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How to Classify Historical, Implied, and Forecasting Volatility Models

Article Quant Q&A · Author: Jase
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Summary

The answer groups volatility methods by the kind of information they use and the task they serve. Historical realized measures, including standard deviation and range methods, summarize past price or return behavior. Implied volatility translates derivative prices into volatility measures, while forecasting models such as many GARCH variants use historical observations to estimate future volatility. It also identifies intraday measures such as Pearson and Garman–Klass methods as a subcategory.

The central lesson is to classify models before comparing them: methods that measure past variation, infer volatility from option prices, and forecast future dynamics address different empirical questions. The response offers no head-to-head performance evidence or detailed criteria for choosing among models within a category. Its broad categories are a starting framework, and the answer itself acknowledges that it does not compare each individual model.

Key ideas

  • Historical realized volatility measures variation in past prices or returns.
  • Implied volatility derives a volatility measure from derivative prices.
  • Forecasting models use past data to estimate future volatility dynamics and levels.
  • Intraday volatility measures form a distinct subcategory in the proposed classification.
  • Comparisons are more meaningful when models are grouped by purpose and input data.

Tags

VolatilityStatisticsDerivatives pricing
Full text
# So many volatility models. Any comparisons of them?


# So many volatility models. Any comparisons of them?












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?

- Wavelet multiresolution volatility

- EWMA

- GARCH family

- range volatility

- derivative implied volatility, models from stochastic finance. SABR etc.

## Answer by Matt Wolf (score 18, accepted)

https://quant.stackexchange.com/a/8058

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.

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