A Bayesian realized threshold measurement GARCH framework for financial tail risk forecasting

TL;DR

This paper introduces a Bayesian realized threshold GARCH model that improves tail risk forecasting by incorporating a nonlinear threshold measurement equation and leverage effects, evaluated through empirical and simulation studies.

Contribution

It develops a novel threshold measurement equation within a Bayesian Realized-GARCH framework, enhancing tail risk prediction accuracy over existing models.

Findings

Competitive tail risk forecasting performance

Effective modeling of leverage effects

Validated through empirical and simulation studies

Abstract

This paper proposes an innovative threshold measurement equation to be employed in a Realized-GARCH framework. The proposed framework incorporates a nonlinear threshold regression specification to consider the leverage effect and model the contemporaneous dependence between the observed realized measure and hidden volatility. A Bayesian Markov Chain Monte Carlo method is adapted and employed for model estimation, with its validity assessed via a simulation study. The validity of incorporating the proposed measurement equation in Realized-GARCH type models is evaluated via an empirical study, forecasting the 1% and 2.5% Value-at-Risk and Expected Shortfall on six market indices with two different out-of-sample sizes. The proposed framework is shown to be capable of producing competitive tail risk forecasting results in comparison to the GARCH and Realized-GARCH type models.