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.
