IDEAS home Printed from https://ideas.repec.org/a/eee/finlet/v53y2023ics1544612323000387.html
   My bibliography  Save this article

Traders’ heterogeneous beliefs about stock volatility and the implied volatility skew in financial options markets

Author

Listed:
  • Nappo, Giovanna
  • Marchetti, Fabio Massimo
  • Vagnani, Gianluca

Abstract

The paper represents an initial effort to unfold some of the determinants of the implied volatility skew empirically observed in financial (derivative) markets. In particular, in a general stochastic volatility model, we theoretically relate traders’ heterogenous expectations about the underlying stock volatility to the emergence of the implied volatility skew. We also used our model to predict sampled option prices. The analysis provides new characterizations of the behavior of the equilibrium option price as a mixture of Black and Scholes prices, and the associated Black and Scholes implied volatility that hold promise for practical modeling and forecasting.

Suggested Citation

  • Nappo, Giovanna & Marchetti, Fabio Massimo & Vagnani, Gianluca, 2023. "Traders’ heterogeneous beliefs about stock volatility and the implied volatility skew in financial options markets," Finance Research Letters, Elsevier, vol. 53(C).
  • Handle: RePEc:eee:finlet:v:53:y:2023:i:c:s1544612323000387
    DOI: 10.1016/j.frl.2023.103664
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S1544612323000387
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.frl.2023.103664?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. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    2. Dennis, Patrick & Mayhew, Stewart, 2002. "Risk-Neutral Skewness: Evidence from Stock Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 37(3), pages 471-493, September.
    3. Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 45-60.
    4. Elyas Elyasiani & Luca Gambarelli & Silvia Muzzioli, 2021. "The skewness index: uncovering the relationship with volatility and market returns," Applied Economics, Taylor & Francis Journals, vol. 53(31), pages 3619-3635, July.
    5. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    6. Rubinstein, Mark, 1985. "Nonparametric Tests of Alternative Option Pricing Models Using All Reported Trades and Quotes on the 30 Most Active CBOE Option Classes from August 23, 1976 through August 31, 1978," Journal of Finance, American Finance Association, vol. 40(2), pages 455-480, June.
    7. Frijns, Bart & Lehnert, Thorsten & Zwinkels, Remco C.J., 2010. "Behavioral heterogeneity in the option market," Journal of Economic Dynamics and Control, Elsevier, vol. 34(11), pages 2273-2287, November.
    8. Jungah Yoon & Xinfeng Ruan & Jin E. Zhang, 2022. "VIX option‐implied volatility slope and VIX futures returns," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(6), pages 1002-1038, June.
    9. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    10. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    11. Hellwig, Martin F., 1980. "On the aggregation of information in competitive markets," Journal of Economic Theory, Elsevier, vol. 22(3), pages 477-498, June.
    12. Vagnani, Gianluca, 2009. "The Black-Scholes model as a determinant of the implied volatility smile: A simulation study," Journal of Economic Behavior & Organization, Elsevier, vol. 72(1), pages 103-118, October.
    13. Dmitriy Muravyev, 2016. "Order Flow and Expected Option Returns," Journal of Finance, American Finance Association, vol. 71(2), pages 673-708, April.
    14. Gianluca Vagnani, 2009. "The Black-Scholes model as a determinant of the implied volatility smile: A simulation study," Post-Print hal-00736952, HAL.
    15. Tao Li, 2013. "Investors' Heterogeneity and Implied Volatility Smiles," Management Science, INFORMS, vol. 59(10), pages 2392-2412, October.
    16. Andrew M. McKenzie & Michael R. Thomsen & Michael K. Adjemian, 2022. "Characterizing implied volatility functions from agricultural options markets," American Journal of Agricultural Economics, John Wiley & Sons, vol. 104(5), pages 1605-1624, October.
    17. M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 73-88.
    18. Grossman, Sanford J, 1976. "On the Efficiency of Competitive Stock Markets Where Trades Have Diverse Information," Journal of Finance, American Finance Association, vol. 31(2), pages 573-585, May.
    19. Damiano Brigo & Fabio Mercurio & Giulio Sartorelli, 2003. "Alternative asset-price dynamics and volatility smile," Quantitative Finance, Taylor & Francis Journals, vol. 3(3), pages 173-183.
    20. Ziegler, Alexandre, 2002. "State-price densities under heterogeneous beliefs, the smile effect, and implied risk aversion," European Economic Review, Elsevier, vol. 46(8), pages 1539-1557, September.
    21. Chew Lian Chua & Sarantis Tsiaplias, 2019. "Information flows and stock market volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(1), pages 129-148, January.
    22. Engle, Robert F. & Mustafa, Chowdhury, 1992. "Implied ARCH models from options prices," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 289-311.
    23. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    24. Andrea Buraschi & Alexei Jiltsov, 2006. "Model Uncertainty and Option Markets with Heterogeneous Beliefs," Journal of Finance, American Finance Association, vol. 61(6), pages 2841-2897, December.
    25. Kaushik I. Amin & Charles M. C. Lee, 1997. "Option Trading, Price Discovery, and Earnings News Dissemination," Contemporary Accounting Research, John Wiley & Sons, vol. 14(2), pages 153-192, June.
    26. Yongmin Zhang & Shusheng Ding & Meryem Duygun, 2019. "Derivatives pricing with liquidity risk," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(11), pages 1471-1485, November.
    27. Kian Guan Lim & Da Zhi, 2002. "Pricing options using implied trees: Evidence from FTSE‐100 options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 22(7), pages 601-626, July.
    28. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    29. Robin K. Chou & San‐Lin Chung & Yu‐Jen Hsiao & Yaw‐Huei Wang, 2011. "The impact of liquidity on option prices," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 31(12), pages 1116-1141, December.
    30. Yue, Tian & Gehricke, Sebastian A. & Zhang, Jin E. & Pan, Zheyao, 2021. "The implied volatility smirk in the Chinese equity options market," Pacific-Basin Finance Journal, Elsevier, vol. 69(C).
    31. David S. Bates, 2022. "Empirical Option Pricing Models," Annual Review of Financial Economics, Annual Reviews, vol. 14(1), pages 369-389, November.
    32. Eric Renault & Nizar Touzi, 1996. "Option Hedging And Implied Volatilities In A Stochastic Volatility Model1," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 279-302, July.
    33. Qin, Zhenjiang, 2013. "Speculations in option markets enhance allocation efficiency with heterogeneous beliefs and learning," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 4675-4694.
    34. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    35. J. Michael Harrison & David M. Kreps, 1978. "Speculative Investor Behavior in a Stock Market with Heterogeneous Expectations," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 92(2), pages 323-336.
    36. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhao, Mengyang & Zhang, Lingxiao, 2023. "Foreign ownership, heterogeneous beliefs, and stock market volatility," Finance Research Letters, Elsevier, vol. 55(PA).

