Tail risk forecasting using Bayesian realized EGARCH models

TL;DR

This paper introduces a Bayesian realized EGARCH model that incorporates multiple realized volatility measures and heavy-tailed distributions, improving tail risk forecasts like VaR and ES.

Contribution

It develops a Bayesian framework for realized EGARCH models with multiple realized measures and heavy-tailed distributions, enhancing tail risk forecasting accuracy.

Findings

Bayesian estimators outperform maximum likelihood in simulations.

Models with skewed Student-t distribution and sub-sampled realized range excel in tail risk forecasts.

Realized EGARCH models provide superior one-step-ahead VaR and ES predictions.

Abstract

This paper develops a Bayesian framework for the realized exponential generalized autoregressive conditional heteroskedasticity (realized EGARCH) model, which can incorporate multiple realized volatility measures for the modelling of a return series. The realized EGARCH model is extended by adopting a standardized Student-t and a standardized skewed Student-t distribution for the return equation. Different types of realized measures, such as sub-sampled realized variance, sub-sampled realized range, and realized kernel, are considered in the paper. The Bayesian Markov chain Monte Carlo (MCMC) estimation employs the robust adaptive Metropolis algorithm (RAM) in the burn in period and the standard random walk Metropolis in the sample period. The Bayesian estimators show more favourable results than maximum likelihood estimators in a simulation study. We test the proposed models with several indices to forecast one-step-ahead Value at Risk (VaR) and Expected Shortfall (ES) over a period of 1000 days. Rigorous tail risk forecast evaluations show that the realized EGARCH models employing the standardized skewed Student-t distribution and incorporating sub-sampled realized range are favored, compared to a range of models.