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Understanding the Non-Convergence of Agricultural Futures via Stochastic Storage Costs and Timing Options

Author

Listed:
  • Kevin Guo
  • Tim Leung
Abstract
This paper studies the market phenomenon of non-convergence between futures and spot prices in the grains market. We postulate that the positive basis observed at maturity stems from the futures holder's timing options to exercise the shipping certificate delivery item and subsequently liquidate the physical grain. In our proposed approach, we incorporate stochastic spot price and storage cost, and solve an optimal double stopping problem to give the optimal strategies to exercise and liquidate the grain. Our new models for stochastic storage rates lead to explicit no-arbitrage prices for the shipping certificate and associated futures contract. We calibrate our models to empirical futures data during the periods of observed non-convergence, and illustrate the premium generated by the shipping certificate.

Suggested Citation

  • Kevin Guo & Tim Leung, 2016. "Understanding the Non-Convergence of Agricultural Futures via Stochastic Storage Costs and Timing Options," Papers 1610.09403, arXiv.org, revised Apr 2017.
    • Handle: RePEc:arx:papers:1610.09403
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    References listed on IDEAS

    as
    1. Tim Leung & Jiao Li & Xin Li & Zheng Wang, 2016. "Speculative Futures Trading under Mean Reversion," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 23(4), pages 281-304, December.
    2. Nicole M. Aulerich & Raymond P. H. Fishe & Jeffrey H. Harris, 2011. "Why do expiring futures and cash prices diverge for grain markets?," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 31(6), pages 503-533, June.
    3. Jana Hranaiova & Robert A. Jarrow & William G. Tomek, 2005. "Estimating The Value Of Delivery Options In Futures Contracts," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 28(3), pages 363-383, September.
    4. Francesca Biagini & Tomas Björk, 2007. "On The Timing Option In A Futures Contract," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 267-283, April.
    5. Tim Leung & Xin Li, 2016. "Optimal Mean Reversion Trading:Mathematical Analysis and Practical Applications," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9839, December.
    6. Tim Leung & Xin Li & Zheng Wang, 2015. "Optimal Multiple Trading Times Under the Exponential OU Model with Transaction Costs," Papers 1504.04682, arXiv.org.
    7. Tim Leung & Xin Li, 2016. "Futures Trading Under Mean Reversion," World Scientific Book Chapters, in: Optimal Mean Reversion Trading Mathematical Analysis and Practical Applications, chapter 5, pages 105-127, World Scientific Publishing Co. Pte. Ltd..
    8. Kevin Guo & Tim Leung, 2016. "Understanding the Tracking Errors of Commodity Leveraged ETFs," Papers 1610.09404, arXiv.org.
    9. Eugene F. Fama & Kenneth R. French, 2015. "Commodity Futures Prices: Some Evidence on Forecast Power, Premiums, and the Theory of Storage," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 4, pages 79-102, World Scientific Publishing Co. Pte. Ltd..
    10. Gary B. Gorton & Fumio Hayashi & K. Geert Rouwenhorst, 2013. "The Fundamentals of Commodity Futures Returns," Review of Finance, European Finance Association, vol. 17(1), pages 35-105.
    11. Nicholas Kaldor, 1939. "Speculation and Economic Stability," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 7(1), pages 1-27.
    12. Scott H. Irwin & Philip Garcia & Darrel L. Good & Eugene L. Kunda, 2011. "Spreads and Non-Convergence in Chicago Board of Trade Corn, Soybean, and Wheat Futures: Are Index Funds to Blame?," Applied Economic Perspectives and Policy, Agricultural and Applied Economics Association, vol. 33(1), pages 116-142.
    13. Tim Leung & Brian Ward, 2015. "The golden target: analyzing the tracking performance of leveraged gold ETFs," Studies in Economics and Finance, Emerald Group Publishing Limited, vol. 32(3), pages 278-297, August.
    14. Leland L. Johnson, 1960. "The Theory of Hedging and Speculation in Commodity Futures," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 27(3), pages 139-151.
    15. Irwin, Scott H. & Garcia, Philip & Good, Darrel L. & Kunda, Eugene L., 2009. "Poor Convergence Performance of CBOT Corn, Soybean and Wheat Futures Contracts: Causes and Solutions," Marketing and Outlook Research Reports 183475, University of Illinois at Urbana-Champaign, Department of Agricultural and Consumer Economics.
    16. Tim Leung & Xin Li, 2015. "Optimal Mean Reversion Trading With Transaction Costs And Stop-Loss Exit," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 1-31.
    17. Tim Leung & Xin Li & Zheng Wang, 2014. "Optimal Starting-Stopping and Switching of a CIR Process with Fixed Costs," Papers 1411.6080, arXiv.org.
    18. Deaton, Angus & Laroque, Guy, 1996. "Competitive Storage and Commodity Price Dynamics," Journal of Political Economy, University of Chicago Press, vol. 104(5), pages 896-923, October.
    19. Adjemian, Michael K. & Garcia, Philip & Irwin, Scott & Smith, Aaron, 2013. "Non-Convergence in Domestic Commodity Futures Markets: Causes, Consequences, and Remedies," Economic Information Bulletin 155381, United States Department of Agriculture, Economic Research Service.
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    Cited by:

    1. Tim Leung & Jiao Li & Xin Li, 2018. "Optimal Timing to Trade along a Randomized Brownian Bridge," IJFS, MDPI, vol. 6(3), pages 1-23, August.
    2. Tim Leung & Brian Ward, 2020. "Tracking VIX with VIX Futures: Portfolio Construction and Performance," World Scientific Book Chapters, in: John B Guerard & William T Ziemba (ed.), HANDBOOK OF APPLIED INVESTMENT RESEARCH, chapter 21, pages 557-596, World Scientific Publishing Co. Pte. Ltd..
    3. Kevin Guo & Tim Leung & Brian Ward, 2019. "How to mine gold without digging," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 1-30, March.

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    More about this item

    JEL classification:

    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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