    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. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers 2006-28, Center for Research in Economics and Statistics.
    2. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    3. Vagnani, Gianluca, 2009. "The Black-Scholes model as a determinant of the implied volatility smile: A simulation study," Journal of Economic Behavior & Organization, Elsevier, vol. 72(1), pages 103-118, October.
    4. Zhu, Ke & Ling, Shiqing, 2015. "Model-based pricing for financial derivatives," Journal of Econometrics, Elsevier, vol. 187(2), pages 447-457.
    5. Jin Zhang & Yi Xiang, 2008. "The implied volatility smirk," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 263-284.
    6. David S. Bates, 1995. "Testing Option Pricing Models," NBER Working Papers 5129, National Bureau of Economic Research, Inc.
    7. Christoffersen, Peter & Heston, Steve & Jacobs, Kris, 2006. "Option valuation with conditional skewness," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 253-284.
    8. Han, Bin, 2004. "Limits of Arbitrage, Sentiment and Pricing Kernal: Evidences from Index Options," Working Paper Series 2004-2, Ohio State University, Charles A. Dice Center for Research in Financial Economics.
    9. Don M. Chance & Thomas A. Hanson & Weiping Li & Jayaram Muthuswamy, 2017. "A bias in the volatility smile," Review of Derivatives Research, Springer, vol. 20(1), pages 47-90, April.
    10. David Edelman & Thomas Gillespie, 2000. "The Stochastically Subordinated Poisson Normal Process for Modelling Financial Assets," Annals of Operations Research, Springer, vol. 100(1), pages 133-164, December.
    11. Carol Alexander & Leonardo M. Nogueira, 2006. "Hedging Options with Scale-Invariant Models," ICMA Centre Discussion Papers in Finance icma-dp2006-03, Henley Business School, University of Reading.
    12. K. Ronnie Sircar & George Papanicolaou, 1999. "Stochastic volatility, smile & asymptotics," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(2), pages 107-145.
    13. Alexander, Carol & Nogueira, Leonardo M., 2007. "Model-free hedge ratios and scale-invariant models," Journal of Banking & Finance, Elsevier, vol. 31(6), pages 1839-1861, June.
    14. Anatoliy Swishchuk, 2013. "Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8660, January.
    15. René Garcia & Richard Luger & Eric Renault, 2000. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Working Papers 2000-57, Center for Research in Economics and Statistics.
    16. F. Fornari & A. Mele, 1998. "ARCH Models and Option Pricing : The Continuous Time Connection," THEMA Working Papers 98-30, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    17. Carol Alexander & Leonardo Nogueira, 2007. "Model-free price hedge ratios for homogeneous claims on tradable assets," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 473-479.
    18. Guidolin, Massimo & Timmermann, Allan, 2003. "Option prices under Bayesian learning: implied volatility dynamics and predictive densities," Journal of Economic Dynamics and Control, Elsevier, vol. 27(5), pages 717-769, March.
    19. Stentoft, Lars, 2011. "American option pricing with discrete and continuous time models: An empirical comparison," Journal of Empirical Finance, Elsevier, vol. 18(5), pages 880-902.
    20. Lei Shi, 2010. "Portfolio Analysis and Equilibrium Asset Pricing with Heterogeneous Beliefs," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 9, July-Dece.

    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:finlet:v:53:y:2023:i:c:s1544612323000387. 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.elsevier.com/locate/frl .

    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.