Multivariate option price models and extremes

We consider the Cox-Ross-Rubinstein model of option prices which is a simple binomial model and deal with its multivariate extensions. The model consists of n independent up or down movements of the (multivariate) price. We discuss the model in the view of the limiting distributions for the price as well for the extreme changes of the prices during a period T which is split up into n small price changes, which depend on n (with nh = T). Interesting is also whether the components of the prices and of the extremes are asymptotically dependent.