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Spanning, Valuation and Options

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Author Info
Donald J. Brown () (Cowles Foundation, Yale University)
Stephen A. Ross

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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.

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File URL: http://cowles.econ.yale.edu/P/cd/d08b/d0873.pdf
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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 873.

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Length: 20 pages
Date of creation: Jun 1988
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Handle: RePEc:cwl:cwldpp:873

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Securities portfolios assets arbitrage marketed assets

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Bick, Avi, 1982. "Comments on the valuation of derivative assets," Journal of Financial Economics, Elsevier, vol. 10(3), pages 331-345, November. [Downloadable!] (restricted)
  2. Ross, Stephen A, 1978. "A Simple Approach to the Valuation of Risky Streams," Journal of Business, University of Chicago Press, vol. 51(3), pages 453-75, July. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
  4. Avi Bick., 1982. "Comments on the Valuation of Derivative Assets," Research Program in Finance Working Papers 125, University of California at Berkeley.
  5. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," Journal of Business, University of Chicago Press, vol. 51(4), pages 621-51, October. [Downloadable!] (restricted)
  6. Jarrow, Robert A., 1986. "A characterization theorem for unique risk neutral probability measures," Economics Letters, Elsevier, vol. 22(1), pages 61-65. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Alexandre Baptista, 2000. "Options and Efficiency in Multiperiod Security Markets," Econometric Society World Congress 2000 Contributed Papers 0299, Econometric Society. [Downloadable!]
  2. Charalambos Aliprantis & Donald J. Brown & Werner, J., 1997. "Hedging with Derivatives in Incomplete Markets," Cowles Foundation Discussion Papers 1126R, Cowles Foundation, Yale University. [Downloadable!]
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