IDEAS home Printed from https://ideas.repec.org/p/hhs/cbsfin/2002_004.html
   My bibliography  Save this paper

Stochastic Volatility and Seasonality in Commodity Futures and Options: The Case of Soybeans

Author

Listed:
  • Richter, Martin

    (Finansbanken)

  • Sørensen, Carsten

    (Department of Finance, Copenhagen Business School)

Abstract

This paper sets up and estimates a continuous-time stochastic volatility model using panel data of soybean futures and options in an integrated time-series study. The model of commodity price dynamics is within the class of affine asset pricing models, and option prices are determined using a standard inversion of characteristic func- tions approach. Our modeling acknowledges that commodities exhibit seasonality patterns in both spot price level and volatility. The estimation method is based on a state space formulation of the model and a quasi maximum likelihood approach. Es- timation results are obtained based on weekly observations of soybean futures prices and options prices from the Chicago Board of Trade in the period October 1984 to March 1999. The empirical results support the conceptual ideas in the theory of storage, but not the view that convenience yields behave like timing options.

Suggested Citation

  • Richter, Martin & Sørensen, Carsten, 2002. "Stochastic Volatility and Seasonality in Commodity Futures and Options: The Case of Soybeans," Working Papers 2002-4, Copenhagen Business School, Department of Finance.
  • Handle: RePEc:hhs:cbsfin:2002_004
    as

    Download full text from publisher

    File URL: http://openarchive.cbs.dk/cbsweb/handle/10398/7179
    Download Restriction: no

