This is to some extent a theoretical question and maybe we can work together to produce some input and output.
Diverse option pricing models are reported to be misspecified in various studies. One example is the paper of Baksi et. al (1997) called "Empirical performance of alternative option pricing models". The authors come to this conclusion by estimating the implied volatilities for a full dataset, and then re-estimating these implied volatilities for six subsets based on the moneyness-maturity categories. They find differences between the values of the implied volatilities. I quote:
"if each candidate option pricing model were correctly specified, the six sets of option prices, formed across either moneyness or maturity, should not have resulted in different implied parameter volatility values nor should the “implied-parameter matrix” treatment have led to any performance improvement."
My first question is, what does misspecified actually mean? Isn't this difference between the implied parameters due to the presence of the volatility smile; in that case, one should say that the models are not misspecified, but that this is a result due to the data.
Secondly, how do some models allow for this misspecification? If for instance, a specific model is misspecified during a particular period, it is imaginable that it produces a smaller pricing error during a different sub-period. One example I heard is the GARCH option pricing model; a constant GARCH model is nested within the GARCH framework, so that it allows for misspecification. I don't entirely understand this concept, so maybe someone can help me out?