Abstract
Embraced by the Basel accords, value-at-risk and expected shortfall are the major measures of financial risk. This research thus proposes a realized hysteretic GARCH model that is a three-regime nonlinear framework combined with daily returns and realized volatility. The hysteresis model with two thresholds is similar to a three-regime realized GARCH model, but when the hysteresis variable lies in a hysteresis zone, our set-up allows the mean and volatility switching in a regime to be delayed. The characteristic of this nonlinear model presents explosive persistence and dynamic conditional volatility in regime one in order to capture extreme cases. We employ the Bayesian Markov chain Monte Carlo (MCMC) procedure to estimate all model parameters efficiently and to forecast volatility, VaR, and ES. A simulation study illustrates favorable precision in estimation and forecasting. We also implement the realized GARCH and the realized threshold GARCH models for comparing their quantile forecasts, incorporate the skew student-t distribution into the risk models for estimation and forecasting, and carry out Bayesian risk forecasting via predictive distributions on four international stock markets as our empirical demonstration. The out-of-sample period covers the recent four years by a rolling window approach, which includes the COVID-19 pandemic period. Among the realized models, the realized hysteretic GARCH model outperforms at the 1% level in terms of violation rates and backtests.