IDEAS home Printed from https://ideas.repec.org/a/eee/ecolet/v76y2002i3p443-447.html
   My bibliography  Save this article

Markets that don't replicate any option

Author

Listed:
  • Aliprantis, Charalambos D.
  • Tourky, Rabee

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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Aliprantis, Charalambos D. & Tourky, Rabee, 2002. "Markets that don't replicate any option," Economics Letters, Elsevier, vol. 76(3), pages 443-447, August.
    • Handle: RePEc:eee:ecolet:v:76:y:2002:i:3:p:443-447
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165-1765(02)00084-8
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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(1), pages 117-138, March.
    2. 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(2), pages 199-222, June.
    3. Brown, Donald J & Ross, Stephen A, 1991. "Spanning, Valuation and Options," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 3-12, January.
    4. Leland, Hayne E, 1980. "Who Should Buy Portfolio Insurance?," Journal of Finance, American Finance Association, vol. 35(2), pages 581-594, May.
    5. Stephen A. Ross, 1976. "Options and Efficiency," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(1), pages 75-89.
    6. 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.
    7. Broadie, Mark & Cvitanic, Jaksa & Soner, H Mete, 1998. "Optimal Replication of Contingent Claims under Portfolio Constraints," The Review of Financial Studies, Society for Financial Studies, vol. 11(1), pages 59-79.
    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 637-654, May-June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Aliprantis, Charalambos D. & Florenzano, Monique & Tourky, Rabee, 2005. "Linear and non-linear price decentralization," Journal of Economic Theory, Elsevier, vol. 121(1), pages 51-74, March.
    2. Aloisio Araujo & Alain Chateauneuf & José Faro, 2012. "Pricing rules and Arrow–Debreu ambiguous valuation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 49(1), pages 1-35, January.
    3. 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.
    4. Christos Kountzakis & Ioannis Polyrakis, 2006. "The completion of security markets," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 29(1), pages 1-21, May.
    5. 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.
    6. Alexandre Baptista, 2007. "On the Non-Existence of Redundant Options," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(2), pages 205-212, May.
    7. Doojin Ryu & Jinyoung Yu, 2021. "Informed options trading around holidays," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(5), pages 658-685, May.
    8. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Aliprantis, Charalambos D. & Polyrakis, Yiannis A. & Tourky, Rabee, 2002. "The cheapest hedge," Journal of Mathematical Economics, Elsevier, vol. 37(4), pages 269-295, July.
    2. Aliprantis, C. D. & Brown, D. J. & Werner, J., 2000. "Minimum-cost portfolio insurance," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1703-1719, October.
    3. Huang, Kevin X. D., 2002. "On infinite-horizon minimum-cost hedging under cone constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 27(2), pages 283-301, December.
    4. Boyle, Phelim & Tian, Weidong, 2008. "The design of equity-indexed annuities," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 303-315, December.
    5. Alexandre M. Baptista, 2005. "Options And Efficiency In Multidate Security Markets," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 569-587, October.
    6. Baptista, Alexandre M., 2003. "Spanning with American options," Journal of Economic Theory, Elsevier, vol. 110(2), pages 264-289, June.
    7. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    8. Hu, Yuan & Lindquist, W. Brent & Rachev, Svetlozar T. & Shirvani, Abootaleb & Fabozzi, Frank J., 2022. "Market complete option valuation using a Jarrow-Rudd pricing tree with skewness and kurtosis," Journal of Economic Dynamics and Control, Elsevier, vol. 137(C).
    9. Gunther Capelle-Blancard & Séverine Vandelanoite, 2000. "Intraday relations between CAC 40 cash index and CAC 40 index options [Relations intrajournalières entre l'indice CAC 40 et les options sur indice. Quel est le marché préféré des investisseurs info," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03727911, HAL.
    10. Galvani, Valentina, 2007. "A note on spanning with options," Mathematical Social Sciences, Elsevier, vol. 54(1), pages 106-114, July.
    11. Joel Vanden, 2006. "Exact Superreplication Strategies for a Class of Derivative Assets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(1), pages 61-87.
    12. Gunther Capelle-Blancard & Séverine Vandelanoite, 2002. "Relations intrajournalières entre l'indice CAC 40 et les options sur indice : Quel est le marché préféré des investisseurs informés ?," Annals of Economics and Statistics, GENES, issue 66, pages 143-177.
    13. Atmaz, Adem & Basak, Suleyman, 2019. "Option prices and costly short-selling," Journal of Financial Economics, Elsevier, vol. 134(1), pages 1-28.
    14. Galvani, Valentina, 2009. "Option spanning with exogenous information structure," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 73-79, January.
    15. Niushan Gao & Foivos Xanthos, 2016. "Option spanning beyond $L_p$-models," Papers 1603.01288, arXiv.org, revised Sep 2016.
    16. 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.
    17. Liu, Jun & Pan, Jun, 2003. "Dynamic derivative strategies," Journal of Financial Economics, Elsevier, vol. 69(3), pages 401-430, September.
    18. Hansjörg Albrecher & Philipp Mayer, 2010. "Semi-Static Hedging Strategies For Exotic Options," World Scientific Book Chapters, in: Rüdiger Kiesel & Matthias Scherer & Rudi Zagst (ed.), Alternative Investments And Strategies, chapter 14, pages 345-373, World Scientific Publishing Co. Pte. Ltd..
    19. Bakshi, Gurdip & Madan, Dilip & Panayotov, George, 2010. "Returns of claims on the upside and the viability of U-shaped pricing kernels," Journal of Financial Economics, Elsevier, vol. 97(1), pages 130-154, July.
    20. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.

    More about this item

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ecolet:v:76:y:2002:i:3:p:443-447. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ecolet .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.