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, and, within this class, find, in the case of two assets, the model for which the price of the basket option is smallest. This price, as discoveredby Rapuch and Roncalli is associated to the lower Fr\'echet copula. We complement their result in this paper by describing an optimal subreplicating strategy. This strategy is associated to a remarkable portfolio, we refer to as the STP, which consists of being long and short a series of calls with strikes chosen as the zeros of an auxiliary function.