In Sharpe's binomial model, an option can be hedged perfectly, just as in the Black-Scholes-Merton model. The theoretical price of an option is then determined, as in the Black-Scholes-Merton analysis, by the argument that a perfectly hedged portfolio must earn the riskless rate of interest. If the market price of an option deviates from that theoretical price, arbitrage is possible. Investors' attitudes to risk need not be considered, and there is no need to know the probabilities that the stock will move "up" or "down" in price. It is arbitrage, not those probabilities or investors' beliefs about them, that determines the price of an option.

Donald MacKenzie, An Engine, Not a Camera, loc. 608