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I'm looking for a reference algorithm for calculating historical volatility to price options. I know there are several volatility calculation models that use the time series of the underlying's returns. Is there a reference method for determining the number of days to consider for the calculation?

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    $\begingroup$ Use a time period having the same order of magnitude as your option's tenor. Please do not try and trade around the price you find. It will be fairly different from what sophisticated market participants work with (i.e. in trading with them you would lose money). $\endgroup$ – Brian B Jan 10 at 19:29
  • $\begingroup$ There is no agreement as to how many days to use to compute historical volatitliy. Some years ago S. Figlewski suggested that you should use as many days of history as the maturity of the option you consider. For example for a 3 month option you should use 3 months of daily data. This is just a heuristic which he suggested based on some empirical tests. $\endgroup$ – noob2 Jan 10 at 19:51
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You should review the difference between implied volatility and realised volatility. Historical volatility is the realised volatility that happen in the past but an option price will have to be determined by the view of the market about volatility in the future for a given period. Normally you do the inverse, ie the option price is given by the market but you can work out the implied volatility from that price.

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