Summary
We model the space of marketed assets as a Riesz space of commoditics. In this setting two altenative characterizations are given of the space of continuous options on a bounded asset,s, with limited liability. The first characterization represents every continuous option ons as the uniform limit of portfolios of calls ons. The second characterization represents an option as a continuous sum (or integral) of Arrow-Debreu securities, with respect tos. 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.
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Research supported in part by NSF Grant SES83-19611
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Brown, D.J., Ross, S.A. Spanning, valuation and options. Econ Theory 1, 3–12 (1991). https://doi.org/10.1007/BF01210570
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DOI: https://doi.org/10.1007/BF01210570