We propose a family of nonparametric estimators for an option price that require only the use of underlying return data, but can also easily incorporate available option prices. Each estimator comes from a risk-neutral measure minimizing generalized entropy according to a different Cressie-Read discrepancy function. In a large-scale empirical application with S&P 500 options, we investigate their out-of-sample pricing accuracy using different amounts of option data in the estimation. Relying only on underlying returns, our estimators significantly outperform the Black-Scholes and GARCH option pricing models. Using up to three options, our method delivers performance comparable to (and often better than) the ad-hoc Black-Scholes that exploits information from the whole cross-section of options. Overall, we provide a powerful option pricing technique suitable for limited option data availability.