Abstract
In this paper, we propose a commodity pricing model that extends Gibson-Schwartz two-factor model to incorporate the effect of linear relations among commodity prices, which include co-integration under certain conditions. We derive futures and call option pricing formulae, and show that unlike Duan and Pliska (2004), the linear relations among commodity prices, or the error correction term, should affect the commodity derivative prices even if volatilities of commodity returns are constant. Using crude oil and heating oil market data, we estimate the proposed model. The result suggests that the error correction between these commodity prices partly explains the deviation of drifts from risk-free rate, which has been treated as convenience yield in preceding models, in commodity returns, and hence affects their derivative prices empirically.
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