We compare the ability of the parametric Black and Scholes, Corrado and Su models, and Artificial Neural Networks to price European call options on the S&P 500 using daily data for the period January 1998 to August 2001. We use several historical and implied parameter measures. Beyond the standard neural networks, in our analysis we include hybrid networks that incorporate information from the parametric models. Our results are significant and differ from previous literature. We show that the Black and Scholes based hybrid artificial neural network models outperform the standard neural networks and the parametric ones. We also investigate the economic significance of the best models using trading strategies (extended with the Chen and Johnson modified hedging approach). We find that there exist profitable opportunities even in the presence of transaction costs.