Realized Volatility as a Proxy for Latent True Volatility
Summary
The discussion distinguishes volatility estimated from observed price changes from the underlying volatility in a model. Empirical standard deviation estimates a theoretical standard deviation, while realized volatility—calculated from daily or intraday returns—can serve as a practical reference when comparing estimators such as close-to-close or range-based methods. Intraday observations, often sampled at five-minute intervals, are cited as a way to construct realized volatility for estimator comparisons.
For volatility trading, the relevant target is future realized volatility, modeled as a predictor of the volatility measure used in decisions against implied volatility. The answers do not give a definitive, directly observable value for “true” volatility: it depends on the assumed stochastic model, and realized volatility is an estimate or building block rather than certainty about the future. The discussion offers conceptual guidance but no empirical comparison, calculation details, or evidence that one estimator is best.
Key ideas
- Theoretical volatility is a property of an assumed data-generating model.
- Sample standard deviation estimates the model's theoretical standard deviation.
- Realized volatility from daily or intraday returns can benchmark other volatility estimators.
- Forecasts of future realized volatility can inform comparisons with implied volatility.
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# What does "true"volatility mean in volatility comparison?
# What does "true"volatility mean in volatility comparison?
In Sinclair's book, wee need to compare standard deviation with "true volatility" to check the power of the model suggested, close -to-cloce, or Parkinson formula, etc.
What do we mean here by "true" volatility when we calculate standard deviation, with what we have to compare it with?
## Answer by Matt Wolf (score 2)
https://quant.stackexchange.com/a/11199
Sinclair also writes: "volatility measurement is something of an art."
One aspect of volatility trading, and the one which you allude to, is to trade deviations of future realized volatility against implied volatility. So, the task is to estimate/model future realized volatility as a predictor of true volatility and Sinclair simply said that realized volatility (whether it be daily or intraday) functions as building block for many models to predict true volatility, that volatility measure utilized to trade against implied volatility.
## Answer by opt (score 0)
https://quant.stackexchange.com/a/11201
It is becoming more and more common to calculate realized vol using intraday data, usually 5 minutes. This is used to compare performance of other volatility estimators.
## Answer by Marco Breitig (score 0)
https://quant.stackexchange.com/a/11214
I haveen't read that book, but I'll try to answer anyway from a pure statistics point of view.
You assume a model and some random variables or a stochastic process which models the part of reality you are interested in, i.e. the value of a stock or its return in time. If the model is true this stochastic process is assumed to have generated the data you can observe and the task at hand is to estimate certain proberties of the stochastic process.
I assume with standard derivation Sinclair means the empirical standard derivation, which is an estimator of the theoretical standard derivation, i.e. the true volatility in the model. This is along the same lines as the mean of a sample $$ \frac{1}{n}\sum_{i=1}^{n} x_{i} $$ is an estimator for the expected value of the theoretical quantity that generated your sample, according to your model.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
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