    References listed on IDEAS

    as
    1. Williams,Jeffrey C. & Wright,Brian D., 2005. "Storage and Commodity Markets," Cambridge Books, Cambridge University Press, number 9780521023399, March.
    2. Eduardo Schwartz & James E. Smith, 2000. "Short-Term Variations and Long-Term Dynamics in Commodity Prices," Management Science, INFORMS, vol. 46(7), pages 893-911, July.
    3. David Backus & Silverio Foresi & Chris Telmer, 1996. "Affine Models of Currency Pricing," NBER Working Papers 5623, National Bureau of Economic Research, Inc.
    4. Jimmy E. Hilliard & Jorge A. Reis, 1999. "Jump Processes in Commodity Futures Prices and Options Pricing," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 81(2), pages 273-286.
    5. Bessembinder, Hendrik, et al, 1995. " Mean Reversion in Equilibrium Asset Prices: Evidence from the Futures Term Structure," Journal of Finance, American Finance Association, vol. 50(1), pages 361-375, March.
    6. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
    7. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    8. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    9. Angus Deaton & Guy Laroque, 1992. "On the Behaviour of Commodity Prices," Review of Economic Studies, Oxford University Press, vol. 59(1), pages 1-23.
    10. Schwartz, Eduardo S, 1997. " The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, vol. 52(3), pages 923-973, July.
    11. Bryan R. Routledge & Duane J. Seppi & Chester S. Spatt, 2000. "Equilibrium Forward Curves for Commodities," Journal of Finance, American Finance Association, vol. 55(3), pages 1297-1338, June.
    12. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    13. Gibson, Rajna & Schwartz, Eduardo S, 1990. " Stochastic Convenience Yield and the Pricing of Oil Contingent Claims," Journal of Finance, American Finance Association, vol. 45(3), pages 959-976, July.
    14. Miltersen, Kristian R. & Schwartz, Eduardo S., 1998. "Pricing of Options on Commodity Futures with Stochastic Term Structures of Convenience Yields and Interest Rates," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(01), pages 33-59, March.
    15. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    16. Qiang Dai & Kenneth J. Singleton, 2000. "Specification Analysis of Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 55(5), pages 1943-1978, October.
    17. Pearson, Neil D & Sun, Tong-Sheng, 1994. " Exploiting the Conditional Density in Estimating the Term Structure: An Application to the Cox, Ingersoll, and Ross Model," Journal of Finance, American Finance Association, vol. 49(4), pages 1279-1304, September.
    18. Chernov, Mikhail & Ghysels, Eric, 2000. "A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation," Journal of Financial Economics, Elsevier, vol. 56(3), pages 407-458, June.
    19. Brennan, Michael J & Schwartz, Eduardo S, 1985. "Evaluating Natural Resource Investments," The Journal of Business, University of Chicago Press, vol. 58(2), pages 135-157, April.
    20. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    21. 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.
    22. Chambers, Marcus J & Bailey, Roy E, 1996. "A Theory of Commodity Price Fluctuations," Journal of Political Economy, University of Chicago Press, vol. 104(5), pages 924-957, October.
    23. Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, Oxford University Press, vol. 101(4), pages 707-727.
    24. Darren L. Frechette, 1997. "The Dynamics of Convenience and the Brazilian Soybean Boom," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 79(4), pages 1108-1118.
    25. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    26. Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," Review of Financial Studies, Society for Financial Studies, vol. 9(4), pages 1211-1250.
    27. Cox, John C. & Ingersoll, Jonathan Jr. & Ross, Stephen A., 1981. "The relation between forward prices and futures prices," Journal of Financial Economics, Elsevier, vol. 9(4), pages 321-346, December.
    28. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    29. Lester G. Telser, 1958. "Futures Trading and the Storage of Cotton and Wheat," Journal of Political Economy, University of Chicago Press, vol. 66, pages 233-233.
    30. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    31. Hilliard, Jimmy E. & Reis, Jorge, 1998. "Valuation of Commodity Futures and Options under Stochastic Convenience Yields, Interest Rates, and Jump Diffusions in the Spot," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(01), pages 61-86, March.
    32. Singleton, Kenneth J., 2001. "Estimation of affine asset pricing models using the empirical characteristic function," Journal of Econometrics, Elsevier, vol. 102(1), pages 111-141, May.
    33. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
    34. Hannan, E J & Terrell, R D & Tuckwell, N E, 1970. "The Seasonal Adjustment of Economic Time Series," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 11(1), pages 24-52, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Chad E. Hart & Sergio H. Lence & Dermot J. Hayes & Na Jin, 2016. "Price Mean Reversion, Seasonality, and Options Markets," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 98(3), pages 707-725.
    2. Back, Janis & Prokopczuk, Marcel & Rudolf, Markus, 2013. "Seasonality and the valuation of commodity options," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 273-290.
    3. Ke Du, 2013. "Commodity Derivative Pricing Under the Benchmark Approach," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2.
    4. Na Jin & Sergio Lence & Chad Hart & Dermot Hayes, 2012. "The Long-Term Structure of Commodity Futures," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 94(3), pages 718-735.
    5. Zulauf, Carl R. & Zhou, Haijiang & Roberts, Matthew C., 2005. "Updating the Estimation of the Supply of Storage Model," 2005 Annual meeting, July 24-27, Providence, RI 19122, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    6. Lorenz Schneider & Bertrand Tavin, 2015. "Seasonal Stochastic Volatility and Correlation together with the Samuelson Effect in Commodity Futures Markets," Papers 1506.05911, arXiv.org.
    7. repec:spr:fininn:v:3:y:2017:i:1:d:10.1186_s40854-017-0066-9 is not listed on IDEAS
    8. Delphine Lautier & Alain Galli, 2010. "Dynamic hedging strategies: an application to the crude oil market," Post-Print halshs-00640802, HAL.
    9. Lorenz Schneider & Bertrand Tavin, 2018. "The Samuelson Effect and Seasonal Stochastic Volatility in Agricultural Futures Markets," Papers 1802.01393, arXiv.org.
    10. Dempster, M.A.H. & Medova, Elena & Tang, Ke, 2008. "Long term spread option valuation and hedging," Journal of Banking & Finance, Elsevier, vol. 32(12), pages 2530-2540, December.
    11. Anders B. Trolle & Eduardo S. Schwartz, 2006. "Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives," NBER Working Papers 12744, National Bureau of Economic Research, Inc.
    12. repec:eee:eneeco:v:67:y:2017:i:c:p:182-201 is not listed on IDEAS
    13. Leif Andersen, 2010. "Markov models for commodity futures: theory and practice," Quantitative Finance, Taylor & Francis Journals, vol. 10(8), pages 831-854.
    14. Nazliben, Kamil, 2015. "Essays on asset pricing," Other publications TiSEM ccdafa8c-ba56-40f0-9917-e, Tilburg University, School of Economics and Management.
    15. Arismendi, Juan C. & Back, Janis & Prokopczuk, Marcel & Paschke, Raphael & Rudolf, Markus, 2016. "Seasonal Stochastic Volatility: Implications for the pricing of commodity options," Journal of Banking & Finance, Elsevier, vol. 66(C), pages 53-65.
    16. repec:wsi:ijtafx:v:16:y:2013:i:06:n:s0219024913500325 is not listed on IDEAS
    17. Rodriguez, J.C., 2007. "A Preference-Free Formula to Value Commodity Derivatives," Discussion Paper 2007-92, Tilburg University, Center for Economic Research.
    18. Anh Ngoc Lai & Constantin Mellios, 2016. "Valuation of commodity derivatives with an unobservable convenience yield," Post-Print halshs-01183166, HAL.
    19. Finbarr Murphy & Ehud Ronn, 2015. "The valuation and information content of options on crude-oil futures contracts," Review of Derivatives Research, Springer, vol. 18(2), pages 95-106, July.

    More about this item

    Keywords

    Commodity derivatives; stochastic volatility; seasonality; integrated time-series estimation;

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hhs:cbsfin:2002_004. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Lars Nondal). General contact details of provider: http://edirc.repec.org/data/cbschdk.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.