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A class of risk neutral densities with heavy tails

Author

Listed:
  • Niels VÖver Hartvig

    (Department of Theoretical Statistics, Department of Mathematical Sciences and MaPhySto, Ny Munkegade, DK-8000 Aarhus C, Denmark Manuscript)

  • Jens Ledet Jensen

    (Department of Theoretical Statistics, Department of Mathematical Sciences and MaPhySto, Ny Munkegade, DK-8000 Aarhus C, Denmark Manuscript)

  • Jan Pedersen

    (Department of Theoretical Statistics, Department of Mathematical Sciences and MaPhySto, Ny Munkegade, DK-8000 Aarhus C, Denmark Manuscript)

Abstract

From observed bid and ask prices of European call and put options we estimate the risk neutral density of a stock at some future time $t>0$. We restrict attention to a class of densities with heavy tails and use a Bayesian formulation in order to study the variation in the distributions fitting the data. Heavy tails are here meant in the intuitive sense of being heavier than the tails of a normal distribution. From the fitted risk neutral density we also consider the inverse problem of finding the volatility in a diffusion model for the price process. Finally, we apply our methods to data on the S&P 500 index.

Suggested Citation

  • Niels VÖver Hartvig & Jens Ledet Jensen & Jan Pedersen, 2001. "A class of risk neutral densities with heavy tails," Finance and Stochastics, Springer, vol. 5(1), pages 115-128.
    • Handle: RePEc:spr:finsto:v:5:y:2001:i:1:p:115-128
    Note: received: June 1999 / final version received: March 2000
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    Citations

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    Cited by:

    1. Lina M. Cortés & Javier Perote & Andrés Mora-Valencia, 2017. "Implicit probability distribution for WTI options: The Black Scholes vs. the semi-nonparametric approach," Documentos de Trabajo de Valor Público 15923, Universidad EAFIT.
    2. Cortés, Lina M. & Mora-Valencia, Andrés & Perote, Javier, 2020. "Retrieving the implicit risk neutral density of WTI options with a semi-nonparametric approach," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    3. R. Fernández-Pascual & M. Ruiz-Medina & J. Angulo, 2003. "Multiscale estimation of processes related to the fractional Black-Scholes equation," Computational Statistics, Springer, vol. 18(3), pages 401-415, September.

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