The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging

TLDR

The study compares three mean‑reverting commodity price models to evaluate their ability to price existing futures contracts and to assess implications for valuing other financial and real assets. Using a Kalman filter, the authors estimate a one‑factor spot‑price model, a two‑factor model including convenience yield, and a three‑factor model adding stochastic interest rates for copper, oil, and gold, then analyze the resulting term structure, hedging strategies, and capital‑budgeting decisions. The analysis shows strong mean reversion in commercial commodity prices.

Abstract

ABSTRACT In this article we compare three models of the stochastic behavior of commodity prices that take into account mean reversion, in terms of their ability to price existing futures contracts, and their implication with respect to the valuation of other financial and real assets. The first model is a simple one‐factor model in which the logarithm of the spot price of the commodity is assumed to follow a mean reverting process. The second model takes into account a second stochastic factor, the convenience yield of the commodity, which is assumed to follow a mean reverting process. Finally, the third model also includes stochastic interest rates. The Kalman filter methodology is used to estimate the parameters of the three models for two commercial commodities, copper and oil, and one precious metal, gold. The analysis reveals strong mean reversion in the commercial commodity prices. Using the estimated parameters, we analyze the implications of the models for the term structure of futures prices and volatilities beyond the observed contracts, and for hedging contracts for future delivery. Finally, we analyze the implications of the models for capital budgeting decisions.