A Closer Look at ADC Multivariate GARCH

Abstract

In the past thirty years, academia and the marketplace have devoted signi cant e ort and resources toward gaining a better understanding of how volatility changes over time in the nancial markets and how changes in one market a ect changes in another. All of these attempts involve modeling the covariance matrix of two or more asset returns using the period-earlier covariance matrix. In this paper, we outline the volatility modeling process for an Antisymmetric Dynamic Covariance (ADC) multivariate Generalized Autoregressive Conditional Heteroskedacity (GARCH) model, explain the math involved, and attempt to estimate the parameters of the model using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) optimization algorithm. We nd several barriers to estimating parameters using BFGS and suggest using alternative algorithms to estimate the ADC multivariate GARCH in the future.