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Implied Risk-Neutral probability Density functions from options prices : A comparison of estimation methods

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  • Rihab Bedoui
  • Haykel Hamdi
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    Abstract

    This paper compares the goodness-of-fit of eight option-based approaches used to extract risk-neutral probability density functions from a high-frequency CAC 40 index options during a normal and troubled period. Our findings show that the kernel estimator generates a strong volatility smile with respect to the moneyness, and the kernel smiles shape varies with the chosen time to maturity. The mixture of log-normals, Edgeworth expansion, hermite polynomials, jump diffusion and Heston models are more in line and have heavier tails than the log-normal distribution. Moreover, according to the goodness of fit criteria we compute, the jump diffusion model provides a much better fit than the other models on the period just-before the crisis for relatively short maturities. However, during this same period, the mixture of log-normal models performs better for more than three month maturity. Furthermore, in the troubled period and the period just-after the crisis, we find that semi-parametric models are the methods with the best accuracy in fitting observed option prices for all maturities with a minimal difference towards the mixture of log-normals model.

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    File URL: http://economix.fr/pdf/dt/2010/WP_EcoX_2010-16.pdf
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    Bibliographic Info

    Paper provided by University of Paris West - Nanterre la Défense, EconomiX in its series EconomiX Working Papers with number 2010-16.

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    Length: 42 pages
    Date of creation: 2010
    Date of revision:
    Handle: RePEc:drm:wpaper:2010-16

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    Related research

    Keywords: Risk-neutral density; mixture of log-normal distributions; Edgeworth expansions; Hermite polynomials; tree-based methods; kernel regression; Heston’s stochastic volatility model; jump diffusion model;

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    1. Jondeau, Eric & Rockinger, Michael, 2001. "Gram-Charlier densities," Journal of Economic Dynamics and Control, Elsevier, vol. 25(10), pages 1457-1483, October.
    2. Karim Abadir & Michael Rockinger, . "Density-Embedding Functions," Discussion Papers 97/16, Department of Economics, University of York.
    3. Jondeau, E. & Rockinger, M., 1998. "Reading the Smile: The Message Conveyed by Methods Which Infer Risk Neutral," Working papers 47, Banque de France.
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