Bayesian Tail Risk Forecasting using Realised GARCH

Abstract

A Realised Volatility GARCH model is developed within a Bayesian framework for the purpose of forecasting Value at Risk and Conditional Value at Risk. Student-t and Skewed Student-t return distributions are combined with Gaussian and Student-t distributions in the measurement equation in a GARCH framework to forecast tail risk in eight international equity index markets over a four year period. Three Realised Volatility proxies are considered within this framework. Realised Volatility GARCH models show a marked improvement compared to ordinary GARCH for both Value at Risk and Conditional Value at Risk forecasting. This improvement is consistent across a variety of data, volatility model speci_cations and distributions, and demonstrates that Realised Volatility is superior when producing volatility forecasts. Realised Volatility models implementing a Skewed Student-t distribution for returns in the GARCH equation are favoured.