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

Abstract

Expected shortfall (ES) and value at risk (VaR) are two of the most widely used risk measures in economics and finance. In this paper, we incorporate realized variance measures into structural models for the two risk measures. Our estimation procedure is semiparametric and relies on using a class of consistent loss functions proposed by Fissler and Ziegel (2016). We develop an efficient and stable two-stage method to implement the estimations. We then compare performances of out-of-sample forecasts from the estimated structural models with some existing methods, including several recently proposed novel models. We demonstrate that the proposed structure models with realized variance measures overall deliver superior forecasts of ES and VaR for major stock indices than the considered existing methods. An analysis of model averaging further shows that aggregating information from different methods can improve performances of the forecasts, and information from models with realized variance measures is indispensable for generating a superior model averaging forecast.

Keywords: Expected shortfall, Forecast, Realized variance measure, Semiparametric estimation, Value-at-risk

JEL Classification: C22, C53, C58, G17