IDEAS home Printed from https://ideas.repec.org/a/taf/quantf/v14y2014i1p73-85.html
   My bibliography  Save this article

Non-parametric calibration of the local volatility surface for European options using a second-order Tikhonov regularization

Author

Listed:
  • Jian Geng
  • I. Michael Navon
  • Xiao Chen

Abstract

We calibrate the local volatility surface for European options across all strikes and maturities of the same underlying. There is no interpolation or extrapolation of either the option prices or the volatility surface. We do not make any assumption regarding the shape of the volatility surface except to assume that it is smooth. Due to the smoothness assumption, we apply a second-order Tikhonov regularization. We choose the Tikhonov regularization parameter as one of the singular values of the Jacobian matrix of the Dupire model. Finally we perform extensive numerical tests to assess and verify the aforementioned techniques for both volatility models with known analytical solutions of European option prices and real market option data.

Suggested Citation

  • Jian Geng & I. Michael Navon & Xiao Chen, 2014. "Non-parametric calibration of the local volatility surface for European options using a second-order Tikhonov regularization," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 73-85, January.
    • Handle: RePEc:taf:quantf:v:14:y:2014:i:1:p:73-85
    DOI: 10.1080/14697688.2013.819988
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/14697688.2013.819988
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/14697688.2013.819988?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kai Yin & Anirban Mondal, 2023. "Bayesian uncertainty quantification of local volatility model," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 290-324, May.
    2. Hsuan-Chu Lin & Ren-Raw Chen & Oded Palmon, 2016. "Explaining the volatility smile: non-parametric versus parametric option models," Review of Quantitative Finance and Accounting, Springer, vol. 46(4), pages 907-935, May.
    3. Soobin Kwak & Youngjin Hwang & Yongho Choi & Jian Wang & Sangkwon Kim & Junseok Kim, 2022. "Reconstructing the Local Volatility Surface from Market Option Prices," Mathematics, MDPI, vol. 10(14), pages 1-12, July.
    4. Y. Esmaeelzade Aghdam & H. Mesgarani & A. Amin & J. F. Gómez-Aguilar, 2024. "An Efficient Numerical Scheme to Approach the Time Fractional Black–Scholes Model Using Orthogonal Gegenbauer Polynomials," Computational Economics, Springer;Society for Computational Economics, vol. 64(1), pages 211-224, July.

    More about this item

    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:taf:quantf:v:14:y:2014:i:1:p:73-85. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RQUF20 .

    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.