IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2301.07830.html
   My bibliography  Save this paper

Fixed-point iterative algorithm for SVI model

Author

Listed:
  • Shuzhen Yang
  • Wenqing Zhang

Abstract

The stochastic volatility inspired (SVI) model is widely used to fit the implied variance smile. Presently, most optimizer algorithms for the SVI model have a strong dependence on the input starting point. In this study, we develop an efficient iterative algorithm for the SVI model based on a fixed-point and least-square optimizer. Furthermore, we present the convergence results in certain situations for this novel iterative algorithm. Compared with the quasi-explicit SVI method, we demonstrate the advantages of the fixed-point iterative algorithm using simulation and market data.

Suggested Citation

  • Shuzhen Yang & Wenqing Zhang, 2023. "Fixed-point iterative algorithm for SVI model," Papers 2301.07830, arXiv.org.
    • Handle: RePEc:arx:papers:2301.07830
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2301.07830
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jim Gatheral & Antoine Jacquier, 2014. "Arbitrage-free SVI volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 59-71, January.
    2. Roger W. Lee, 2004. "The Moment Formula For Implied Volatility At Extreme Strikes," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 469-480, July.
    3. Martin Forde & Antoine Jacquier & Aleksandar Mijatovic, 2009. "Asymptotic formulae for implied volatility in the Heston model," Papers 0911.2992, arXiv.org, revised May 2010.
    4. Yacine Aït-Sahalia & Chenxu Li & Chen Xu Li, 2021. "Implied Stochastic Volatility Models [Testing continuous-time models of the spot interest rate]," The Review of Financial Studies, Society for Financial Studies, vol. 34(1), pages 394-450.
    5. Jim Gatheral & Antoine Jacquier, 2011. "Convergence of Heston to SVI," Quantitative Finance, Taylor & Francis Journals, vol. 11(8), pages 1129-1132.
    6. Yacine Aït-Sahalia & Chenxu Li & Chen Xu Li & Ralph Koijen, 2021. "Implied Stochastic Volatility Models," Review of Economic Studies, Oxford University Press, vol. 34(1), pages 394-450.
    7. Arianna Mingone, 2022. "No arbitrage global parametrization for the eSSVI volatility surface," Papers 2204.00312, arXiv.org.
    8. A. Mingone, 2022. "No arbitrage global parametrization for the eSSVI volatility surface," Quantitative Finance, Taylor & Francis Journals, vol. 22(12), pages 2205-2217, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Vimal Raval & Antoine Jacquier, 2023. "The log‐moment formula for implied volatility," Mathematical Finance, Wiley Blackwell, vol. 33(4), pages 1146-1165, October.
    2. 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.
    3. Li, Chen Xu & Li, Chenxu & Li, Chun, 2025. "Implied local volatility models," Journal of Empirical Finance, Elsevier, vol. 80(C).
    4. Jacquier, Antoine & Roome, Patrick, 2016. "Large-maturity regimes of the Heston forward smile," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1087-1123.
    5. Florence Guillaume & Wim Schoutens, 2014. "Heston Model: The Variance Swap Calibration," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 76-89, April.
    6. 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.
    7. Ruben Wiedemann & Antoine Jacquier & Lukas Gonon, 2024. "Operator Deep Smoothing for Implied Volatility," Papers 2406.11520, arXiv.org, revised Jun 2025.
    8. Sergey Badikov & Mark H. A. Davis & Antoine Jacquier, 2018. "Perturbation analysis of sub/super hedging problems," Papers 1806.03543, arXiv.org, revised May 2021.
    9. Mnacho Echenim & Emmanuel Gobet & Anne-Claire Maurice, 2022. "Unbiasing and robustifying implied volatility calibration in a cryptocurrency market with large bid-ask spreads and missing quotes," Papers 2207.02989, arXiv.org.
    10. Archil Gulisashvili & Frederi Viens & Xin Zhang, 2015. "Small-time asymptotics for Gaussian self-similar stochastic volatility models," Papers 1505.05256, arXiv.org, revised Mar 2016.
    11. Arianna Mingone, 2022. "Smiles in delta," Papers 2209.00406, arXiv.org.
    12. Stefano De Marco & Caroline Hillairet & Antoine Jacquier, 2013. "Shapes of implied volatility with positive mass at zero," Papers 1310.1020, arXiv.org, revised May 2017.
    13. 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.
    14. repec:hal:wpaper:hal-03715921 is not listed on IDEAS
    15. Tahar Ferhati, 2020. "Robust Calibration For SVI Model Arbitrage Free," Working Papers hal-02490029, HAL.
    16. Antoine Jacquier & Aleksandar Mijatović, 2014. "Large Deviations for the Extended Heston Model: The Large-Time Case," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 21(3), pages 263-280, September.
    17. Cristian Homescu, 2011. "Implied Volatility Surface: Construction Methodologies and Characteristics," Papers 1107.1834, arXiv.org.
    18. Hadrien De March & Pierre Henry-Labordere, 2019. "Building arbitrage-free implied volatility: Sinkhorn's algorithm and variants," Papers 1902.04456, arXiv.org, revised Jul 2023.
    19. Martin Forde & Antoine Jacquier, 2011. "The large-maturity smile for the Heston model," Finance and Stochastics, Springer, vol. 15(4), pages 755-780, December.
    20. Claude Martini & Arianna Mingone, 2021. "Explicit no arbitrage domain for sub-SVIs via reparametrization," Papers 2106.02418, arXiv.org.
    21. Mehdi El Amrani & Antoine Jacquier & Claude Martini, 2019. "Dynamics of symmetric SSVI smiles and implied volatility bubbles," Papers 1909.10272, arXiv.org, revised Feb 2021.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2301.07830. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.