I have a question for Black-Scholes. It is a continuous approach, but the real market closes every day. So for the Black-Scholes, how do we count the time effect of during the time when the market is closed? or do we just ignore that time and count the business day time?
With theoretical modeling you just put in the number of days till expiration in years. If time to expiration is less than 1 year, it will just be some decimal. That means you can put in any time to expiration you want.
In practice, how you model the decay overnight depends on your own analysis, judgement, modeling, trading strategy etc.. You could do the same and have time to expiration continuously decrease linearly. Or you can just immediately decay it by a day (non linear). Sometimes the product may not decay much overnight, but decay quickly 30 minutes after open - which makes sense for this type of modeling. It just depends on your situation and goals.