Why Historical Volatility Estimators Have No Fixed Ranking
Summary
The document asks whether several historical volatility estimators can be ranked from largest to smallest: close-to-close variants and range-based estimators including Parkinson, Garman–Klass, Rogers–Satchell, and Yang–Zhang. The answer says a universal ordering is ill-posed because these estimators rely on different assumptions and do not generally differ only by a fixed constant.
A simple comparison is possible for two familiar sample variance formulas, since their results differ by a constant factor. That does not establish a ranking among the listed volatility estimators. Their relative outputs can vary with the data and with nuisance parameters, and each estimator is optimal only when its assumptions hold. The answer recommends choosing an estimator based on desired properties, then assessing those properties using data with known volatility, such as simulated samples. Observed estimates alone cannot establish which method is more reasonable when the true volatility is unknown.
Key ideas
- The listed historical volatility estimators do not have a stable universal size ranking.
- A ranking can hold when two formulas differ only by a constant factor, but that reasoning does not extend to distinct estimators.
- Each estimator’s performance depends on whether its assumptions fit the data generating process.
- Estimator choice should follow the desired properties, which can be studied with simulations where volatility is known.
Tags
Full text
# Ranking volatilty measures
# Ranking volatilty measures
I am creating a SQL query for a model I am developing that uses historical volatility. I am using the below methods to determine historical volatility:
- close to close zero mean
- close to close standard calculation for sample
- parkinson
- garman klass
- rogers satchell
- yang zhang
Generally speaking, how would these be ranked in terms of size? Which measure produces the largest value, second largest value, ..., smallest?
Thank you
## Answer by Dave Harris (score 3)
https://quant.stackexchange.com/a/68956
Your question is ill-posed.
This type of question appears quite a bit in the field of statistics and is intrinsically problematic.
Consider the two most common standard estimators of variance for a normally distributed variable. $$\hat{\sigma}^2_F=\frac{\sum_{i=1}^n(x_i-\bar{x})^2}{n-1}$$ and $$\hat{\sigma}^2_L=\frac{\sum_{i=1}^n(x_i-\bar{x})^2}{n}.$$
Although both estimates are built on the same foundational axioms, they are constructed under different assumptions. It will always be true that $\hat{\sigma}^2_F>\hat{\sigma}^2_L$ but that is completely unimportant.
Now it seems like a simple ranking is possible, but that is because they differ by a constant.
Each of the varying formulas that you have chosen does not differ by constants. There would never be a stable ranking, except possibly in some local dataset. All methods are optimal if and only if their assumptions are met.
There is no way to assess reasonableness by looking at their values because you do not know the ground truth. If you have fictional data with a defined volatility and ran thousands of Monte Carlo simulations, then you could assess their properties. The issue is a bit problematic because the formulas contain assumptions that require you to add nuisance parameters and may vary strongly with those nuisance parameters.
They have official properties but you can look at others such as robustness or breakdown point that are not part of the official derivations or assumptions.
The proper solution is to work backward and ignore the observed answers.
What properties do you want to have in an estimator?Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.