The Role of Model Risk in Extreme Value Theory for Capital Adequacy

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 second order effects. We find that this can lead to severe value-at-risk and expected shortfall underestimations and should be reflected in regulatory capital models.

Keywords: extreme value theory, model risk, capital requirements, value-at-risk, expected shortfall