A semi-parametric conditional autoregressive joint value-at-risk and expected shortfall modeling framework incorporating realized measures

Abstract

A class of realized semi-parametric conditional autoregressive joint Value-at-Risk (VaR) and Expected Shortfall (ES) models is proposed. This class includes novel specifications that allow separate dynamics for VaR and ES, driven by realized measures of volatility. A measurement equation is included in the model class for risk modeling, meaning it generalizes the parametric Realized-GARCH model into the semi-parametric realm. The proposed models implicitly allow the conditional return distribution to change over time via the relationship between VaR and ES. Employing a quasi-likelihood built on the asymmetric Laplace distribution, a Bayesian Markov Chain Monte Carlo method is used for model estimation, whose finite sample properties are assessed via simulation. In a forecasting study applied to 7 indices and 7 assets, one-day-ahead 1% and 2.5% VaR and ES forecasting results support the proposed model class.

Keywords:

• Quantile regression
• Realized measure
• Markov chain Monte Carlo
• Value-at-risk
• Expected shortfall

Acknowledgment

We wish to thank the Editor and two referees for their insightful comments that greatly helped improve the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).