COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Post Office Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 873

"Spanning, Valuation and Options"

Donald J. Brown and Stephen A. Ross

June 1988

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.

JEL Classification: 313, 213, 311

Keywords: Securities, portfolios, assets, arbitrage, marketed assets