iid standardized residuals addresses this, and the tail quantile can be rescaled by current volatility. Removing high-volatility periods discards the very tail data of interest.

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