A program in C++ was used to evaluate American calls using both the approaches of Monte Carlo Simulation and Dynamic Programming. Its main purpose is to evaluate expanding options in a developed oil field. The investment is considered under both economic and technical uncertainties, what is common place in petroleum exploration and production problems. In order to model the commodity price, the Dias and Schwartzs mean reversion processes were used. The influences of the risk free rate, the exercise price, the mean reversion speed, the field depletion, the volatility and the oil long term price in the value of the real option were studied. Besides that, optimal exercise frontiers were obtained as a rule for the early exercise. The results obtained in this dissertation were compared to the results expected by the financial option theory, which models stocks prices using the Geometric Brownian Motion.