Efficient Stock

A Two-Factor Model for Commodity Prices and Futures Valuation∗

Diana R. Ribeiro† Stewart D. Hodges‡ August 25, 2004

Abstract This paper develops a reduced form two-factor model for commodity spot prices and futures valuation. This model extends the Gibson and Schwartz (1990)-Schwartz (1997) two-factor model by adding two new features. First the Ornstein-Uhlenbeck process for the convenience yield is replaced by a Cox-Ingersoll-Ross (CIR) process. This ensures that our model is arbitrage-free. Second, spot price volatility is proportional to the square root of the convenience yield level. We empirically test both models using weekly crude oil futures data from 17th of March 1999 to the 24th of December 2003. In both cases, we estimate the models parameters using the Kalman filter.

We would like to thank Elizabeth Whalley and Mathias Muck for their helpful comments. Earlier versions of this paper were presented at the Finance Seminar Series at the Warwick Business School, the European Financial Management Association 2004 meeting and the Bachelier Finance Society Third World Congress. Comments from the seminar and conference participants were much appreciated. The first author would like to thank the financial support from the Fundacao para a Ciencia e Tecnologia, Portugal. † Doctoral Researcher at the Warwick Business School, University of Warwick, Coventry, CV4 7AL, United Kingdom, phone +44 (0)24 76524465, fax: +44 (0)24 7652 7167 and email: D.Ribeiro@wbs.ac.uk ‡ Director of the Financial Options Research Center (FORC), Warwick Business School, University of Warwick, Coventry CV4 7AL, United Kingdom, phone: +44 (0)24 76523606, fax: +44 (0)24 7652 4176 and email Stewart.Hodges@wbs.ac.uk

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Introduction

In this paper, we introduce a new reduced form model for commodity spot prices and futures valuation which builds on and extends the reduced form models in the literature. The earliest reduced form model for commodity prices appears to be due...