Valuation of an Unexplored Oilfield Under Uncertain Oil Price and Reservoir Condition : A Stochastic Dynamic Programming Approach With Simulationbased Reward Function

Abstract

We develop an unexplored oilfield valuation model under uncertain exploration outcomes, reservoir conditions, and oil prices. The exploration outcomes follow a binomial process, while oil prices are represented using the Schwartz-Smith model. The reservoir conditions are characterized by the joint probability distribution of postdiscovery parameters estimated using a machine learning approach. The corresponding valuation model is a typical stochastic dynamic programming problem with a simulation-based reward function. The net cash flow lattice takes the form of a recombining quadrinomial derived from the discrete representation of the Schwartz-Smith oil price model. We apply backward induction with embedded real-coded genetic algorithms to the net cash flow lattice to calculate the oilfield value. The model allows for field abandonment before lease expiration if the remaining reserve is uneconomical. To improve computational efficiency, we combine the Latin hypercube sampling and antithetic variates to reduce the variances. The model is implemented in an unexplored oilfield under two scenarios of oil presence probability: 100% and 75%. In the first scenario, we obtained a mean oilfield value of US$5.5 million with a CVaR of US$0.79 million, while in the second, we came up with a mean of -US$0.77 million and a CVaR of US$31.74 million.