Spanning, Valuation and Options

Donald Brown () and Stephen A. Ross

No 873, Cowles Foundation Discussion Papers from Cowles Foundation, Yale University

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-Litzenberger pricing formula is shown to be a direct consequence of the integral representation theorem.

Keywords: Securities; portfolios; assets; arbitrage; marketed assets (search for similar items in EconPapers)
Date: 1988-06
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Published in Economic Theory (1991), 1(1): 3-12

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