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Nonparametric estimates of option prices via Hermite basis functions
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Nonparametric estimates of option prices via Hermite basis functions

Author

Listed:
  • Carlo Marinelli

    (University College London)

  • Stefano d’Addona

    (Università di Roma Tre)

Abstract

We consider approximate pricing formulas for European options based on approximating the logarithmic return’s density of the underlying by a linear combination of rescaled Hermite polynomials. The resulting models, that can be seen as perturbations of the classical Black-Scholes one, are nonpararametric in the sense that the distribution of logarithmic returns at fixed times to maturity is only assumed to have a square-integrable density. We extensively investigate the empirical performance, defined in terms of out-of-sample relative pricing error, of this class of approximating models, depending on their order (that is, roughly speaking, the degree of the polynomial expansion) as well as on several ways to calibrate them to observed data. Empirical results suggest that such approximate pricing formulas, when compared with simple nonparametric estimates based on interpolation and extrapolation on the implied volatility curve, perform reasonably well only for options with strike price not too far apart from the strike prices of the observed sample.

Suggested Citation

  • Carlo Marinelli & Stefano d’Addona, 2023. "Nonparametric estimates of option prices via Hermite basis functions," Annals of Finance, Springer, vol. 19(4), pages 477-522, December.
    • Handle: RePEc:kap:annfin:v:19:y:2023:i:4:d:10.1007_s10436-023-00431-4
    DOI: 10.1007/s10436-023-00431-4
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    References listed on IDEAS

    as
    1. Carlo Marinelli, 2021. "On certain representations of pricing functionals," Papers 2109.05564, arXiv.org.
    2. Marinelli, Carlo & d’Addona, Stefano, 2017. "Nonparametric estimates of pricing functionals," Journal of Empirical Finance, Elsevier, vol. 44(C), pages 19-35.
    3. Xiu, Dacheng, 2014. "Hermite polynomial based expansion of European option prices," Journal of Econometrics, Elsevier, vol. 179(2), pages 158-177.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Option pricing; Nonparametric models; Hermite polynomials; Implied volatility;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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