Tail risk forecasting of realized volatility CAViaR models

This research proposes a new class of RES-CAViaR (conditional autoregressive value-at-risk) models, that incorporate daily realized volatility and expected shortfall (ES) to forecast VaR and ES simultaneously. We further consider weekly and monthly realized volatilities in the proposed model to approximate a long-memory process. We employ the Bayesian adaptive Markov chain Monte Carlo approach to estimate all unknown parameters and to jointly predict daily VaR and ES over a 4-year out-of-sample period including the COVID-19 pandemic. Our results show that the realized CAViaR-type models outperform in terms of three backtests, four loss-function criteria, and ES measurement at the 1% level. © 2022 Elsevier Inc.