Pricing futures on geometric indexes: A discrete time approach |
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| Authors: | Arie Harel Giora Harpaz Jack Clark Francis |
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| Institution: | (1) Zicklin School of Business, Baruch College, City University of New York, Box B11-220, 55 Lexington Avenue, One Bernard Baruch Way, New York, NY 10010-5585, USA |
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| 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.
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| Keywords: | Geometric indexes Futures pricing Risk-neutral valuation Discrete time model |
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