Model Risk of Expected Shortfall

In this paper we study the model risk of Expected Shortfall (ES), extending the results of Boucher et al. (2014) on model risk of Value-at-Risk (VaR). We propose a correction formula for ES based on passing three backtests. Our results show that for the DJIA index, the smallest corrections are required for the ES estimates built using GARCH models. Furthermore, the 2.5% ES requires smaller corrections for model risk than the 1% VaR, which advocates the replacement of VaR with ES as recommended by the Basel Committee. Also, if the model risk of VaR is taken into account, then the correction made to ES estimates reduces by 50% on average.

Keywords: model risk, Expected Shortfall, backtesting.

JEL classi cation: C15, C22, C52, C53, G15.