Backtesting VaR Estimates of HEAVY Models Using the Geometric-VaR Test

This paper examines the Geometric-VaR test of Pelletier and Wei (2016) as a framework for backtesting Value-at-Risk (VaR) estimates. This study confirms that the test provides good power properties against various forms of misspecification of VaR estimates, although slightly lower power is reported for smaller sample sizes compared to earlier research. The Geometric-VaR test is subsequently employed to investigate the HEAVY model of Shephard and Sheppard (2010) – an adaption of a standard GARCH model that incorporates realised measures – in the context of VaR estimation. Additionally, an asymmetric extension of the HEAVY model is introduced. 19 different models are tested using data of 21 equity indices over the period 2000-2017. A semi-parametric approach using Filtered Historical Simulation is found to provide better results than fully-parametric approaches. Additionally, this paper finds no evidence that the HEAVY models provide better VaR estimates than their GARCH counterparts over the entire sample period investigated. Notably, the HEAVY models perform significantly better during the global financial crisis of 2008, thus suggesting that they can be a valuable addition to a risk manager’s toolkit during volatile periods.