Journal of Risk

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The role of model risk in extreme value theory for capital adequacy

Harald Scheule, Ralf Kellner and Daniel Rösch

  • We study the impact of model risk on methods from extreme value theory when determining the Value-at-Risk and Expected Shortfall.
  • We distinguish between first order effects of model risk, which consist of misspecification and estimation risk, and second order effects of model risk which refer to the dispersion of risk measure estimates.
  • Our results show that methods from extreme value theory are less prone to first order effects of model risk, however, they exhibit a higher sensitivity to-wards second order effects of model risk. This can lead to severe underesti-mations in extreme cases.

ABSTRACT

In the recent literature, methods from extreme value theory (EVT) have frequently been applied to the estimation of tail risk measures. While previous analyses show that EVT methods often lead to accurate estimates for risk measures, a potential drawback lies in large standard errors of the point estimates in these methods, as only a fraction of the data set is used. Thus, we comprehensively study the impact of model risk on EVT methods when determining the value-at-risk and expected shortfall. We distinguish between first-order effects of model risk, which consist of misspecification and estimation risk, and second-order effects of model risk, which refer to the dispersion of risk measure estimates, and show that EVT methods are less prone to first-order effects. However, they show a greater sensitivity toward secondorder effects. We find that this can lead to severe value-at-risk and expected shortfall underestimations and should be reflected in regulatory capital models.

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