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Rev Deriv Res (2010) 13:2543 DOI 10.1007/s11147-009-9042-5
Convenience yields
Robert A. Jarrow
Published online: 18 August 2009 Springer Science+Business Media, LLC 2009
Abstract This paper revisits the notion of a convenience yield in the context of modern option pricing theory. We show that, with a proper specication of the cash ows to holding a commodity, a convenience yield as a separate concept does not exist. Rather, a convenience yield is best viewed as a label given to certain cash ows generated from storing a commodity. In particular, it represents the payoffs from two embedded options which we call the scarcity and usage options. This characterization of a convenience yield is new to the literature, although consistent with its existing interpretations and uses.
Keywords Forwards Futures Commodities Option pricing Contango
Backwardation
JEL Classication G13 G12
1 Introduction
When studying forward and futures prices, the notion of a convenience yield has a long tradition in economics. It was introduced to help explain market situations where the spot price trades above the futures price. Of course, given positive storage costs, this can only occur if there is some additional benet obtained from storing the commodity rather than purchasing it in the futures market.
Thanks are expressed to Bill Tomek and Stuart Turnbull for helpful comments.
R. A. Jarrow (B)
Johnson Graduate School of Management, Cornell University, Ithaca, NY 14853, USA e-mail: [email protected]
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But net carrying cost also depends on a third factor: the yield of goods. In normal circumstances, stocks of all goods possess a yield, measured in terms of themselves, and this yield which is a compensation to the holder of stocks, must be deducted from carrying costs proper in calculating net carrying cost. This later can, therefore, be negative or positive (from Kaldor [19], p. 3).1
The early economics literature characterized storage equilibrium by exogenously specifying this convenience yield as a function of inventory size (see Kaldor 1939; Working 1948, 1949; Telser 1958; Brennan 1958). Only more recently has the convenience yield been determined endogenously in simple equilibrium models (e.g. see Heinkel et al. 1990; Routledge et al. 2000; Gorton et al. 2007).
Since its inception, the commodity option pricing literature has always viewed the convenience yield an exogenously given...