The two-factor price process in optimal sequential exploration

Abstract

In a group of exploration prospects with common geological features, drilling a well reveals information about chances of success in others. In addition, oil prices vary during the exploration campaign and with them so do the economics of wells and the optimal decision to drill. With these dependencies and price dynamics, where do we drill first and what comes next given success or failure in previous wells? The solution to this valuation problem should compare the value of learning (drilling wells that provide valuable information) with the uncertain value of earning (drilling wells that have large payoffs, yet uncertain). We calculate a joint distribution for geological outcomes by applying information-theoretic methods and construct a two-dimensional binomial sequence to represent a two-factor stochastic price process. We then propose a Markov decision process that solves the optimal exploration problem. An Excel® VBA software implementation of this algorithm accompanies this paper.