Before revision: We consider as given a discrete time financial market with a risky asset and options written on that asset and determine the sub-hedging price of an American option in the model independent framework of ArXiv: 1301.5568. We also show that the order of min and max in the dual representation of the price can be exchanged .
After revision: We consider as given a discrete time financial market with a risky asset and options written on that asset and determine the sub-hedging price of an American option in the model independent framework of ArXiv: 1305.6008. We obtain the duality of results for the super- and sub-hedging prices. Then assuming that the path space is compact, we construct a discretization of the path space and demonstrate the convergence of the hedging prices at the optimal rate. The latter result would be useful for numerical computation of the hedging prices .