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Nonparametric estimates of pricing functionals

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  • Carlo Marinelli
  • Stefano d'Addona

Abstract

We analyze the empirical performance of several non-parametric estimators of the pricing functional for European options, using historical put and call prices on the S&P500 during the year 2012. Two main families of estimators are considered, obtained by estimating the pricing functional directly, and by estimating the (Black-Scholes) implied volatility surface, respectively. In each case simple estimators based on linear interpolation are constructed, as well as more sophisticated ones based on smoothing kernels, \`a la Nadaraya-Watson. The results based on the analysis of the empirical pricing errors in an extensive out-of-sample study indicate that a simple approach based on the Black-Scholes formula coupled with linear interpolation of the volatility surface outperforms, both in accuracy and computational speed, all other methods.

Suggested Citation

  • Carlo Marinelli & Stefano d'Addona, 2015. "Nonparametric estimates of pricing functionals," Papers 1506.06568, arXiv.org, revised Sep 2017.
    • Handle: RePEc:arx:papers:1506.06568
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    References listed on IDEAS

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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
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    6. Grith, Maria & Härdle, Wolfgang Karl & Schienle, Melanie, 2010. "Nonparametric estimation of risk-neutral densities," SFB 649 Discussion Papers 2010-021, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    7. Brendan K. Beare & Lawrence D. W. Schmidt, 2016. "An Empirical Test of Pricing Kernel Monotonicity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(2), pages 338-356, March.
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    9. Chernov, Mikhail & Ghysels, Eric, 2000. "A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation," Journal of Financial Economics, Elsevier, vol. 56(3), pages 407-458, June.
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    Citations

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    Cited by:

    1. Carlo Marinelli, 2024. "On certain representations of pricing functionals," Annals of Finance, Springer, vol. 20(1), pages 91-127, March.
    2. 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.
    3. Carlo Marinelli & Stefano d'Addona, 2022. "Nonparametric estimates of option prices via Hermite basis functions," Papers 2209.09656, arXiv.org, revised Aug 2023.

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    More about this item

    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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