Forums > Pricing & Modelling > Hourly to Daily Volatility Conversion

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 ps1212 Total Posts: 3 Joined: Sep 2017
 Posted: 2022-07-29 20:32 Most security price volatility seems to be measured using daily data to create a daily volatility, then it can be converted to monthly or annual by multiplying by sqrt(12) and sqrt(252) respectively. If my starting point is hourly data instead of daily data the same technique would convert S&P 500 futures hourly volatility to daily by multiplying by something in the range of sqrt(6.5) to sqrt(24) with something close to the low end of the range possibly making the most sense to me initially since there are 6.5 hours in the cash equity day and those are the most liquid and active hours for the futures. When I do this however, multiplying the hourly volatility by anything makes the value much higher than the daily data - at least for the periods I've explored. If I do multiply by sqrt(6.5) then the daily volatility derived from the hourly volatility seems way too high. Can someone guide me here on the correct way to convert hourly volatility to a daily volatility number?
 ConditionalExpectations Total Posts: 12 Joined: Jul 2021
 Posted: 2022-07-30 03:40 Your formula is correct for writing hourly volatility in the same units as daily volatility. This is not the daily volatility of the security; it is simply the hourly volatility of your security, represented with different units. There cannot exist a formula to convert hourly volatility to daily volatility. Imagine a security with tremendous hourly volatility that resets to the same price at the end of each day, and a security with similar hourly volatility that reaches a new high at the end of each day; any such formula would assign the same daily volatility to both securities, a contradiction.When you say that this formula gives a quantity that seems way too high, could it be because you are comparing it to the properly calculated daily volatility (a completely different quantity)? Silence Dogood No. 4
 nikol Total Posts: 1483 Joined: Jun 2005
 Posted: 2022-07-30 08:08 A structure in transition probabilities of price evolution or saying differently presence of autoregressions will inevitably lead to deviation from pure sqrt. Your finding indicates that autocorrelation coeff is negative.https://en.m.wikipedia.org/wiki/Autoregressive_model ... What is a man If his chief good and market of his time Be but to sleep and feed? (c)
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