The timing of development and the optimal production scale: A real option approach to oilfield E&P

Petroleum exploration in Brazil is performed throughout a bidding process coordinated by the National Petroleum Agency (NPA), where the exploration and production (E&P) firms need to evaluate concessions performing financial and economic analyses routinely. Since oil is a public resource with economic and strategic value for the country, the governmental agency should have control over the financial and economic pricing techniques. The E&P firm holds the investment opportunity to develop a delineated oilfield. The oilfield development investment plan shall be presented to NPA until a specific date or the oilfield rights returns back to NPA. The oilfield can be developed up to a specific time through three mutually exclusive alternatives representing the oilfield production and exploration scale. The developed oilfield is proportional to the price of oil, which evolves according to a stochastic differential equation. The E&P firm considers three mutually exclusive alternatives of scale to exploit the oilfield, with different investment costs. The investment opportunity is analogous to an American call option with finite time to maturity and payoff equal to that of the developed oilfield (underlying asset) minus the development cost of the optimal alternative (exercise price). We obtain the investment opportunity value and the optimal development rule for the oilfield, i.e., the optimal development timing and the optimal production scale as function of the current oil price and the economic uncertainty of the market.