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Options And Efficiency In Multidate Security Markets

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  • Alexandre M. Baptista

Abstract

This paper extends the work of Ross (1976; Q. J. Econ. (90)1, 75–89) to multidate security markets. First, we show that if a primitive security separates states at the terminal date, then there exist multiperiod European options on that security generating dynamically complete markets. Second, we show that if a primitive security conditionally separates states at the terminal date, then there exist multiperiod European options on that security generating generically dynamically complete markets provided that certain conditions hold. Third, we show that there are economies for which the minimum number of multiperiod European options on a primitive security generating generically dynamically complete markets is relatively large. Finally, we show that in these economies, a relatively small number of multiperiod European options on possibly different portfolio strategies of primitive securities generates generically dynamically complete markets.

Suggested Citation

  • Alexandre M. Baptista, 2005. "Options And Efficiency In Multidate Security Markets," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 569-587, October.
  • Handle: RePEc:bla:mathfi:v:15:y:2005:i:4:p:569-587
    DOI: 10.1111/j.1467-9965.2005.00251.x
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    File URL: https://doi.org/10.1111/j.1467-9965.2005.00251.x
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    References listed on IDEAS

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    1. Darrell Duffie & Chi-Fu Huang, 2005. "Implementing Arrow-Debreu Equilibria By Continuous Trading Of Few Long-Lived Securities," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 4, pages 97-127, World Scientific Publishing Co. Pte. Ltd..
    2. Isabelle Bajeux‐Besnainou & Jean‐Charles Rochet, 1996. "Dynamic Spanning: Are Options An Appropriate Instrument?1," Mathematical Finance, Wiley Blackwell, vol. 6(1), pages 1-16, January.
    3. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    4. David C. Nachman, 1988. "Spanning and Completeness with Options," Review of Financial Studies, Society for Financial Studies, vol. 1(3), pages 311-328.
    5. 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.
    6. Stephen A. Ross, 1976. "Options and Efficiency," The Quarterly Journal of Economics, Oxford University Press, vol. 90(1), pages 75-89.
    7. Nachman, David C., 1987. "Efficient funds for meager asset spaces," Journal of Economic Theory, Elsevier, vol. 43(2), pages 335-347, December.
    8. Gabrielle Demange & Guy Laroque, 1999. "Efficiency and options on the market index," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(1), pages 227-235.
    9. Friesen, Peter H, 1979. "The Arrow-Debreu Model Extended to Financial Markets," Econometrica, Econometric Society, vol. 47(3), pages 689-707, May.
    10. 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.
    11. 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.
    12. Hakansson, Nils H, 1978. "Welfare Aspects of Options and Supershares," Journal of Finance, American Finance Association, vol. 33(3), pages 759-776, June.
    13. Nils H. Hakansson., 1978. "Welfare Aspects of Options and Supershares," Research Program in Finance Working Papers 68, University of California at Berkeley.
    14. Baptista, Alexandre M., 2003. "Spanning with American options," Journal of Economic Theory, Elsevier, vol. 110(2), pages 264-289, June.
    15. Magill, Michael J. P. & Shafer, Wayne J., 1990. "Characterisation of generically complete real asset structures," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 167-194.
    16. 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.
    17. 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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    Cited by:

    1. Niushan Gao & Foivos Xanthos, 2016. "Option spanning beyond $L_p$-models," Papers 1603.01288, arXiv.org, revised Sep 2016.
    2. Christos E. Kountzakis, 2010. "The Completion of Real-Asset Markets by Options," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2010, pages 1-20, February.
    3. 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.
    4. Ioannis Polyrakis & Foivos Xanthos, 2011. "Maximal submarkets that replicate any option," Annals of Finance, Springer, vol. 7(3), pages 407-423, August.
    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. Galvani, Valentina, 2009. "Option spanning with exogenous information structure," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 73-79, January.

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