Why exercise early and give up the time premium. Just sell them. If an option is trading at parity you may be assigned early but extremely unlikely if there is any premium and if it does happen it's a gift.
The way I understand it there is only one time it makes sense (financially) to exercise a call early. That is when there is little to no time premuim and the expected dividends are greater than the cost of carrying the underlying. As for puts, it makes sense to exercise early when there is little or no time premium and the cost of carrying the underlying is greater than the same strike call. Put/Call parity...
What I mean is that with the deep in the money options if they have a higher chance of getting assigned one can write the same options ( with the same expiration month ) many times before rolling call writing to the next month. On the other hand if they didn't get assigned one would collect a huge premium for the deep ITM options. Would it be correct thinking?
Not sure about what exactly you're trying to say in the first part, but in order to collect that "huge" premium on deep ITM options the option must expire OTM. If the stock doesn't move anywhere then the intrinsic value will remain and while the time value will decay it is very small for deep ITM options to start with, so there won't be any profit.
About the deep ITM...when expiration comes, a deep ITM will surely be auto-assigned/ auto-settled. I guess you know this. Im not sure what you mean??