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Markets that don't replicate any option

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  • Aliprantis, Charalambos D.
  • Tourky, Rabee
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    Abstract

    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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    Bibliographic Info

    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

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    Web page: http://www.elsevier.com/locate/ecolet

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    1. 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.
    2. 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.
    3. Hayne E. Leland., 1979. "Who Should Buy Portfolio Insurance?," Research Program in Finance Working Papers 95, University of California at Berkeley.
    4. 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.
    5. Brown, Donald J & Ross, Stephen A, 1991. "Spanning, Valuation and Options," Economic Theory, Springer, vol. 1(1), pages 3-12, January.
    6. Ross, Stephen A, 1976. "Options and Efficiency," The Quarterly Journal of Economics, MIT Press, vol. 90(1), pages 75-89, February.
    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. 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.
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    Cited by:
    1. Alexander, Gordon J. & Baptista, Alexandre M., 2006. "Portfolio selection with a drawdown constraint," Journal of Banking & Finance, Elsevier, vol. 30(11), pages 3171-3189, November.
    2. Christos Kountzakis & Ioannis Polyrakis, 2006. "The completion of security markets," Decisions in Economics and Finance, Springer, vol. 29(1), pages 1-21, 05.
    3. Charalambos Aliprantis & Monique Florenzano & Rabee Tourky, 2005. "Linear and non-linear price decentralization," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00086101, HAL.
    4. Ioannis Polyrakis & Foivos Xanthos, 2011. "Maximal submarkets that replicate any option," Annals of Finance, Springer, vol. 7(3), pages 407-423, August.
    5. Aliprantis, Charalambos D. & Monteiro, Paulo K. & Tourky, Rabee, 2004. "Non-marketed options, non-existence of equilibria, and non-linear prices," Journal of Economic Theory, Elsevier, vol. 114(2), pages 345-357, February.
    6. Galvani, Valentina & Troitsky, Vladimir G., 2010. "Options and efficiency in spaces of bounded claims," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 616-619, July.
    7. Alexandre Baptista, 2007. "On the Non-Existence of Redundant Options," Economic Theory, Springer, vol. 31(2), pages 205-212, May.
    8. Aloisio Araujo & Alain Chateauneuf & José Faro, 2012. "Pricing rules and Arrow–Debreu ambiguous valuation," Economic Theory, Springer, vol. 49(1), pages 1-35, January.
    9. repec:hal:journl:halshs-00086101 is not listed on IDEAS

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