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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

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.

Suggested Citation

  • Rihab Bedoui & Haykel Hamdi, 2010. "Implied Risk-Neutral probability Density functions from options prices : A comparison of estimation methods," EconomiX Working Papers 2010-16, University of Paris Nanterre, EconomiX.
  • Handle: RePEc:drm:wpaper:2010-16
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    File URL: http://economix.fr/pdf/dt/2010/WP_EcoX_2010-16.pdf
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    References listed on IDEAS

    as
    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, "undated". "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.
    Full references (including those not matched with items on IDEAS)

    More about this item

    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;

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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