Explaining the volatility smile: Non-parametric versus parametric option models

Hsuan Chu Lin*, Ren Raw Chen, Oded Palmon

*Corresponding author for this work

Research output: Contribution to journalJournal Article peer-review

2 Scopus citations


We employ a “non-parametric” pricing approach of European options to explain the volatility smile. In contrast to “parametric” models that assume that the underlying state variable(s) follows a stochastic process that adheres to a strict functional form, “non-parametric” models directly fit the end distribution of the underlying state variable(s) with statistical distributions that are not represented by parametric functions. We derive an approximation formula which prices SandP 500 index options in closed form which corresponds to the lower bound recently proposed by Lin et al. (Rev Quant Financ Account 38(1):109–129, 2012). Our model yields option prices that are more consistent with the data than the option prices that are generated by several widely used models. Although a quantitative comparison with other non-parametric models is more difficult, there are indications that our model is also more consistent with the data than these models.

Original languageEnglish
Pages (from-to)907-935
Number of pages29
JournalReview of Quantitative Finance and Accounting
Issue number4
StatePublished - 01 05 2016
Externally publishedYes

Bibliographical note

Publisher Copyright:
© Springer Science+Business Media New York 2014.


  • Non-parametric
  • Option pricing
  • SandP 500 index
  • Volatility smile


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