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On implied volatility for options—Some reasons to smile and more to correct

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  • Chen, Song Xi
  • Xu, Zheng

Abstract

We analyze the properties of the implied volatility, the commonly used volatility estimator by direct option price inversion. It is found that the implied volatility is subject to a systematic bias in the presence of pricing errors, which makes it inconsistent to the underlying volatility. We propose an estimator of the underlying volatility by first estimating nonparametrically the option price function, followed by inverting the nonparametrically estimated price. It is shown that the approach removes the adverse impacts of the pricing errors and produces a consistent volatility estimator for a wide range of option price models. We demonstrate the effectiveness of the proposed approach by numerical simulation and empirical analysis on S&P 500 option data.

Suggested Citation

  • Chen, Song Xi & Xu, Zheng, 2014. "On implied volatility for options—Some reasons to smile and more to correct," Journal of Econometrics, Elsevier, vol. 179(1), pages 1-15.
    • Handle: RePEc:eee:econom:v:179:y:2014:i:1:p:1-15
    DOI: 10.1016/j.jeconom.2013.10.007
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    References listed on IDEAS

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    Cited by:

    1. Antunes, João Marques & Fuinhas, José Alberto & Marques, António Cardoso, 2014. "Modelização VAR da volatilidade dos preços do ouro e dos índices dos mercados financeiros [Modelling the volatility of gold prices and financial stock indexes: a VAR approach]," MPRA Paper 57017, University Library of Munich, Germany.
    2. Shu Ling Chiang & Ming Shann Tsai, 2019. "Valuation of an option using non-parametric methods," Review of Derivatives Research, Springer, vol. 22(3), pages 419-447, October.
    3. Beer, Simone & Braun, Alexander, 2022. "Market-consistent valuation of natural catastrophe risk," Journal of Banking & Finance, Elsevier, vol. 134(C).
    4. Zheng Xu, 2016. "An alternative circular smoothing method to nonparametric estimation of periodic functions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(9), pages 1649-1672, July.
    5. Piccotti, Louis R. & Schreiber, Ben Z., 2015. "Information shares of two parallel currency options markets: Trading costs versus transparency/tradability," Journal of Empirical Finance, Elsevier, vol. 32(C), pages 210-229.
    6. Martin Wallmeier, 2024. "Quality issues of implied volatilities of index and stock options in the OptionMetrics IvyDB database," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(5), pages 854-875, May.
    7. Dalderop, Jeroen, 2020. "Nonparametric filtering of conditional state-price densities," Journal of Econometrics, Elsevier, vol. 214(2), pages 295-325.

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    More about this item

    Keywords

    Bias correction; Implied volatility; Kernel estimator; Pricing errors;
    All these keywords.

    JEL classification:

    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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