I'm trying to incorporate the daily high and low ranges in addition to the closing prices to get a more accurate idea of 1-week and 1-month realized volatility for an instrument. Any suggestions or links on how I should do this? Using just the closing/settlement prices is simple. but it leaves out and does not capture the intraday volatility (high or low) that may have taken place throughout the trading session.
it depends on what your trading. For products that are not continuous (equities) you should use yang zhang. For products that are continuous (fx, futures) you should use garman.klass. Many programming languages have packages that will do this for you. However if you are looking for just the math, the bottom of this page will give you all the formulas https://www.rdocumentation.org/packages/TTR/versions/0.23-4/topics/volatility
This is only a partial truth. The best overall volatility estimator out-of-the-box is the yang-zhang volatility estimator due to its independence of opening gaps, minimum estimation error, and in the presence of numerous opening gaps it degrades nicely to standard volatility estimation. The yang-zhang estimator is an extension of the garman klass estimator, and so using one you get the other. This is invariant of the underlying you are trading. I would be very, very interested in the math you used to arrive at the parent estimator (garman klass) being more effective than it's improvement (yang-zhang) on any specific instrument. Choosing one estimator over the other really depends on the bias of the sector and available data, not a particular investment vehicle. There are many mathematical considerations to using a volatility estimator of any kind on rolled data. This exercise is left to the reader. There are many, many papers on various estimation correction calculations you can use as rolled data will be biased significantly over a large enough estimation period.
I used to use garman alot until a poster here corrected me. 100% agree with you yang zhang is the best out of the box estimator! And definetely best used for equities. However when you have a process that does not have opening jumps, I do not see a need to use yang.zhang. I have not tested the efficiency or bias of the two on a non jumping process. Maybe you have some insight there?
Thanks for all your feedback. Let's say I want to start with trying to accurately estimate realized vol in commodity futures, and would like to utilize the yang zhang methodology. Any examples how I could implement this into an excel spreadsheet?
It does really matter what estimator you are using since the error on your estimate are much larger than the difference between different estimators. What matters more is how well does the future volatility track your estimate, if there is any persistent error, does the asset need de-jumping etc. In commodity futures, an important bit is the Samuelson/expirty effect which will matter way more than the estimator you are using.