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Implied Volatility Surface: Construction Methodologies and Characteristics

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  • Cristian Homescu

Abstract

The implied volatility surface (IVS) is a fundamental building block in computational finance. We provide a survey of methodologies for constructing such surfaces. We also discuss various topics which can influence the successful construction of IVS in practice: arbitrage-free conditions in both strike and time, how to perform extrapolation outside the core region, choice of calibrating functional and selection of numerical optimization algorithms, volatility surface dynamics and asymptotics.

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  • Cristian Homescu, 2011. "Implied Volatility Surface: Construction Methodologies and Characteristics," Papers 1107.1834, arXiv.org.
    • Handle: RePEc:arx:papers:1107.1834
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    Cited by:

    1. Yasaman Karami & Kenichiro Shiraya, 2018. "An approximation formula for normal implied volatility under general local stochastic volatility models," CARF F-Series CARF-F-427, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. Martin Magris & Perttu Barholm & Juho Kanniainen, 2017. "Implied volatility smile dynamics in the presence of jumps," Papers 1711.02925, arXiv.org, revised May 2020.
    3. Miloš Kopa & Sebastiano Vitali & Tomáš Tichý & Radek Hendrych, 2017. "Implied volatility and state price density estimation: arbitrage analysis," Computational Management Science, Springer, vol. 14(4), pages 559-583, October.
    4. Matúš Maciak & Sebastiano Vitali, 2024. "Using interpolated implied volatility for analysing exogenous market changes," Computational Management Science, Springer, vol. 21(1), pages 1-21, June.
    5. Emmanuel Gnabeyeu & Omar Karkar & Imad Idboufous, 2024. "Solving The Dynamic Volatility Fitting Problem: A Deep Reinforcement Learning Approach," Papers 2410.11789, arXiv.org.
    6. Zheng Gong & Wojciech Frys & Renzo Tiranti & Carmine Ventre & John O'Hara & Yingbo Bai, 2022. "A new encoding of implied volatility surfaces for their synthetic generation," Papers 2211.12892, arXiv.org, revised Jun 2023.
    7. David Berger & Ian Dew-Becker & Stefano Giglio, 2020. "Uncertainty Shocks as Second-Moment News Shocks," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 87(1), pages 40-76.
    8. Yaxiong Zeng & Diego Klabjan, 2017. "Online Adaptive Machine Learning Based Algorithm for Implied Volatility Surface Modeling," Papers 1706.01833, arXiv.org, revised Jun 2018.
    9. Nicola F. Zaugg & Leonardo Perotti & Lech A. Grzelak, 2024. "Volatility Parametrizations with Random Coefficients: Analytic Flexibility for Implied Volatility Surfaces," Papers 2411.04041, arXiv.org, revised Nov 2024.
    10. Shuaiqiang Liu & Anastasia Borovykh & Lech A. Grzelak & Cornelis W. Oosterlee, 2019. "A neural network-based framework for financial model calibration," Papers 1904.10523, arXiv.org.
    11. Sebastiano Vitali & Miloš Kopa & Gabriele Giana, 2023. "Implied volatility smoothing at COVID-19 times," Computational Management Science, Springer, vol. 20(1), pages 1-42, December.
    12. Fernández, J.L. & Ferreiro, A.M. & García-Rodríguez, J.A. & Leitao, A. & López-Salas, J.G. & Vázquez, C., 2013. "Static and dynamic SABR stochastic volatility models: Calibration and option pricing using GPUs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 55-75.
    13. Stefano Giglio & Ian Dew-Becker & David Berger, 2016. "Contractionary Volatility or Volatile Contractions?," 2016 Meeting Papers 673, Society for Economic Dynamics.
    14. Kotzé, Antonie & Labuschagne, Coenraad C.A. & Nair, Merell L. & Padayachi, Nadine, 2013. "Arbitrage-free implied volatility surfaces for options on single stock futures," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 380-399.
    15. Maria Cristina Recchioni & Gabriele Tedeschi, 2016. "From bond yield to macroeconomic instability: The effect of negative interest rates," Working Papers 2016/06, Economics Department, Universitat Jaume I, Castellón (Spain).
    16. Yasaman Karami & Kenichiro Shiraya, 2018. "An approximation formula for normal implied volatility under general local stochastic volatility models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(9), pages 1043-1061, September.

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