Pricing futures on geometric indexes: A discrete time approach

Authors: Harel, Arie¹; Harpaz, Giora²; Francis, Jack³

Source: Review of Quantitative Finance and Accounting, Volume 28, Number 3, April 2007 , pp. 227-240(14)

Publisher: Springer

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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.

Keywords: Geometric indexes; Futures pricing; Risk-neutral valuation; Discrete time model

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s11156-006-0015-6

Affiliations: 1: Email: Arie_Harel@baruch.cuny.edu 2: Email: Giora_Harpaz@baruch.cuny.edu 3: Email: jfrancis@snet.net

Publication date: 2007-04-01