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A maximum (non-extensive) entropy approach to equity options bid–ask spread

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  • Tapiero, Oren J.
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    Abstract

    The cross-section of options bid–ask spreads with their strikes are modelled by maximising the Kaniadakis entropy. A theoretical model results with the bid–ask spread depending explicitly on the implied volatility; the probability of expiring at-the-money and an asymmetric information parameter (κ). Considering AIG as a test case for the period between January 2006 and October 2008, we find that information flows uniquely from the trading activity in the underlying asset to its derivatives. Suggesting that κ is possibly an option implied measure of the current state of trading liquidity in the underlying asset.

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    Bibliographic Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 392 (2013)
    Issue (Month): 14 ()
    Pages: 3051-3060

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    Handle: RePEc:eee:phsmap:v:392:y:2013:i:14:p:3051-3060

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    Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

    Related research

    Keywords: Kaniadakis Entropy; Bid–ask spread; Asymmetric information;

    References

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    1. L. Borland & J. P. Bouchaud, 2004. "A Non-Gaussian Option Pricing Model with Skew," Papers cond-mat/0403022, arXiv.org, revised Mar 2004.
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    3. Fabio Clementi & Mauro Gallegati & Giorgio Kaniadakis, 2012. "A new model of income distribution: the κ-generalized distribution," Journal of Economics, Springer, vol. 105(1), pages 63-91, January.
    4. Cao, Melanie & Wei, Jason, 2010. "Option market liquidity: Commonality and other characteristics," Journal of Financial Markets, Elsevier, vol. 13(1), pages 20-48, February.
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    8. David Easley & Maureen O'Hara & P.S. Srinivas, 1998. "Option Volume and Stock Prices: Evidence on Where Informed Traders Trade," Journal of Finance, American Finance Association, vol. 53(2), pages 431-465, 04.
    9. Marco Avellaneda & Craig Friedman & Richard Holmes & Dominick Samperi, 1997. "Calibrating volatility surfaces via relative-entropy minimization," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(1), pages 37-64.
    10. Michael A. H. Dempster & Elena A. Medova & Seung W. Yang, 2007. "Empirical Copulas For Cdo Tranche Pricing Using Relative Entropy," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 679-701.
    11. Buchen, Peter W. & Kelly, Michael, 1996. "The Maximum Entropy Distribution of an Asset Inferred from Option Prices," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(01), pages 143-159, March.
    12. Tsallis, Constantino & Anteneodo, Celia & Borland, Lisa & Osorio, Roberto, 2003. "Nonextensive statistical mechanics and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 89-100.
    13. Norden, Lars, 2003. "Asymmetric option price distribution and bid-ask quotes: consequences for implied volatility smiles," Journal of Multinational Financial Management, Elsevier, vol. 13(4-5), pages 423-441, December.
    14. Constantino Tsallis & Celia Anteneodo & Lisa Borland & Roberto Osorio, 2003. "Nonextensive statistical mechanics and economics," Papers cond-mat/0301307, arXiv.org.
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