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Volatility Smile Interpolation With Radial Basis Functions

Author

Listed:
  • HERMANN AZEMTSA DONFACK

    (Department of Finance and Investment Management, University of Johannesburg, Johannesburg, Gauteng, South Africa)

  • CELESTIN WAFO SOH

    (Department of Finance and Investment Management, University of Johannesburg, Johannesburg, Gauteng, South Africa†Department of Mathematics and Statistical Sciences, College of Science Engineering and Technology, Jackson State University, Jackson Mississipi 39217, USA)

  • ANTONIE KOTZE

    (Department of Finance and Investment Management, University of Johannesburg, Johannesburg, Gauteng, South Africa)

Abstract

The Radial Basis Functions (RBF) interpolation is a popular approximation technique used to smooth scattered data in various dimensions. This study uses RBF interpolation to interpolate the volatility skew of the S&P500 index options. The interpolated skews are used to construct the risk-neutral densities of the index and its local volatility surface. The RBF interpolation is contrasted throughout the study with the cubic spline interpolation. An analysis of the densities and the local volatility shows that RBF are an effective and practical tool for interpolating the implied volatility surface.

Suggested Citation

  • Hermann Azemtsa Donfack & Celestin Wafo Soh & Antonie Kotze, 2022. "Volatility Smile Interpolation With Radial Basis Functions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 25(07n08), pages 1-23, November.
    • Handle: RePEc:wsi:ijtafx:v:25:y:2022:i:07n08:n:s0219024922500303
    DOI: 10.1142/S0219024922500303
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