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Bias-reduced nonparametric local volatility: Stable numerical method without building the continuous implied volatility surface

Author

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  • Cho, Junhyun
  • Jeong, Wooyeol
  • Yang, Donghee
  • Lee, Sungchul

Abstract

We propose a stable numerical method for constructing a bias-reduced nonparametric local volatility surface without relying on a pre-constructed continuous implied volatility surface.

Suggested Citation

  • Cho, Junhyun & Jeong, Wooyeol & Yang, Donghee & Lee, Sungchul, 2026. "Bias-reduced nonparametric local volatility: Stable numerical method without building the continuous implied volatility surface," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 246(C), pages 229-246.
    • Handle: RePEc:eee:matcom:v:246:y:2026:i:c:p:229-246
    DOI: 10.1016/j.matcom.2026.01.030
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    References listed on IDEAS

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    1. Kim, Junseok & Kim, Taekkeun & Jo, Jaehyun & Choi, Yongho & Lee, Seunggyu & Hwang, Hyeongseok & Yoo, Minhyun & Jeong, Darae, 2016. "A practical finite difference method for the three-dimensional Black–Scholes equation," European Journal of Operational Research, Elsevier, vol. 252(1), pages 183-190.
    2. J. Michael Harrison & Stanley R. Pliska, 1981. "Martingales and Stochastic Integrals in the Theory of Continous Trading," Discussion Papers 454, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. H. Berestycki & J. Busca & I. Florent, 2002. "Asymptotics and calibration of local volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 61-69.
    4. Christa Cuchiero & Wahid Khosrawi & Josef Teichmann, 2020. "A Generative Adversarial Network Approach to Calibration of Local Stochastic Volatility Models," Risks, MDPI, vol. 8(4), pages 1-31, September.
    5. Marc Chataigner & Stéphane Crépey & Matthew Dixon, 2020. "Deep Local Volatility," Risks, MDPI, vol. 8(3), pages 1-18, August.
    6. Matthias Fengler, 2009. "Arbitrage-free smoothing of the implied volatility surface," Quantitative Finance, Taylor & Francis Journals, vol. 9(4), pages 417-428.
    7. Christa Cuchiero & Wahid Khosrawi & Josef Teichmann, 2020. "A generative adversarial network approach to calibration of local stochastic volatility models," Papers 2005.02505, arXiv.org, revised Sep 2020.
    8. Patrick Hagan & Graeme West, 2006. "Interpolation Methods for Curve Construction," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(2), pages 89-129.
    9. Marc Chataigner & St'ephane Cr'epey & Matthew Dixon, 2020. "Deep Local Volatility," Papers 2007.10462, arXiv.org.
    10. Yang, Wensheng & Ma, Jingtang & Cui, Zhenyu, 2025. "A general valuation framework for rough stochastic local volatility models and applications," European Journal of Operational Research, Elsevier, vol. 322(1), pages 307-324.
    11. Gaoyue Guo & Antoine Jacquier & Claude Martini & Leo Neufcourt, 2016. "Generalized Arbitrage-Free SVI Volatility Surfaces," Post-Print hal-05564337, HAL.
    12. E. Mammen & C. Thomas‐Agnan, 1999. "Smoothing Splines and Shape Restrictions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(2), pages 239-252, June.
    13. Li, Chen Xu & Li, Chenxu & Li, Chun, 2025. "Implied local volatility models," Journal of Empirical Finance, Elsevier, vol. 80(C).
    14. Marc Chataigner & Stéphane Crépey & Matthew Dixon, 2020. "Deep Local Volatility," Post-Print hal-03910122, HAL.
    15. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    16. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    17. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    18. D’Amato, Valeria & Levantesi, Susanna & Piscopo, Gabriella, 2022. "Deep learning in predicting cryptocurrency volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
    19. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    20. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    21. Recchioni, Maria Cristina & Iori, Giulia & Tedeschi, Gabriele & Ouellette, Michelle S., 2021. "The complete Gaussian kernel in the multi-factor Heston model: Option pricing and implied volatility applications," European Journal of Operational Research, Elsevier, vol. 293(1), pages 336-360.
    22. Zhe Wang & Ameir Shaa & Nicolas Privault & Claude Guet, 2021. "Deep self-consistent learning of local volatility," Papers 2201.07880, arXiv.org, revised Feb 2025.
    23. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    24. Gaoyue Guo & Antoine Jacquier & Claude Martini & Leo Neufcourt, 2012. "Generalised arbitrage-free SVI volatility surfaces," Papers 1210.7111, arXiv.org, revised May 2016.
    25. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
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