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If I assume a given empirical price-series is a brownian motion, I can estimate the drift and standard deviation as long as I know what the time step was when the process was 'generated'.

But since this is an empirical price-series, how can I know what dt is supposed to be?

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  • $\begingroup$ What is the frequency of your empirical price data? If you are using daily data then $\Delta t$ is one day (i.e. 0.0039 years), for monthly data it is 1/12= 0.083 years, etc. $\endgroup$ – noob2 May 22 at 11:29
  • $\begingroup$ @noob2 It's minute data. So are you saying t is in units of years, regardless of the frequency of the price-series? $\endgroup$ – wildbunny May 22 at 11:59
  • $\begingroup$ (1) With minute data you have to be careful, there can be "micro-structure" phenomena like bid ask bounce which you might want to filter out before fitting a brownian motion (2) Year is the unit I like to use (for use with options), but you can use another unit more appropriate to what you are trying to do. $\endgroup$ – noob2 May 22 at 12:45

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