This paper deals with the pricing of American options by solving an optimal stopping problem. We tested two methods for the optimal stop decision, one based on numerical approximations and the other on a neural network, and compared these methods with the binomial pricing, which is the most common method for pricing American options. In the simulations, assets from the Brazilian market were used, divided into 3 asset classes according to their volatility (low, medium and high). It was observed that the options priced with the use of neural networks present lower RMSE for assets classified with medium volatility, higher RMSE for the high volatility case and lower RMSE in the tails (deep in the money and deep out of the money regions) for the low volatility case.