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

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  • 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
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    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.

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