Static-arbitrage optimal subreplicating strategies for basket options

In this paper we investigate the possible values of basket options. Instead of postulating a model and pricing the basket option using that model, we consider the set of all models which are consistent with the observed prices of vanilla options of all strikes. In the case of basket options on two components we find, within this class, the model for which the price of the basket option is smallest. This price, as discovered by Rapuch and Roncalli, is associated to the lower Fréchet copula. We complement their result in this paper by describing an optimal subreplicating strategy. This strategy is associated with an explicit portfolio which consists of being long and short a series of calls with strikes chosen as the zeros of an auxiliary function.