A Two-Factor Model for Commodity Prices and Futures Valuation

Abstract

This paper develops a new reduced form two-factor model for commodity spot prices and futures valuation. This models extends Schwartz's (1997) two-factor model by adding two new features. First we replace the Ornstein-Uhlenbeck process for the convenience yield by a Cox-Ingersoll-Ross (CIR) process. This ensures that our model is arbitrage free while Schwartz's model does not rule out arbitrage possibilities. Second, we introduce a time-varying volatility for the spot price process. In particular, we consider the spot price volatility is proportional to the square root of the convenience yield level. This implicitly implies that the spot price volatility depends on inventory levels of the commodity as predicted by the theory of storage. We empirically test both models using weekly crude oil futures data from 5th of March 1999 to the 15th of October 2003. In both cases, we estimate the model's parameters using the Kalman filter.

Keywords: commodity prices, futures, Kalman filter, reduced-form model