IDEAS home Printed from https://ideas.repec.org/a/taf/eurjfi/v3y1997i1p73-85.html

Implied volatility skews and stock return skewness and kurtosis implied by stock option prices

Author

Listed:
  • C. J. Corrado
  • Tie Su

Abstract

The Black-Scholes* option pricing model is commonly applied to value a wide range of option contracts. However, the model often inconsistently prices deep in-the-money and deep out-of-the-money options. Options professionals refer to this well-known phenomenon as a volatility ‘skew’ or ‘smile’. In this paper, we examine an extension of the Black-Scholes model developed by Corrado and Su that suggests skewness and kurtosis in the option-implied distributions of stock returns as the source of volatility skews. Adapting their methodology, we estimate option-implied coefficients of skewness and kurtosis for four actively traded stock options. We find significantly nonnormal skewness and kurtosis in the option-implied distributions of stock returns.

Suggested Citation

  • C. J. Corrado & Tie Su, 1997. "Implied volatility skews and stock return skewness and kurtosis implied by stock option prices," The European Journal of Finance, Taylor & Francis Journals, vol. 3(1), pages 73-85, March.
    • Handle: RePEc:taf:eurjfi:v:3:y:1997:i:1:p:73-85
    DOI: 10.1080/135184797337543
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/135184797337543
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/135184797337543?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Charles J. Corrado & Tie Su, 1996. "Skewness And Kurtosis In S&P 500 Index Returns Implied By Option Prices," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 19(2), pages 175-192, June.
    2. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    3. Charles J. Corrado & Tie Su, 1996. "Skewness And Kurtosis In S&P 500 Index Returns Implied By Option Prices," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 19(2), pages 175-192, June.
    4. 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.
    5. Barone-Adesi, Giovanni & Whaley, Robert E., 1986. "The valuation of American call options and the expected ex-dividend stock price decline," Journal of Financial Economics, Elsevier, vol. 17(1), pages 91-111, September.
    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. Nikkinen, Jussi, 2003. "Normality tests of option-implied risk-neutral densities: evidence from the small Finnish market," International Review of Financial Analysis, Elsevier, vol. 12(2), pages 99-116.
    2. Saurabha, Rritu & Tiwari, Manvendra, 2007. "Empirical Study of the effect of including Skewness and Kurtosis in Black Scholes option pricing formula on S&P CNX Nifty index Options," MPRA Paper 6329, University Library of Munich, Germany.
    3. Marie Brière & Kamal Chancari, 2004. "Perception des risques sur les marchés, construction d'un indice élaboré à partir des smiles d'options et test de stratégies," Revue d'économie politique, Dalloz, vol. 114(4), pages 527-555.
    4. Robert Tompkins, 2001. "Implied volatility surfaces: uncovering regularities for options on financial futures," The European Journal of Finance, Taylor & Francis Journals, vol. 7(3), pages 198-230.
    5. 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.
    6. Hosam Ki & Byungwook Choi & Kook‐Hyun Chang & Miyoung Lee, 2005. "Option pricing under extended normal distribution," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 25(9), pages 845-871, September.
    7. Williamson, Brendon & Villano, Renato A. & Fleming, Euan M., 2008. "Structuring Exotic Options Contracts on Water to Improve the Efficiency of Resource Allocation in the Water Spot Market," 2008 Conference (52nd), February 5-8, 2008, Canberra, Australia 5992, Australian Agricultural and Resource Economics Society.
    8. Yanhui Shen, 2023. "American Option Pricing using Self-Attention GRU and Shapley Value Interpretation," Papers 2310.12500, arXiv.org.
    9. Fleming, Euan & Villano, Renato & Williamson, Brendon, 2013. "Structuring Exotic Options Contracts on Water to Improve the Efficiency of Resource Allocation in the Australian Water Market," Papers 234295, University of Melbourne, Melbourne School of Land and Environment.
    10. Maciej Wysocki & Robert Ślepaczuk, 2024. "Construction and Hedging of Equity Index Options Portfolios," Working Papers 2024-14, Faculty of Economic Sciences, University of Warsaw.
    11. Sofiane Aboura & Didier Maillard, 2016. "Option Pricing Under Skewness and Kurtosis Using a Cornish–Fisher Expansion," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 36(12), pages 1194-1209, December.
    12. Wysocki, Maciej & Ślepaczuk, Robert, 2025. "Systematic index option-writing strategies with Black-Scholes-Merton and Variance-Gamma Models," Economic Modelling, Elsevier, vol. 152(C).
    13. Weihan Li & Jin E. Zhang & Xinfeng Ruan & Pakorn Aschakulporn, 2024. "An empirical study on the early exercise premium of American options: Evidence from OEX and XEO options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(7), pages 1117-1153, July.
    14. Charles J. Corrado & Tie Su, 1996. "Skewness And Kurtosis In S&P 500 Index Returns Implied By Option Prices," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 19(2), pages 175-192, June.
    15. Pakorn Aschakulporn & Jin E. Zhang, 2026. "Option-pricing formulas with skewness and kurtosis," Review of Derivatives Research, Springer, vol. 29(1), pages 1-23, December.
    16. Gangadhar Nayak & Subhranshu Sekhar Tripathy & Agbotiname Lucky Imoize & Chun-Ta Li, 2024. "Application of Extended Normal Distribution in Option Price Sensitivities," Mathematics, MDPI, vol. 12(15), pages 1-18, July.
    17. Gabriele Fiorentini & Angel León & Gonzalo Rubio, "undated". "Short-term options with stochastic volatility: Estimation and empirical performance," Studies on the Spanish Economy 02, FEDEA.
    18. Bodo Herzog & Sufyan Osamah, 2019. "Reverse Engineering of Option Pricing: An AI Application," IJFS, MDPI, vol. 7(4), pages 1-12, November.
    19. Yuji Yamada & James Primbs, 2004. "Properties of Multinomial Lattices with Cumulants for Option Pricing and Hedging," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(3), pages 335-365, September.
    20. Vahamaa, Sami, 2005. "Option-implied asymmetries in bond market expectations around monetary policy actions of the ECB," Journal of Economics and Business, Elsevier, vol. 57(1), pages 23-38.

    More about this item

    Statistics

    Access and download statistics

    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:taf:eurjfi:v:3:y:1997:i:1:p:73-85. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/REJF20 .

    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.