How do you best incorporate the weekends in the calculation of the Black Scholes historical volatility? (Of course historical volatility serves as approximation, if the market price of the options is not available).
In the book "Options, Futures and other Derivatives" by John C. Hull, it is described that over the weekend (from Friday till Monday) the variance is only 1.5 times higher than during the workweek (Monday-Friday), by using as example of a future (orange-juice futures) that is dependent on information that changes just as much during the weekend as through the week namely the weather; which shows that volatility is for a big part caused by trading and not by new information coming into the market. But still it seems to me that you would need some way to adapt to the weekend.
The volatility of the daily log-normal returns: ln(P1/P0)