Valuing Real Options using Implied Binomial Trees and Commodity Futures Options

Abstract

A real option on a commodity is valued using an implied binomial tree (IBT) calibrated using commodity futures options prices. Estimating an IBT in the absence of spot options (the norm for commodities) allows real option models to be calibrated for the first time to market-implied probability distributions for commodity prices. Also, the existence of long-dated futures options means that good volatility estimates may now be incorporated into capital budgeting evaluations of real options projects with long planning horizons. An example is given using gold futures options and a real option to extract gold from a mine. We include a unique out-of-sample test that shows how option pricing errors evolve on sub-trees emanating from future levels of the underlying.