Diagnosing Option Model Misspecification from Implied Volatility Patterns

Summary

The document raises a model-validation question using an empirical study that estimates implied volatilities for a full option sample and then for subsets split by moneyness and maturity. Differences among the subset estimates are presented as evidence that candidate pricing models may be misspecified. The discussion asks whether such variation merely reflects the volatility smile in observed prices, and what it means for a model to allow for misspecification.

The example illustrates a practical diagnostic: compare model-implied parameters across economically distinct slices of the option surface. If a model is correctly specified under its assumptions, systematic differences across those slices may signal that its structure does not adequately capture the data. The post also mentions GARCH as a framework that can contain a simpler constant specification, though it does not explain the nesting argument in detail. No new empirical results are provided, and parameter variation alone does not identify the source of model failure; the interpretation depends on the model assumptions, sample, and estimation method.

Key ideas

• Estimating implied volatility across moneyness and maturity groups can reveal parameter instability.
• Systematic differences across option subsets may indicate that a pricing model fails to capture the observed surface.
• A volatility smile may be a feature that a model needs to explain, rather than an automatic excuse for inconsistent implied parameters.
• Nested model frameworks can include simpler specifications, but the document does not fully explain how this addresses misspecification.

Tags

# Do some option pricing models allow for misspecification and what does it mean?


# Do some option pricing models allow for misspecification and what does it mean?












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?

Thank you.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.