COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
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 |
