IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v392y2013i14p3051-3060.html
   My bibliography  Save this article

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

Author

Listed:
  • Tapiero, Oren J.

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.

Suggested Citation

  • Tapiero, Oren J., 2013. "A maximum (non-extensive) entropy approach to equity options bid–ask spread," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(14), pages 3051-3060.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:14:p:3051-3060
    DOI: 10.1016/j.physa.2013.03.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437113002185
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2013.03.015?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. 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.
    2. L. Borland & J. P. Bouchaud, 2004. "A Non-Gaussian Option Pricing Model with Skew," Papers cond-mat/0403022, arXiv.org, revised Mar 2004.
    3. 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(1), pages 143-159, March.
    4. 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.
    5. Cao, Melanie & Wei, Jason, 2010. "Option market liquidity: Commonality and other characteristics," Journal of Financial Markets, Elsevier, vol. 13(1), pages 20-48, February.
    6. 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.
    7. F. Clementi & M. Gallegati & G. Kaniadakis, 2007. "κ-generalized statistics in personal income distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 57(2), pages 187-193, May.
    8. 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.
    9. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
    10. Lisa Borland & Jean-Philippe Bouchaud, 2004. "A non-Gaussian option pricing model with skew," Quantitative Finance, Taylor & Francis Journals, vol. 4(5), pages 499-514.
    11. Michael A. H. Dempster & Elena A. Medova & Seung W. Yang, 2007. "Erratum: "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(07), pages 1255-1260.
    12. repec:bla:jfinan:v:53:y:1998:i:2:p:431-465 is not listed on IDEAS
    13. Kaniadakis, G., 2001. "Non-linear kinetics underlying generalized statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 296(3), pages 405-425.
    14. Constantino Tsallis & Celia Anteneodo & Lisa Borland & Roberto Osorio, 2003. "Nonextensive statistical mechanics and economics," Papers cond-mat/0301307, arXiv.org.
    15. 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.
    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. Gottschalk, Sylvia, 2017. "Entropy measure of credit risk in highly correlated markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 478(C), pages 11-19.
    2. Mauro Politi & Nicolas Millot & Anirban Chakraborti, 2011. "The near-extreme density of intraday log-returns," Papers 1106.0039, arXiv.org.
    3. Marian Gidea & Yuri Katz, 2017. "Topological Data Analysis of Financial Time Series: Landscapes of Crashes," Papers 1703.04385, arXiv.org, revised Apr 2017.
    4. Politi, Mauro & Millot, Nicolas & Chakraborti, Anirban, 2012. "The near-extreme density of intraday log-returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 147-155.
    5. Federica De Domenico & Giacomo Livan & Guido Montagna & Oreste Nicrosini, 2023. "Modeling and Simulation of Financial Returns under Non-Gaussian Distributions," Papers 2302.02769, arXiv.org.
    6. Mauro Politi & Nicolas Millot & Anirban Chakraborti, 2011. "The near-extreme density of intraday log-returns," Post-Print hal-00827942, HAL.
    7. Rodrigues, Ana Flávia P. & Cavalcante, Charles C. & Crisóstomo, Vicente L., 2019. "A projection pricing model for non-Gaussian financial returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    8. Trindade, Marco A.S. & Floquet, Sergio & Filho, Lourival M. Silva, 2020. "Portfolio theory, information theory and Tsallis statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    9. Cassio Neri & Lorenz Schneider, 2012. "Maximum entropy distributions inferred from option portfolios on an asset," Finance and Stochastics, Springer, vol. 16(2), pages 293-318, April.
    10. De Domenico, Federica & Livan, Giacomo & Montagna, Guido & Nicrosini, Oreste, 2023. "Modeling and simulation of financial returns under non-Gaussian distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 622(C).
    11. Deng, Xinyang & Deng, Yong, 2014. "On the axiomatic requirement of range to measure uncertainty," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 163-168.
    12. Moretto, Enrico & Pasquali, Sara & Trivellato, Barbara, 2016. "Option pricing under deformed Gaussian distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 446(C), pages 246-263.
    13. Preda, Vasile & Dedu, Silvia & Sheraz, Muhammad, 2014. "New measure selection for Hunt–Devolder semi-Markov regime switching interest rate models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 350-359.
    14. Fabio CLEMENTI & Mauro GALLEGATI, 2017. "NEW ECONOMIC WINDOWS ON INCOME AND WEALTH: THE k-GENERALIZED FAMILY OF DISTRIBUTIONS," Journal of Social and Economic Statistics, Bucharest University of Economic Studies, vol. 6(1), pages 1-15, JULY.
    15. Sylvia Gottschalk, 2016. "Entropy and credit risk in highly correlated markets," Papers 1604.07042, arXiv.org.
    16. Wang, Xiao-Tian & Li, Zhe & Zhuang, Le, 2017. "European option pricing under the Student’s t noise with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 848-858.
    17. Diks, Cees & Hommes, Cars & Zeppini, Paolo, 2013. "More memory under evolutionary learning may lead to chaos," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 808-812.
    18. Gu, Gao-Feng & Ren, Fei & Ni, Xiao-Hui & Chen, Wei & Zhou, Wei-Xing, 2010. "Empirical regularities of opening call auction in Chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(2), pages 278-286.
    19. Devi, Sandhya, 2021. "Asymmetric Tsallis distributions for modeling financial market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).
    20. Zhao, Pan & Pan, Jian & Yue, Qin & Zhang, Jinbo, 2021. "Pricing of financial derivatives based on the Tsallis statistical theory," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).

    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:phsmap:v:392:y:2013:i:14:p:3051-3060. 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.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.