Semiparametric GARCH models for value-at-risk and expected shortfall: an object-driven procedure

Yuanhua Feng and Christian Peitz

Abstract

This paper applies the semiparametric generalized autoregressive conditional heteroscedasticity (GARCH) models to calculate value-at-risk (VaR) and expected shortfall (ES) based on an object-driven smoothing approach. In the first stage, the scale function is estimated with numerous given bandwidths, and different GARCH models are fitted to the descaled returns. Suitable models are then filtered using different backtesting methods, including a recent traffic light approach for backtesting the ES. A new loss function for a firm’s ES is introduced and used as the main object function for selecting the best model in the final stage. Empirical applications demonstrate that the proposed procedure effectively identifies models with good out-of-sample performance for VaR and ES forecasting. Moreover, the proposed object-driven smoothing procedure is applicable to other research areas.