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

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  • Rihab Bedoui

    (EconomiX - EconomiX - UPN - Université Paris Nanterre - CNRS - Centre National de la Recherche Scientifique)

  • Haykel Hamdi

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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  • Rihab Bedoui & Haykel Hamdi, 2010. "Implied Risk-Neutral probability Density functions from options prices: A comparison of estimation methods," Working Papers hal-04140913, HAL.
  • Handle: RePEc:hal:wpaper:hal-04140913
    Note: View the original document on HAL open archive server: https://hal.science/hal-04140913
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    References listed on IDEAS

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