In this paper we build on the possibility that the use of the Cressie–Read family with the non-parametic method for valuing European option might be extended to non-parametric valuation of American options. We derive a suite of non-parametric methods to price and hedge American-style options, utilising the Cressie-Read family of divergences. We test the efficacy of these methods using a large sample of traded American-style options struck on the S&P100 index. We find that in general, our suite of non-parametric valuation schemes generate more accurate price estimates than traditional parametric schemes, especially for longer-dated options.