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The information content of implied volatility, skewness and kurtosis: empirical evidence from long‐term CAC 40 options

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  • Patrick Navatte
  • Christophe Villa

Abstract

Implied standard deviation is widely believed to be the best available forecast of the volatility of returns over the remaining contract life (Jorion, 1995). In this paper, we take this result two steps further to the higher moments of the distribution (skewness and kurtosis) based on a Gram–Charlier series expansion of the normal distribution (Corrado and Su, 1996) using long‐term CAC 40 option prices contract, named PXL. First, we found that implied first moments contain a substantial amount of information for future moments of CAC 40 returns although this amount decreases with respect to the moment’s order. Secondly, we found that the different shapes of the volatility smile are consistent with different distribution of the underlying returns. Based on these results, we also observed that including other implied moments significantly improves the out‐of‐sample pricing performance of the Black–Scholes, (1973) model.

Suggested Citation

  • Patrick Navatte & Christophe Villa, 2000. "The information content of implied volatility, skewness and kurtosis: empirical evidence from long‐term CAC 40 options," European Financial Management, European Financial Management Association, vol. 6(1), pages 41-56, March.
    • Handle: RePEc:bla:eufman:v:6:y:2000:i:1:p:41-56
    DOI: 10.1111/1468-036X.00110
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    Cited by:

    1. Wilkens, Sascha & Roder, Klaus, 2006. "The informational content of option-implied distributions: Evidence from the Eurex index and interest rate futures options market," Global Finance Journal, Elsevier, vol. 17(1), pages 50-74, September.
    2. Kabir K. Dutta & David F. Babbel, 2005. "Extracting Probabilistic Information from the Prices of Interest Rate Options: Tests of Distributional Assumptions," The Journal of Business, University of Chicago Press, vol. 78(3), pages 841-870, May.
    3. Zhang, Hongwei & Zhao, Xinyi & Gao, Wang & Niu, Zibo, 2023. "The role of higher moments in predicting China's oil futures volatility: Evidence from machine learning models," Journal of Commodity Markets, Elsevier, vol. 32(C).
    4. Christoffersen, Peter & Jacobs, Kris & Chang, Bo Young, 2013. "Forecasting with Option-Implied Information," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 581-656, Elsevier.
    5. 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.
    6. Hollstein, Fabian & Nguyen, Duc Binh Benno & Prokopczuk, Marcel, 2019. "Asset prices and “the devil(s) you know”," Journal of Banking & Finance, Elsevier, vol. 105(C), pages 20-35.
    7. Jenke ter Horst & Chris Veld, 2008. "An Empirical Analysis of the Pricing of Bank Issued Options versus Options Exchange Options," European Financial Management, European Financial Management Association, vol. 14(2), pages 288-314, March.
    8. Feunou Bruno & Tafolong Ernest, 2015. "Fourier inversion formulas for multiple-asset option pricing," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(5), pages 531-559, December.
    9. Vipul Kumar Singh & Pawan Kumar, 2024. "Effectiveness of deterministic option pricing models: new evidence from Nifty and Bank Nifty Index options," Journal of Asset Management, Palgrave Macmillan, vol. 25(2), pages 172-189, March.
    10. 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.
    11. Jin Zhang & Yi Xiang, 2008. "The implied volatility smirk," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 263-284.
    12. Wan-Ni Lai, 2014. "Comparison of methods to estimate option implied risk-neutral densities," Quantitative Finance, Taylor & Francis Journals, vol. 14(10), pages 1839-1855, October.
    13. Nikkinen, Jussi, 2003. "Impact of foreign ownership restrictions on stock return distributions: evidence from an option market," Journal of Multinational Financial Management, Elsevier, vol. 13(2), pages 141-159, April.
    14. Gomes, Frederico Pechir & Takami, Marcelo Yoshio & Brandi, Vinicius Ratton, 2008. "Investigating Unusual Changes in Real-Dollar Exchange Rate," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 62(2), October.

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