I have exchange tick data and I was wondering how to calculate intraday volatility without having to resample the data set (e.g. to 1 or 5 minutes).

I have a time series of n rows of the security's traded prices and timestamps.

Do I just do the following:

numerator = sum of all intervals (n - 1 intervals)

where each interval is defined as: R(t(n_1))^2 * dt(n_1)

R(t(n_1)) = ln(P(t(n_1))/P(t(n_0))) dt(n_1) = (t(n_1)-t(n_0))

P(t) = price at time t t(n_x) = timestamp at x row

denominator = sum(of all time intervals)

intraday variance = (numerator/denominator)*sqrt(252)

intraday volatility = sqrt(intraday variance)


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