Published online by Cambridge University Press: 13 September 2010
A multivariate extension of the exponential continuoustime GARCH (p, q)model (ECOGARCH) is introduced and studied.Stationarity and mixing properties of the newstochastic volatility model are investigated, andways to model a component-wise leverage effect arepresented.
The authors are grateful to the editor and twoanonymous referees for their very good commentsand also to Claudia Klüppelberg and Jean Jacod fortheir helpful remarks on a draft of this paper.The second author acknowledges financial supportfrom the Deutsche Forschungsgemeinschaft throughthe graduate program Angewandte AlgorithmischeMathematik at the Technische Universität Münchenduring the initial work on the contents of thispaper.