[This paper shows that economic linkages among commodities create a source of long-term correlation between futures returns. We extend the theory of storage to a multi-commodity level and find that the convenience yield of a commodity depends on its relative scarcity with respect to other related commodities. This implies a feedback effect between commodities that is necessary to replicate the upward-sloping correlation term structure of futures returns observed for related commodities. We present a multi-commodity affine model that validates our theoretical predictions and considerably reduces the pricing errors in out-of-sample crack spread options.]

One distinguishable feature of storable commodities is that they relate to two markets: cash market and storage market. This paper proves that, if no arbitrage exists in the storage-cash dual markets, the commodity convenience yield has to be non-negative. However, classical reduced-form models for futures term structures could allow serious arbitrages due to the high volatility of the convenience yield. To avoid negative convenience yield, this paper proposes a semi-affine arbitrage-free model, which prices futures analytically and fits futures term structures reasonably well. Importantly, our model prices commodity-related contingent claims (such as calendar spread options) quite differently with classical models.

This paper shows that economic linkages among commodities create a source of long-term correlation between futures returns. We extend the theory of storage to a multi-commodity level and find that the convenience yield of a commodity depends on its relative scarcity with respect to other related commodities. This implies a feedback effect between commodities that is necessary to replicate the upward-sloping correlation term structure of futures returns observed for related commodities. We present a multi-commodity affine model that validates our theoretical predictions and considerably reduces the pricing errors in out-of-sample crack spread options.