IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v53y2014icp111-118.html
   My bibliography  Save this article

Spanning with indexes

Author

Listed:
  • Tian, Weidong

Abstract

This paper presents several approximation theorems of a general contingent claim in terms of index options. We demonstrate that any contingent claim on the primitive securities in an infinite state economy can be approximated arbitrarily close by a portfolio of index options. In addition, these index options are associated with the same payout function, which belongs to a large and explicit class of one-variable measurable functions. I also characterize the layer structure of a general contingent claim.

Suggested Citation

  • Tian, Weidong, 2014. "Spanning with indexes," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 111-118.
    • Handle: RePEc:eee:mateco:v:53:y:2014:i:c:p:111-118
    DOI: 10.1016/j.jmateco.2014.06.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406814000871
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2014.06.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    References listed on IDEAS

    as
    1. David C. Nachman, 1988. "Spanning and Completeness with Options," Review of Financial Studies, Society for Financial Studies, vol. 1(3), pages 311-328.
    2. Nachman, David C., 1987. "Efficient funds for meager asset spaces," Journal of Economic Theory, Elsevier, vol. 43(2), pages 335-347, December.
    3. Arditti, Fred D. & John, Kose, 1980. "Spanning the State Space with Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 15(1), pages 1-9, March.
    4. Baptista, Alexandre M., 2003. "Spanning with American options," Journal of Economic Theory, Elsevier, vol. 110(2), pages 264-289, June.
    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. Battig, Robert J & Jarrow, Robert A, 1999. "The Second Fundamental Theorem of Asset Pricing: A New Approach," Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 1219-1235.
    7. 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.
    8. Stephen A. Ross, 1976. "Options and Efficiency," The Quarterly Journal of Economics, Oxford University Press, vol. 90(1), pages 75-89.
    9. Robert A. Jarrow & Xing Jin & Dilip B. Madan, 1999. "The Second Fundamental Theorem of Asset Pricing," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 255-273, July.
    10. 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.
    11. 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.
    12. John, Kose, 1981. "Efficient Funds in a Financial Market with Options: A New Irrelevance Proposition," Journal of Finance, American Finance Association, vol. 36(3), pages 685-695, June.
    13. Galvani, Valentina, 2009. "Option spanning with exogenous information structure," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 73-79, January.
    14. John, Kose, 1984. "Market Resolution and Valuation in Incomplete Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 19(1), pages 29-44, March.
    15. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    16. Galvani, Valentina, 2007. "Underlying assets for which options complete the market," Finance Research Letters, Elsevier, vol. 4(1), pages 59-66, March.
    17. Duan, Jin-Chuan & Moreau, Arthur F. & Sealey, C. W., 1992. "Spanning with Index Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(2), pages 303-309, June.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Galvani, Valentina, 2009. "Option spanning with exogenous information structure," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 73-79, January.
    3. Alexandre M. Baptista, 2005. "Options And Efficiency In Multidate Security Markets," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 569-587, October.
    4. Galvani, Valentina, 2007. "A note on spanning with options," Mathematical Social Sciences, Elsevier, vol. 54(1), pages 106-114, July.
    5. Niushan Gao & Foivos Xanthos, 2016. "Option spanning beyond $L_p$-models," Papers 1603.01288, arXiv.org, revised Sep 2016.
    6. Patrick Roger, 1991. "Options et complétude des marchés," Revue Économique, Programme National Persée, vol. 42(5), pages 787-800.
    7. 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.
    8. Ioannis Polyrakis & Foivos Xanthos, 2011. "Maximal submarkets that replicate any option," Annals of Finance, Springer, vol. 7(3), pages 407-423, August.
    9. Alexandre Baptista, 2000. "Options and Efficiency in Multiperiod Security Markets," Econometric Society World Congress 2000 Contributed Papers 0299, Econometric Society.
    10. Julia Jiang & Weidong Tian, 2019. "Semi-nonparametric approximation and index options," Annals of Finance, Springer, vol. 15(4), pages 563-600, December.
    11. Dilip B. Madan & Frank Milne, 1994. "Contingent Claims Valued And Hedged By Pricing And Investing In A Basis," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 223-245, July.
    12. Niushan Gao & Denny H. Leung, 2017. "Smallest order closed sublattices and option spanning," Papers 1703.09748, arXiv.org.
    13. Galvani, Valentina, 2007. "Underlying assets for which options complete the market," Finance Research Letters, Elsevier, vol. 4(1), pages 59-66, March.
    14. 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.
    15. Protter, Philip, 2001. "A partial introduction to financial asset pricing theory," Stochastic Processes and their Applications, Elsevier, vol. 91(2), pages 169-203, February.
    16. Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M., 2015. "Put–Call Parity and market frictions," Journal of Economic Theory, Elsevier, vol. 157(C), pages 730-762.
    17. Baptista, Alexandre M., 2003. "Spanning with American options," Journal of Economic Theory, Elsevier, vol. 110(2), pages 264-289, June.
    18. Topaloglou, Nikolas & Vladimirou, Hercules & Zenios, Stavros A., 2020. "Integrated dynamic models for hedging international portfolio risks," European Journal of Operational Research, Elsevier, vol. 285(1), pages 48-65.
    19. Tak Kuen Siu & Robert J. Elliott, 2019. "Hedging Options In A Doubly Markov-Modulated Financial Market Via Stochastic Flows," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(08), pages 1-41, December.
    20. Gianluca Cassese, 2017. "Asset pricing in an imperfect world," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(3), pages 539-570, October.

    More about this item

    Keywords

    Index; Spanning; Approximation;
    All these keywords.

    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:mateco:v:53:y:2014:i:c:p:111-118. 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/jmateco .

    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.