Index options : a model-free approach

This paper contains an overview and an extension of the theory on comonotonicity-based model-free upper bounds and super-replicating strategies for stock index options, as presented in Hobson et al. (2005) and Chen et al. (2008). Whereas these authors only consider index call options, here a unified approach for call and put options is presented. Considering a unified framework gives rise to an e¢ cient algorithm for calculating upper bounds and for determining the corresponding superhedging strategies for both cases. The unified framework also allows to extend several existing results, in particular on the optimality of the superhedging strategies. Several practical issues concerning the implementation of the results are discussed. In particular, a simplified algorithm is presented for the situation where for some of the constituent stock in the index there are no options available