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Options And Efficiency In Multidate Security Markets

Author

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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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    References listed on IDEAS

    as
    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..
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    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.
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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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