Risk Management in Commodity Markets: From Shipping to Agriculturals and Energy

12

Mean-Reversion and Structural Breaks in Crude Oil, Copper, and Shipping

Hélyette Geman and Steve Ohana

12.1 INTRODUCTION

Commodity prices have been rising at an unprecedented pace over the last seven years. As depicted in Fig. 12.2, an investment of $100 made in January 2002 in the global Dow Jones AIG Commodity Index had more than doubled by July 2006 while Fig. 12.3 indicates that these $100 invested in the Dow Jones AIG Energy sub-index had turned into $500 in July 2005.

The increase of prices in the last three years has been even more dramatic, with a huge demand coming from China, India, and developing countries. In the case of commodities like copper and crude oil, the issue of exhaustibility and depleting reserves is certainly one element that contributes to the irresistible ascension of prices displayed in Fig. 12.3. As far as shipping is concerned, the explosion of international trade in iron ore, coal and cereals has greatly outpaced the capacity of shipyards and translated into large spikes in freight indexes such as the Baltic Dry Index described in Section 12.2.

The financial literature on commodity price modeling started with the pioneer paper of Gibson and Schwartz (1990), dedicated to the valuation of options on oil. In the spirit of the Black-Scholes-Merton (1973) model, they chose a geometric Brownian motion for the crude oil price process. Given the behavior of commodity prices during the 1990s depicted in Fig. 12.1, Schwartz (1997) decided to turn to a mean-reverting ...