Why are there different estimators for stock volatility? (realized variance, RAV, etc)

Question

I am very confused about why different volatility estimators (RV, RAV, BPV, etc) exist. If the goal is to find the best estimator for stock volatility, and volatility is latent, how do I know which estimator performs the best when the mathematical definition for these estimators are all different?

Realized variance = sum[(return at t)^2] in a day
Realized absolute value = sum|return at t| in a day
Bipower variation = sum |return at t-1|*|return at t| in a day

If I use a linear model and substitute each of these estimators as the regressor, doesn't this mean I can't compare the results directly, but I can only compare how well the linear model is able to predict itself based on MSE, R^2, and so on?

Answer 1

I would not call them "estimators" but rather measures because this is volatility on historical returns.

The reason why there are different such measures is because each one represents volatility in different ways in order to measure the volatility of different dynamics, be it price, return, upside price moves only, down side price moves only, intraday dynamics. For example:

• There are measures of intra-day price volatility, such as Parkinson or Garman-Klass
• Measure that only concerns itself with deviation without regard to signage, such as variance on absolute values or squared deviations
• Measure that represents variability of an asset relative to a benchmark, Beta

There are a lot more but I guess you get the point. In Summary, different measures of volatility in order to capture variation of different dynamics.