Geometric Brownian Motion and structural breaks in oil prices: A quantitative analysis

The purpose of this paper is to present a quantitative analyses of oil price's path. We try to argue that, despite its parsimony and simplicity, Geometric Brownian Motion can perform well as a proxy for the movement of oil prices and for a state variable to evaluate oil deposits. We base our argument on evidences of very low speed of mean reverting (or long half-life), since unit root tests only can reject its null hypothesis in a sample longer than 100 years. On the other hand, we reject the null hypothesis of unit root with two endogenous breaks, showing that the usual rejection can be attributed to omitted structural breaks. We conclude that the average half-life of oil price (between 4 and 8 years depending on the model chosen) is long enough to allow a good approximation as a Geometric Brownian Motion.