Fitting and testing for the implied volatility curve using parametric models

Numerous issues have arisen over the past few decades relating to the implied volatility smile in the options market; however, the extant literature reveals that relatively little effort has thus far been placed into comparing the various implied volatility models, essentially as a result of the lack of any theoretical foundation on which to base such comparative analysis. In this study, we use a comprehensive options database and employ methods of combining the various hypothesis tests to compare the different implied volatility models. To the best of our knowledge, this is the first study of its kind to address this issue using combination tests. Our empirical results reveal that the linear piecewise model is the most appropriate model for capturing the implied volatility smile, with additional robustness checks confirming the validity of this finding.