Valuing Real Options using Implied Binomial Trees and Commodity Futures Options

We show how to value a real option on a commodity using an implied binomial tree (IBT) that is calibrated using commodity futures options prices. Until now it has been assumed that spot options are required to be traded on the underlying asset in order to use an IBT; this requirement is, however, typically not met with commodities. We make two major contributions: First, by showing how to implement an IBT when no directly traded options exist, we open the door to calibration of real option models to market-implied probability distributions for commodity prices—including excess skewness and kurtosis, and perceived likelihood of jumps. This is a significant relaxation of the traditional binomial tree’s rigid assumption that commodity prices be distributed lognormal. Second, the existence of long-dated futures options means that our technique allows good volatility estimates to now be incorporated into capital budgeting evaluations of real options projects with long planning horizons. We give an example using gold futures options and a real option to extract gold from a mine.