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Forecasting Expected Shortfall and Value-at-Risk with the FZ Loss and Realized Variance Measures

Value at risk (VaR) and expected shortfall (ES) are two of the most widely used risk measures in economics and finance. In this paper, we use a semiparametric method, together with realized variance measures, to jointly estimate structural models for the two risk measures. The semiparametric estimations rely on using a class of consistent loss functions recently proposed by Fissler and Ziegel (2016). We develop an efficient and stable two-stage method to implement the estimations. We then compare out-of-sample forecast performances from the estimated structural models with other existing methods. Through comprehensive evaluations with different performance measures, we find the proposed models featuring with the realized variance measures as exogenous variables can deliver comparable or even better performances on forecasting VaR and ES of major stock indices around the world than the existing methods.