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Option spanning with exogenous information structure

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  • Galvani, Valentina

Abstract

Supplementing a finite state-space static securities market with options written on an injective claim obtains market completeness. This study concludes that options maintain this spanning property in the infinite state-space static securities market models of interest in the extant literature. In addition, underlyers for which options bring about market completeness are shown to be dense.

Suggested Citation

  • Galvani, Valentina, 2009. "Option spanning with exogenous information structure," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 73-79, January.
  • Handle: RePEc:eee:mateco:v:45:y:2009:i:1-2:p:73-79
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Stephen A. Ross, 1976. "Options and Efficiency," The Quarterly Journal of Economics, Oxford University Press, vol. 90(1), pages 75-89.
    5. Nachman, David C., 1987. "Efficient funds for meager asset spaces," Journal of Economic Theory, Elsevier, vol. 43(2), pages 335-347, December.
    6. 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.
    7. Alexandre M. Baptista, 2005. "Options And Efficiency In Multidate Security Markets," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 569-587.
    8. Arditti, Fred D. & John, Kose, 1980. "Spanning the State Space with Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 15(01), pages 1-9, March.
    9. 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(02), pages 303-309, June.
    10. Brown, Donald J. & Ross, Stephen, 1983. "Spanning and arbitrage in securities markets with options: A state preference aproach," Mathematical Social Sciences, Elsevier, vol. 4(2), pages 186-186, April.
    11. 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.
    12. John, Kose, 1984. "Market Resolution and Valuation in Incomplete Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 19(01), pages 29-44, March.
    13. 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. Tian, Weidong, 2014. "Spanning with indexes," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 111-118.
    2. Niushan Gao & Foivos Xanthos, 2016. "Option spanning beyond $L_p$-models," Papers 1603.01288, arXiv.org, revised Sep 2016.
    3. Ioannis Polyrakis & Foivos Xanthos, 2011. "Maximal submarkets that replicate any option," Annals of Finance, Springer, vol. 7(3), pages 407-423, August.
    4. 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.
    5. Niushan Gao & Denny H. Leung, 2017. "Smallest order closed sublattices and option spanning," Papers 1703.09748, arXiv.org.

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    Keywords

    Option spanning Market completeness;

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