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Implied volatility and skewness surface

Author

Listed:
  • Bruno Feunou

    (Bank of Canada)

  • Jean-Sébastien Fontaine

    (Bank of Canada)

  • Roméo Tédongap

    (ESSEC Business School)

Abstract

The Homoscedastic Gamma (HG) model characterizes the distribution of returns by its mean, variance and an independent skewness parameter. The HG model preserves the parsimony and the closed form of the Black–Scholes–Merton (BSM) while introducing the implied volatility (IV) and skewness surface. Varying the skewness parameter of the HG model can restore the symmetry of IV curves. Practitioner’s variants of the HG model improve pricing (in-sample and out-of-sample) and hedging performances relative to practitioners’ BSM models, with as many or less parameters. The pattern of improvements in Delta-Hedged gains across strike prices accord with predictions from the HG model. These results imply that expanding around the Gaussian density does not offer sufficient flexibility to match the skewness implicit in options. Consistent with the model, we also find that conditioning on implied skewness increases the predictive power of the volatility spread for excess returns.

Suggested Citation

  • Bruno Feunou & Jean-Sébastien Fontaine & Roméo Tédongap, 2017. "Implied volatility and skewness surface," Review of Derivatives Research, Springer, vol. 20(2), pages 167-202, July.
  • Handle: RePEc:kap:revdev:v:20:y:2017:i:2:d:10.1007_s11147-016-9127-x
    DOI: 10.1007/s11147-016-9127-x
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    as
    1. Jondeau, Eric & Rockinger, Michael, 2001. "Gram-Charlier densities," Journal of Economic Dynamics and Control, Elsevier, vol. 25(10), pages 1457-1483, October.
    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. León, à ngel & Mencía, Javier & Sentana, Enrique, 2009. "Parametric Properties of Semi-Nonparametric Distributions, with Applications to Option Valuation," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(2), pages 176-192.
    4. David S. Bates, "undated". "Testing Option Pricing Models," Rodney L. White Center for Financial Research Working Papers 14-95, Wharton School Rodney L. White Center for Financial Research.
    5. Christoffersen, Peter & Heston, Steve & Jacobs, Kris, 2006. "Option valuation with conditional skewness," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 253-284.
    6. Bates, David S., 2005. "Hedging the smirk," Finance Research Letters, Elsevier, vol. 2(4), pages 195-200, December.
    7. Tim Bollerslev & George Tauchen & Hao Zhou, 2009. "Expected Stock Returns and Variance Risk Premia," Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4463-4492, November.
    8. Galai, Dan, 1983. "The Components of the Return from Hedging Options against Stocks," The Journal of Business, University of Chicago Press, vol. 56(1), pages 45-54, January.
    9. 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.
    10. Peter Christoffersen & Redouane Elkamhi & Bruno Feunou & Kris Jacobs, 2010. "Option Valuation with Conditional Heteroskedasticity and Nonnormality," Review of Financial Studies, Society for Financial Studies, vol. 23(5), pages 2139-2183.
    11. Gurdip Bakshi & Dilip Madan, 2006. "A Theory of Volatility Spreads," Management Science, INFORMS, vol. 52(12), pages 1945-1956, December.
    12. Gurdip Bakshi & Nikunj Kapadia, 2003. "Delta-Hedged Gains and the Negative Market Volatility Risk Premium," Review of Financial Studies, Society for Financial Studies, vol. 16(2), pages 527-566.
    13. Bo-Young Chang & Peter Christoffersen & Kris Jacobs & Gregory Vainberg, 2011. "Option-Implied Measures of Equity Risk," Review of Finance, European Finance Association, vol. 16(2), pages 385-428.
    14. Robert JARROW & Andrew RUDD, 2008. "Approximate Option Valuation For Arbitrary Stochastic Processes," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 1, pages 9-31, World Scientific Publishing Co. Pte. Ltd..
    15. Kim, Tae-Hwan & White, Halbert, 2004. "On more robust estimation of skewness and kurtosis," Finance Research Letters, Elsevier, vol. 1(1), pages 56-73, March.
    16. Leonidas S. Rompolis & Elias Tzavalis, 2010. "Risk Premium Effects On Implied Volatility Regressions," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 33(2), pages 125-151, June.
    17. David S. Bates, 1995. "Testing Option Pricing Models," NBER Working Papers 5129, National Bureau of Economic Research, Inc.
    18. Gurdip Bakshi & Nikunj Kapadia & Dilip Madan, 2003. "Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options," Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 101-143.
    19. Bernard Dumas & Jeff Fleming & Robert E. Whaley, 1998. "Implied Volatility Functions: Empirical Tests," Journal of Finance, American Finance Association, vol. 53(6), pages 2059-2106, December.
    20. Peter Carr & Liuren Wu, 2009. "Variance Risk Premiums," Review of Financial Studies, Society for Financial Studies, vol. 22(3), pages 1311-1341, March.
    21. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, June.
    22. Kraus, Alan & Litzenberger, Robert H, 1976. "Skewness Preference and the Valuation of Risk Assets," Journal of Finance, American Finance Association, vol. 31(4), pages 1085-1100, September.
    23. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
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    Cited by:

    1. José Fajardo, 2017. "A new factor to explain implied volatility smirk," Applied Economics, Taylor & Francis Journals, vol. 49(40), pages 4026-4034, August.

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    More about this item

    Keywords

    SP500 options; Implied skewness; Implied volatility; Volatility spread; Delta-hedged gains;
    All these keywords.

    JEL classification:

    • 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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