# 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?

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.

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.

• Do you have backup for this claim? I am not aware that institutional vol traders peruse specific compressed bar data to calculate realized vol. Some may, but to my knowledge there is no best practices that refer in any way to 5 minute data. – Matthias Wolf May 9 '14 at 10:45

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.

• Consider I have 2 years daily data, time series, and want to apply different volatility models. First simple class of volatility is Standard deviation. Now if I select first sample 25trading days (day1-day25), calculate its standard deviation, next sample from day2 to day26, next day3-day 27, etc. I have to compare these results with standard deviation of population (1 year, 2 years?)? For forecasting I can say if standard deviation in month 1 is x, we expect the standard deviation in month 2 to be close to x? Here what is "true volatility"? – user7985 May 22 '14 at 15:29
• Depends on your model, i.e. on how your model volatility. If you believe that the true volatiliy is a constant given number, you want to estimate it with as much data as possible. If you believe that instantaneous varies, you want a local estimate of this vola process. If you do not have a (semi)-parametric model in mind, using a shorter time span and the standard estimator is a good and valid strategy. If you have data with higher frequency than daily, different estimators might have desirable properties. In general, you'll need a model and some assumptions to make the statements you want. – Marco Breitig May 22 '14 at 15:53