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Spanning, Valuation and Options

  • Brown, Donald J
  • Ross, Stephen A

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.

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Article provided by Springer in its journal Economic Theory.

Volume (Year): 1 (1991)
Issue (Month): 1 (January)
Pages: 3-12

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Handle: RePEc:spr:joecth:v:1:y:1991:i:1:p:3-12
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  1. Bick, Avi, 1982. "Comments on the valuation of derivative assets," Journal of Financial Economics, Elsevier, vol. 10(3), pages 331-345, November.
  2. Avi Bick., 1982. "Comments on the Valuation of Derivative Assets," Research Program in Finance Working Papers 125, University of California at Berkeley.
  3. Jarrow, Robert A., 1986. "A characterization theorem for unique risk neutral probability measures," Economics Letters, Elsevier, vol. 22(1), pages 61-65.
  4. Kreps, David M., 1981. "Arbitrage and equilibrium in economies with infinitely many commodities," Journal of Mathematical Economics, Elsevier, vol. 8(1), pages 15-35, March.
  5. Ross, Stephen A, 1978. "A Simple Approach to the Valuation of Risky Streams," The Journal of Business, University of Chicago Press, vol. 51(3), pages 453-75, July.
  6. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-51, October.
  7. Green, Richard C. & Jarrow, Robert A., 1987. "Spanning and completeness in markets with contingent claims," Journal of Economic Theory, Elsevier, vol. 41(1), pages 202-210, February.
  8. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
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