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Volatility surfaces: theory, rules of thumb, and empirical evidence


  • Toby Daglish
  • John Hull
  • Wulin Suo


Implied volatilities are frequently used to quote the prices of options. The implied volatility of a European option on a particular asset as a function of strike price and time to maturity is known as the asset's volatility surface. Traders monitor movements in volatility surfaces closely. In this paper we develop a no-arbitrage condition for the evolution of a volatility surface. We examine a number of rules of thumb used by traders to manage the volatility surface and test whether they are consistent with the no-arbitrage condition and with data on the trading of options on the S&P 500 taken from the over-the-counter market. Finally we estimate the factors driving the volatility surface in a way that is consistent with the no-arbitrage condition.

Suggested Citation

  • Toby Daglish & John Hull & Wulin Suo, 2007. "Volatility surfaces: theory, rules of thumb, and empirical evidence," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 507-524.
  • Handle: RePEc:taf:quantf:v:7:y:2007:i:5:p:507-524
    DOI: 10.1080/14697680601087883

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    Cited by:

    1. Itkin, Andrey, 2015. "To sigmoid-based functional description of the volatility smile," The North American Journal of Economics and Finance, Elsevier, vol. 31(C), pages 264-291.
    2. Jacinto Marabel Romo, 2012. "Volatility Regimes For The Vix Index," Revista de Economia Aplicada, Universidad de Zaragoza, Departamento de Estructura Economica y Economia Publica, vol. 20(2), pages 111-134, Autumn.
    3. Cristian Homescu, 2011. "Implied Volatility Surface: Construction Methodologies and Characteristics," Papers 1107.1834,
    4. Carr, Peter & Wu, Liuren, 2016. "Analyzing volatility risk and risk premium in option contracts: A new theory," Journal of Financial Economics, Elsevier, vol. 120(1), pages 1-20.
    5. Fengler, Matthias R. & Härdle, Wolfgang & Mammen, Enno, 2003. "Implied volatility string dynamics," SFB 373 Discussion Papers 2003,54, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    6. Frédéric Abergel & Riadh Zaatour, 2012. "What drives option prices ?," Post-Print hal-00687675, HAL.
    7. Wallmeier, Martin, 2012. "Smile in Motion: An Intraday Analysis of Asymmetric Implied Volatility," FSES Working Papers 427, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    8. Carey, Alexander, 2010. "Higher-order volatility: time series," MPRA Paper 21087, University Library of Munich, Germany.
    9. repec:hal:wpaper:hal-00687675 is not listed on IDEAS
    10. repec:eee:ecmode:v:64:y:2017:i:c:p:295-301 is not listed on IDEAS
    11. Matthias Fengler & Wolfgang Härdle & Enno Mammen, 2005. "A Dynamic Semiparametric Factor Model for Implied Volatility String Dynamics," SFB 649 Discussion Papers SFB649DP2005-020, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.


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