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

Hsuan-Chu Lin (), Ren-Raw Chen and Oded Palmon
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Hsuan-Chu Lin: National Cheng-Kung University
Ren-Raw Chen: Fordham University
Oded Palmon: Rutgers University

Review of Quantitative Finance and Accounting, 2016, vol. 46, issue 4, No 8, 907-935

Abstract: Abstract 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 S&P 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.

Keywords: Non-parametric; Option pricing; S&P 500 index; Volatility smile (search for similar items in EconPapers)
JEL-codes: C14 C68 G12 G13 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s11156-014-0491-z

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