Petroleum concessions with extendible options: Investment timing and value using mean reversion and jump processes for oil prices

The owner of a petroleum exploration concession in Brazil has an investment option until the expiration date fixed by the governmental agency, which can be extended by additional cost. The value of these rights and the optimal investment timing are calculated by solving a stochastic optimal control problem of an American call option with extendible maturities. The uncertainty of the oil prices is modeled as a mix diffusion-jump process. Normal information arrival generates continuous mean-reverting process for oil prices, whereas a random abnormal information generates a discrete jump of random size. Comparisons are performed with the popular geometric Brownian process and also the quantification and analysis of alternative timing policies for the petroleum sector.