The Role of Model Risk in Extreme Value Theory for Capital Adequacy
Journal of Risk 18(6), 2016, 39-70
Posted: 28 Feb 2018
Date Written: 2016
In the recent literature, methods from extreme value theory (EVT) have frequently been applied for 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 high standard errors of point estimates of these methods as only a fraction of the data set is used. Thus, the aim of this paper is to comprehensively study the impact of model risk on EVT methods when determining the Value-at-Risk and Expected Shortfall. We distinguish between misspecification, estimation and prediction risk and show that methods from extreme value theory are less prone to misspecification and estimation risk, however, they exhibit a higher sensitivity towards prediction risk. We find that this can lead to more severe Value-at-Risk and Expected Shortfall underestimations than for traditional estimation methods in extreme cases. Hence, we show how sources of model risk should be taken into account for the quantification of capital requirements, in order to provide sufficient capital levels in the presence of model risk.
Keywords: Extreme Value Theory, Model Risk, Capital Requirements, Value-at-Risk, Expected Shortfall
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