A Closer Look at ADC Multivariate GARCH

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