Spanning, Valuation and Options

Donald Brown () and Stephen Ross

Economic Theory, 1991, vol. 1, issue 1, 3-12

Abstract: We model the space of marketed assets as a Riesz space of commodities. In this setting two alternative characterizations are given of the space of continuous options on a bounded asset, [s], with limited liability. The first characterization represents every continuous option on [s] as the uniform limit of portfolios of calls on [s]. The second characterization represents an option as a continuous sum (or integral) of Arrow-Debreu securities, with respect to [s]. The pricing implications of these representations are explored. In particular, the Breeden-Littzenberger pricing formula is shown to be a direct consequence of the integral representation theorem.

Date: 1991
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Working Paper: Spanning, Valuation and Options (1988)
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