Implied volatility surfaces: a comprehensive analysis using half a billion option prices

Maxim Ulrich (), Lukas Zimmer and Constantin Merbecks
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Maxim Ulrich: Karlsruhe Institute of Technology (KIT)
Lukas Zimmer: Karlsruhe Institute of Technology (KIT)
Constantin Merbecks: Karlsruhe Institute of Technology (KIT)

Review of Derivatives Research, 2023, vol. 26, issue 2, No 1, 135-169

Abstract: Abstract This study delves into the critical aspect of accurately estimating single stock volatility surfaces, a task indispensable for option pricing, risk management, and empirical asset pricing. Utilizing a comprehensive dataset consisting of half a billion daily price observations for options on 499 US individual stocks and the S&P 500, the research investigates the accuracy of diverse methods for constructing volatility surfaces. The comparative evaluation of the three-dimensional kernel smoother by OptionMetrics (IvyDB US file and data reference manual, version 5.2, Rev. 01/27/2022, Computer software manual, New York, 2022), the semi-parametric spline by Figlewski (in: Robert F. Engle (ed) Estimating the implied risk neutral density. Volatility and time series econometrics: Essays in honor, Oxford University Press, Oxford, 2008), and a refined one-dimensional kernel smoother reveals the distinct superiority of the latter. This method consistently outperforms its counterparts across all moneyness, maturity, and liquidity categories, with markedly lower error metrics. The study further uncovers significant distortions in the extraction of Bakshi et al. (Rev Financ Stud 16:101–143, 2003) moments and skewness spanning induced by the noise-infused three-dimensional kernel smoother, which could potentially mislead derivative pricing and trading decisions. The findings offer valuable insights to traders, risk managers, investors, and researchers, suggesting a robust, one-size-fits-all method for crafting more accurate and less noisy volatility predictions. The research advances our understanding of option-implied information, its extraction, and broader implications for financial markets.

Keywords: Volatility surface construction; Single stock options; Implied volatility estimation; Prediction accuracy; Kernel smoother; Three-dimensional vs. one-dimensional smoothing (search for similar items in EconPapers)
JEL-codes: C14 C53 G13 G17 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11147-023-09195-5

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