IDEAS home Printed from https://ideas.repec.org/a/kap/rqfnac/v28y2007i3p227-240.html
   My bibliography  Save this article

Pricing futures on geometric indexes: A discrete time approach

Author

Listed:
  • Arie Harel
  • Giora Harpaz
  • Jack Francis

Abstract

Several futures contracts are written against an underlying asset that is a geometric, rather than arithmetic, index. These contracts include: the US Dollar Index futures, the CRB-17 futures, and the Value Line geometric index futures. Due to the geometric averaging, the standard cost-of-carry futures pricing formula is improper for pricing these futures contracts. We assume that asset prices are lognormally distributed, and capital markets are complete. Using the concepts of equivalent martingale measure and the risk-neutral valuation relationships in conjunction with discrete time methodology, we derive closed-form pricing formulas for these contracts. Our pricing formulas are consistent with the ones obtained via a continuous time paradigm. Copyright Springer Science+Business Media, LLC 2007

Suggested Citation

  • Arie Harel & Giora Harpaz & Jack Francis, 2007. "Pricing futures on geometric indexes: A discrete time approach," Review of Quantitative Finance and Accounting, Springer, vol. 28(3), pages 227-240, April.
    • Handle: RePEc:kap:rqfnac:v:28:y:2007:i:3:p:227-240
    DOI: 10.1007/s11156-006-0015-6
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11156-006-0015-6
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11156-006-0015-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. T. Hanan Eytan & Giora Harpaz & Steven Krull, 1988. "The pricing of dollar index futures contracts," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 8(2), pages 127-139, April.
    2. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    3. Robert A. JARROW & George S. OLDFIELD, 2008. "Forward Contracts And Futures Contracts," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 11, pages 237-246, World Scientific Publishing Co. Pte. Ltd..
    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    5. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    6. Eytan, T Hanan & Harpaz, Giora, 1986. "The Pricing of Futures and Options Contracts on the Value Line Index," Journal of Finance, American Finance Association, vol. 41(4), pages 843-855, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    2. Yen, Simon & Wang, Jai Jen, 2009. "Information-time based futures pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(18), pages 3826-3836.
    3. Rodriguez, Ricardo J., 2002. "Lognormal option pricing for arbitrary underlying assets: a synthesis," The Quarterly Review of Economics and Finance, Elsevier, vol. 42(3), pages 577-586.
    4. Guimaraes, Jonathan S. & Cruz, Jose Cesar, 2017. "Future volatility forecast in agricultural commodity markets," 2017 Annual Meeting, July 30-August 1, Chicago, Illinois 258480, Agricultural and Applied Economics Association.
    5. Calum G. Turvey, 2005. "The pricing of degree‐day weather options," Agricultural Finance Review, Emerald Group Publishing Limited, vol. 65(1), pages 59-85, May.
    6. Jondeau, Eric & Rockinger, Michael, 2000. "Reading the smile: the message conveyed by methods which infer risk neutral densities," Journal of International Money and Finance, Elsevier, vol. 19(6), pages 885-915, December.
    7. Gabriele Fiorentini & Angel León & Gonzalo Rubio, "undated". "Short-term options with stochastic volatility: Estimation and empirical performance," Studies on the Spanish Economy 02, FEDEA.
    8. Kam C. Chan & Carl R. Chen & Peter P. Lung, 2010. "Business Cycles and Net Buying Pressure in the S&P 500 Futures Options," European Financial Management, European Financial Management Association, vol. 16(4), pages 624-657, September.
    9. Marie Brière & Kamal Chancari, 2004. "Perception des risques sur les marchés, construction d'un indice élaboré à partir des smiles d'options et test de stratégies," Revue d'économie politique, Dalloz, vol. 114(4), pages 527-555.
    10. Scholes, Myron S, 1998. "Derivatives in a Dynamic Environment," American Economic Review, American Economic Association, vol. 88(3), pages 350-370, June.
    11. Pena, Ignacio & Rubio, Gonzalo & Serna, Gregorio, 1999. "Why do we smile? On the determinants of the implied volatility function," Journal of Banking & Finance, Elsevier, vol. 23(8), pages 1151-1179, August.
    12. Vivek Bhargava & John M. Clark, 2003. "Pricing U.S. Dollar Index Futures Options: An Empirical Investigation," The Financial Review, Eastern Finance Association, vol. 38(4), pages 571-590, November.
    13. Víctor Manuel García de la Vega & Antonio Ruiz Porras, 2009. "Modelos Estocásticos para el Precio Spot y del Futuro de Commodities con Alta Volatilidad y Reversión a la Media," Revista de Administración, Finanzas y Economía (Journal of Management, Finance and Economics), Tecnológico de Monterrey, Campus Ciudad de México, vol. 3(2), pages 1-24.
    14. Chan, Kam C. & Cheng, Louis T. W. & Lung, Peter P., 2003. "Moneyness and the response of the implied volatilities to price changes: The empirical evidence from HSI options," Pacific-Basin Finance Journal, Elsevier, vol. 11(4), pages 527-553, September.
    15. Neuhaus, Holger, 1995. "The information content of derivatives for monetary policy: Implied volatilities and probabilities," Discussion Paper Series 1: Economic Studies 1995,03e, Deutsche Bundesbank.
    16. Mondher Bellalah, 2009. "Derivatives, Risk Management & Value," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7175, September.
    17. Calum G. Turvey & Shihong Yin, 2002. "On the Pricing of Cross Currency Futures Options for Canadian Grains and Livestock," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 50(3), pages 317-332, November.
    18. Carl Chiarella & Xue-Zhong He & Christina Sklibosios Nikitopoulos, 2015. "Derivative Security Pricing," Dynamic Modeling and Econometrics in Economics and Finance, Springer, edition 127, number 978-3-662-45906-5, March.
    19. Turvey, Calum G., 2003. "Conceptual Issues In Livestock Insurance," Research Reports 18171, Rutgers University, Food Policy Institute.
    20. Robert Tompkins, 2001. "Implied volatility surfaces: uncovering regularities for options on financial futures," The European Journal of Finance, Taylor & Francis Journals, vol. 7(3), pages 198-230.

    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:kap:rqfnac:v:28:y:2007:i:3:p:227-240. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://springer.com .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.