Except for the Black-Scholes model, financial models are typically incomplete: claims cannot usually be hedged, and there are infinitely many equivalent martingale measures, implying that options do not have a unique price. We will discuss the possible range for the price of a European option, and show that in some cases it is possible to complete the model by adding to the stock price the price of a traded option. This is a preliminary work, with a few simple results and mainly open questions, even for very elementary incomplete models.