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Pricing futures on geometric indexes: A discrete time approach

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  • 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
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    1. 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..
    2. 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.
    3. 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.
    4. 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.
    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.
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