Empirical Comparison of Multivariate GARCH Models for Estimation of Intraday Value at Risk

Abstract

An empirical comparison of forecasting performance is undertaken for multivariate Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models in the estimation of intraday value at risk (VaR). This comparison aims to evaluate the applicability of such models to risk management using high-resolution intraday data as a possible method for analyzing intraday downside risk. The one-step-ahead VaR is determined using time-transformed data, and performance of five multivariate models is compared on the basis of the frequency that the estimated VaR exceeds the observed data and a likelihood ratio test of this rate with respect to real returns. It is thus revealed that existing GARCH models can be readily employed for risk management in an intraday framework simply by transforming the high-resolution irregularly spaced data into a regular time series. The Dynamic Conditional Correlation model is found to provide the best forecasting performance among the multivariate GARCH models tested, and this model is thus considered favorable for practical risk management.