Review of Derivatives Research

, Volume 13, Issue 1, pp 25–43 | Cite as

Convenience yields



This paper revisits the notion of a convenience yield in the context of modern option pricing theory. We show that, with a proper specification of the cash flows 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 flows 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.


Forwards Futures Commodities Option pricing Contango Backwardation 

JEL Classification

G13 G12 


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  1. Brennan M. (1958) The supply of storage. American Economic Review 48: 50–72Google Scholar
  2. Casassus J., Collin-Dufrensne P. (2005) Stochastic convenience yield implied from commodity futures and interest rates. Journal of Finance 60(5): 2283–2331CrossRefGoogle Scholar
  3. Cherian J., Jacquier E., Jarrow R. (2004) Pricing the convenience yield of treasury securities: Theory and evidence. Review of Derivatives Research 7((2): 79–97CrossRefGoogle Scholar
  4. Cootner P. (1960) Returns to speculators: Telser versus Keynes. Journal of Political Economy 68(4): 396–404CrossRefGoogle Scholar
  5. Cootner P. (1960) Returns to speculators: Rejoinder. Journal of Political Economy 68(4): 415–418CrossRefGoogle Scholar
  6. Detemple J. (2006) American-style derivatives: Valuation and computation. Chapman and Hall/CRC Financial Mathematics Series, New YorkGoogle Scholar
  7. Duffie D. (1989) Futures markets. Prentice Hall, Englewood CliffsGoogle Scholar
  8. Duffie D. (2001) Dynamic asset pricing theory. Princeton University Press, Princeton, NJGoogle Scholar
  9. Duffie D., Schroder M., Skiada C. (1996) Recursive valuation of defaultable securities and the timing of the resolution of uncertainty. Annals of Applied Probability 6: 1075–1090CrossRefGoogle Scholar
  10. Fama E., French K. (1987) Commodity futures prices: Some evidence on forecast power, premiums, and the theory of storage. Journal of Business 60(1): 55–73CrossRefGoogle Scholar
  11. Gibson R., Schwartz E. (1990) Stochastic convenience yield and the pricing of oil contingent claims. Journal of Finance 45(3): 959–976CrossRefGoogle Scholar
  12. Gorton, G., Hayashi, F., & Rouwenhorst, K. G. (2007). The fundamentals of commodity futures returns. NBER working paper.Google Scholar
  13. Heinkel R., Howe M., Hughes J. (1990) Commodity convenience yields as an option profit. Journal of Futures Markets 10(5): 519–533CrossRefGoogle Scholar
  14. Houthakker H. (1957) Can speclators forecast prices?. Review of Economics and Statistics 39(2): 143–151CrossRefGoogle Scholar
  15. Hicks J. (1939) Value and capital. Claredon Press, OxfordGoogle Scholar
  16. Jacod, J., & Protter, P. (2006). Risk neutral compatibility with option prices, preprint.Google Scholar
  17. Jarrow, R., & Protter, P. (2008). Forward and futures prices with bubbles. International Journal of Theoretical and Applied Finance (forthcoming).Google Scholar
  18. Jarrow, R., Protter, P., & Shimbo, K. (2008). Asset price bubbles in incomplete markets. Mathematical Finance (forthcoming).Google Scholar
  19. Kaldor N. (1939) Speculation and economic stability. Review of Economic Studies 7(1): 1–27CrossRefGoogle Scholar
  20. Karatzas, I., & Shreve, S., (1998). Methods of mathematical finance, 2nd printing, Berlin: Springer.Google Scholar
  21. Keynes J.M. (1930) Treatise on money. Macmillan, LondonGoogle Scholar
  22. Margrabe W. (1978) The value of an option to exchange one asset for another. Journal of Finance 33(1): 177–186CrossRefGoogle Scholar
  23. Miltersen K., Schwartz E. (1998) Pricing of options on commodity futures with stochastic term structures of convenience yields and interest rates. Journal of Financial and Quantitative Analysis 33(1): 33–59CrossRefGoogle Scholar
  24. Protter, P. (2005). Applications of mathematics (2nd ed., Vol. 21). Berlin: Springer (Version 2.1).Google Scholar
  25. Routledge B., Seppi D., Spatt C. (2000) Equilibrium forward curves for commodities. Journal of Finance 55: 1297–1338CrossRefGoogle Scholar
  26. Schwartz E. (1997) The stochastic behavior of commodity prices: Implications for valuation and hedging. Journal of Finance 52(3): 923–973CrossRefGoogle Scholar
  27. Schweizer M., Wissel J. (2008) Term structures of implied volatilities: Absence of arbitrage and existence results. Mathematical Finance 18: 77–114Google Scholar
  28. Shreve S. (2004) Stochastic calculus for finance II: Continuous time models. Springer, BerlinGoogle Scholar
  29. Telser L. (1958) Futures trading and the storage of cotton and wheat. Journal of Political Economy 66(3): 233–255CrossRefGoogle Scholar
  30. Telser L. (1960) Returns to speculators: Telser versus Keynes: Reply. Journal of Political Economy 68(4): 405–415CrossRefGoogle Scholar
  31. Working H. (1948) Theory of the inverse carrying charge in futures markets. Journal of Farm Economics 30(1): 1–28CrossRefGoogle Scholar
  32. Working H. (1949) The theory of price of storage. American Economic Review 39(6): 1254–1262Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Johnson Graduate School of ManagementCornell UniversityIthacaUSA

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