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Markets that don't replicate any option

  • Aliprantis, Charalambos D.
  • Tourky, Rabee
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    It is well known from the work of S. Ross that a securities market is complete if and only if each call option can be replicated using available securities. The present short note announces the following surprising complementary result to Ross' important contribution. . If the number of securities is less than half the number of states of the world, then not a single option can be replicated by traded securities. This provides further strong motivation for relaxing the assumption of a perfect market in the theory of option pricing and portfolio insurance.

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    File URL: http://www.sciencedirect.com/science/article/B6V84-45TTKXV-7/2/8087ba61572ee6f3f92f711216e327b9
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    Article provided by Elsevier in its journal Economics Letters.

    Volume (Year): 76 (2002)
    Issue (Month): 3 (August)
    Pages: 443-447

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    Handle: RePEc:eee:ecolet:v:76:y:2002:i:3:p:443-447
    Contact details of provider: Web page: http://www.elsevier.com/locate/ecolet

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    1. Donald J. Brown & Stephen A. Ross, 1988. "Spanning, Valuation and Options," Cowles Foundation Discussion Papers 873, Cowles Foundation for Research in Economics, Yale University.
    2. Broadie, Mark & Cvitanic, Jaksa & Soner, H Mete, 1998. "Optimal Replication of Contingent Claims under Portfolio Constraints," Review of Financial Studies, Society for Financial Studies, vol. 11(1), pages 59-79.
    3. Ross, Stephen A, 1976. "Options and Efficiency," The Quarterly Journal of Economics, MIT Press, vol. 90(1), pages 75-89, February.
    4. Hayne E. Leland., 1979. "Who Should Buy Portfolio Insurance?," Research Program in Finance Working Papers 95, University of California at Berkeley.
    5. Edirisinghe, Chanaka & Naik, Vasanttilak & Uppal, Raman, 1993. "Optimal Replication of Options with Transactions Costs and Trading Restrictions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(01), pages 117-138, March.
    6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    7. Naik, Vasanttilak & Uppal, Raman, 1994. "Leverage Constraints and the Optimal Hedging of Stock and Bond Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(02), pages 199-222, June.
    8. 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.
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