A new realized joint Value-at-Risk (VaR) and expected shortfall (ES) regression framework is proposed, through incorporating a measurement equation into the original joint VaR and ES regression model . The measurement equation models the contemporaneous dependence between the realized measures (e.g. Realized Variance and Realized Range) and the latent conditional quantile. Further, sub-sampling and scaling methods are applied to both the realized range and realized variance, to help deal with the inherent micro-structure noise and inefficiency. An adaptive Bayesian Markov Chain Monte Carlo method is employed for estimation and forecasting, whose properties are assessed and compared with maximum likelihood estimator through simulation study. In a forecasting study , the proposed models are applied to 7 market indices and 2 individual assets, compared to a range of parametric, non-parametric and semi-parametric models, including GARCH, Realized-GARCH, CARE and Taylor (2017) joint VaR and ES quantile regression models, one-day-ahead Value-at-Risk and Expected Shortfall forecasting results favor the proposed models, especially when incorporating the sub-sampled Realized Variance and the sub-sampled Realized Range in the model.
A new realized conditional autoregressive Value-at-Risk (VaR) framework is proposed, through incorporating a measurement equation into the original quantile regression model. The framework is further extended by employing various Expected Shortfall (ES) components, to jointly estimate and forecast VaR and ES . The measurement equation models the contemporaneous dependence between the realized measure (i.e., Realized Variance and Realized Range) and the latent conditional ES. An adaptive Bayesian Markov Chain Monte Carlo method is employed for estimation and forecasting, the properties of which are assessed and compared with maximum likelihood through a simulation study. In a comprehensive forecasting study on 1\% and 2.5 \% quantile levels , the proposed models are compared to a range of parametric, non-parametric and semi-parametric models, based on 7 market indices and 7 individual assets. One-day-ahead VaR and ES forecasting results favor the proposed models, especially when incorporating the sub-sampled Realized Variance and the sub-sampled Realized Range in the model.
R
joint
conditional autoregressive
D
and expected shortfall (ES) regression
R
joint
quantile regression model. The framework is further extended by employing various Expected Shortfall (ES) components, to jointly estimate and forecast
D
regression model
R
measures (e.g.
measure (i.e.,
R
quantile. Further, sub-sampling and scaling methods are applied to both the realized range and realized variance, to help deal with the inherent micro-structure noise and inefficiency.
ES.
R
whose properties
the properties of which
R
estimator through
through a
R
forecasting study
comprehensive forecasting study on 1\% and 2.5 \% quantile levels
D
applied to 7 market indices and 2 individual assets,
R
including GARCH, Realized-GARCH, CARE and Taylor (2017) joint
based on 7 market indices and 7 individual assets. One-day-ahead
D
quantile regression models, one-day-ahead Value-at-Risk and Expected Shortfall