Are there any papers that make an explicit contrast/comparison of the following (or other) vol models in terms of the suitability for addressing some empirical problem?
You may want to first broadly categorize volatility models before comparing between them within each class, it does not make sense to compare standard deviation models with an implied vol model.
I would broadly classify as follows:
Historical realized volatility: Those include standard deviation (sum of squared deviations), realized range volatility models, and essentially anything that is based on past price and return data. Such models strictly deal with past data points and do not bother to make any sort of prediction.
Implied volatility models: Those lead to volatility measures that are the other side of the coin of derivative prices, whereas the implied vol model functions as translation tool. Part of that categorization is the SABR model and essentially most all stochastic models that implement different sorts of Brownian Motion "drivers".
Volatility forecasting models generally utilize past data, contrary to implied volatility models, in order to make predictions about future volatility dynamics and levels. Most Garch volatility models fall under this category.
A sub-category deals with intra-day volatility models such as Pearson or Garman-Klass.
I understand that my answer does not compare each individual volatility model but I believe, or hope, it helps to broadly compare and classify different models.
