I'm looking to take a set of days, they can be at random and have no connection to each other. I would like to calculate the historical volatility for each day. I'm not sure the best way to do this since each disparate day can have it's price "begin" at the middle of a large swing from the day that was prior to it. Since that prior day's prices are not considered, I'm not sure if this is going to inflate the apparent volatility in the results. These are for 24 hour futures prices, so it makes it a bit harder. I'm also not convinced yet of what periodicity I should apply to the volatility. Hourly seems like it could be too little, yet minutely seems too fine grained. Maybe 15 minute? Any suggestions? Has anyone tackled this before?
see euan sinclair's - volatility trading - the book has explanations of typical volatility models... I assume you can use them on shorter timeframes as well, though you would likely have to use a more complex model or a number of different models to get an accurate sample that deals with jumps etc..
Google Yang Zhang Volatility for open Hi Low Close volatility models, the most advancd models allowing for opening gaps up or down from previous close. You could then i suppose use 1 hour OHLC numbers and calcualte the annualised Yang Zhang volatility. Just replace sqrt(254) - the number of trading days in the year, with say say sqrt (254x8) if there are 8 hours of trading in the typical trading day of your share. I played a bit once with 1 minute data and used Yang Zhang volatility for a high frequency trading bot, this was a few yrs ago, so i am rattling all this off from memory, i can't off the top of my head remember any problems, if i had any. Off the subject- the BOT was not a success up slightly before comm...down after comm with hundreds of rountrips a day