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Title: Bayesian modelling and forecasting of value-at-risk via threshold realized volatility Authors:  Cathy W-S Chen - Feng Chia University (Taiwan) [presenting]
Toshiaki Watanabe - Hitotsubashi University (Japan)
Abstract: A threshold realized GARCH is proposed that jointly models daily returns and realized volatility, thereby taking into account the bias and asymmetry of realized volatility. We incorporate this threshold realized GARCH model with skew Student-t innovations as the observation equation, view this model as a sharp transition model, and treat the realized volatility as a proxy for volatility under this nonlinear structure. Through the Bayesian Markov chain Monte Carlo method, the model can jointly estimate the parameters in the return equation, the volatility equation, and the measurement equation. As an illustration, we conduct a simulation study and apply the proposed method to the U.S. and Japan stock markets. Based on quantile forecasting and volatility estimation, we find that the threshold heteroskedastic framework with realized volatility successfully models the asymmetric dynamic structure. We also investigate the predictive ability of volatility by comparing the proposed model with traditional GARCH as well as some popular asymmetric GARCH and realized GARCH models. This threshold realized GARCH model with skew Student-t innovations outperforms the competing risk models in out-of-sample volatility and VaR forecasting.