Realized beta GARCH : a multivariate GARCH model with realized measures of volatility

Abstract

We introduce a multivariate generalized autoregressive conditional heteroskedasticity (GARCH) model that incorporates realized measures of variances and covariances. Realized measures extract information about the current levels of volatilities and correlations from high-frequency data, which is particularly useful for modeling financial returns during periods of rapid changes in the underlying covariance structure. When applied to market returns in conjunction with returns on an individual asset, the model yields a dynamic model specification of the conditional regression coefficient that is known as the beta. We apply the model to a large set of assets and find the conditional betas to be far more variable than usually found with rolling-window regressions based exclusively on daily returns. In the empirical part of the paper, we examine the cross-sectional as well as the time variation of the conditional beta series during the financial crises.