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The Factor Structure in Equity Options

Author

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  • Peter Christoffersen
  • Mathieu Fournier
  • Kris Jacobs

Abstract

Equity options display a strong factor structure. The first principal components of the equity volatility levels, skews, and term structures explain a substantial fraction of the cross-sectional variation. Furthermore, these principal components are highly correlated with the S&P 500 index option volatility, skew, and term structure, respectively. We develop an equity option valuation model that captures this factor structure. The model predicts that firms with higher market betas have higher implied volatilities, steeper moneyness slopes, and a term structure that covaries more with the market. The model provides a good fit, and the equity option data support the model’s cross-sectional implications. Received December 20, 2013; editorial decision April 15, 2017 by Editor Leonid Kogan.

Suggested Citation

  • Peter Christoffersen & Mathieu Fournier & Kris Jacobs, 2018. "The Factor Structure in Equity Options," The Review of Financial Studies, Society for Financial Studies, vol. 31(2), pages 595-637.
    • Handle: RePEc:oup:rfinst:v:31:y:2018:i:2:p:595-637.
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    File URL: http://hdl.handle.net/10.1093/rfs/hhx089
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    Cited by:

    1. Jozef Barunik & Mattia Bevilacqua & Michael Ellington, 2023. "Common Firm-level Investor Fears: Evidence from Equity Options," Papers 2309.03968, arXiv.org.
    2. Doshi, Hitesh & Ericsson, Jan & Fournier, Mathieu & Seo, Sang Byung, 2024. "The risk and return of equity and credit index options," Journal of Financial Economics, Elsevier, vol. 161(C).
    3. Eric Renault & Thijs Van Der & Bas J M Werker, 2023. "Arbitrage Pricing Theory for Idiosyncratic Variance Factors," Journal of Financial Econometrics, Oxford University Press, vol. 21(5), pages 1403-1442.
    4. Matthias Buechner & Bryan T. Kelly, 2021. "A Factor Model For Option Returns," NBER Working Papers 29369, National Bureau of Economic Research, Inc.
    5. Borochin, Paul & Wu, Zekun & Zhao, Yanhui, 2021. "The effect of option-implied skewness on delta- and vega-hedged option returns," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 74(C).
    6. Song, Shiyu & Tang, Dan & Xu, Guangli & Yin, Xunbai, 2023. "An analytical GARCH valuation model for spread options with default risk," International Review of Economics & Finance, Elsevier, vol. 83(C), pages 1-20.
    7. Kalnina, Ilze & Tewou, Kokouvi, 2025. "Cross-sectional dependence in idiosyncratic volatility," Journal of Econometrics, Elsevier, vol. 249(PB).
    8. Büchner, Matthias & Kelly, Bryan, 2022. "A factor model for option returns," Journal of Financial Economics, Elsevier, vol. 143(3), pages 1140-1161.
    9. Bai, Jennie & Goldstein, Robert S. & Yang, Fan, 2019. "The leverage effect and the basket-index put spread," Journal of Financial Economics, Elsevier, vol. 131(1), pages 186-205.
    10. Michel van der Wel & Sait R. Ozturk & Dick van Dijk, 2015. "Dynamic Factor Models for the Volatility Surface," CREATES Research Papers 2015-13, Department of Economics and Business Economics, Aarhus University.
    11. Li, Yifan & Nolte, Ingmar & Pham, Manh Cuong, 2024. "Parametric risk-neutral density estimation via finite lognormal-Weibull mixtures," Journal of Econometrics, Elsevier, vol. 241(2).
    12. Rombouts, Jeroen V.K. & Stentoft, Lars & Violante, Francesco, 2020. "Pricing individual stock options using both stock and market index information," Journal of Banking & Finance, Elsevier, vol. 111(C).
    13. Barletta, Andrea & Santucci de Magistris, Paolo & Sloth, David, 2019. "It only takes a few moments to hedge options," Journal of Economic Dynamics and Control, Elsevier, vol. 100(C), pages 251-269.
    14. Mohrschladt, Hannes & Schneider, Judith C., 2021. "Option-implied skewness: Insights from ITM-options," Journal of Economic Dynamics and Control, Elsevier, vol. 131(C).
    15. Chen, Ding & Guo, Biao & Zhou, Guofu, 2023. "Firm fundamentals and the cross-section of implied volatility shapes," Journal of Financial Markets, Elsevier, vol. 63(C).
    16. Wang, Jinzhong & Chen, Shijiang & Tao, Qizhi & Zhang, Ting, 2017. "Modelling the implied volatility surface based on Shanghai 50ETF options," Economic Modelling, Elsevier, vol. 64(C), pages 295-301.
    17. R'emy Chicheportiche & Jean-Philippe Bouchaud, 2013. "A nested factor model for non-linear dependences in stock returns," Papers 1309.3102, arXiv.org.
    18. Ruan, Xinfeng, 2020. "Volatility-of-volatility and the cross-section of option returns," Journal of Financial Markets, Elsevier, vol. 48(C).
    19. Erik Vogt, 2014. "Option-implied term structures," Staff Reports 706, Federal Reserve Bank of New York.
    20. Bevilacqua, Mattia & Tunaru, Radu, 2021. "The SKEW index: Extracting what has been left," Journal of Financial Stability, Elsevier, vol. 53(C).
    21. Dmitriy Muravyev & Neil D Pearson & Stijn Van Nieuwerburgh, 2020. "Options Trading Costs Are Lower than You Think," The Review of Financial Studies, Society for Financial Studies, vol. 33(11), pages 4973-5014.
    22. Bevilacqua, Mattia & Tunaru, Radu, 2021. "The SKEW index: extracting what has been left," LSE Research Online Documents on Economics 108198, London School of Economics and Political Science, LSE Library.
    23. Andrea Frazzini & Lasse Heje Pedersen, 2022. "Embedded Leverage [Asset pricing with liquidity risk]," The Review of Asset Pricing Studies, Society for Financial Studies, vol. 12(1), pages 1-52.
    24. Zhe Li, 2020. "Equity Option Pricing with Systematic and Idiosyncratic Volatility and Jump Risks," JRFM, MDPI, vol. 13(1), pages 1-18, January.
    25. Akash Deep & Chris Monico & W. Brent Lindquist & Svetlozar T. Rachev & Frank J. Fabozzi, 2025. "Binary Tree Option Pricing Under Market Microstructure Effects: A Random Forest Approach," Papers 2507.16701, arXiv.org.

    More about this item

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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