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

Rihab Bedoui and Haykel Hamdi

No 2010-16, EconomiX Working Papers from University of Paris Nanterre, EconomiX

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.

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 (search for similar items in EconPapers)
JEL-codes: C02 C14 C65 G13 (search for similar items in EconPapers)
Pages: 42 pages
Date: 2010
New Economics Papers: this item is included in nep-ecm
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