In my understanding, it makes sense to execute in-the-money american call options early ahead of the dividend when the extrinsic option value (related to time, volatility, etc.) is smaller than the dividend amount. I wonder, how often is a call option assigned early in the above situation in practice? For instance, you are short an in the money call that expires this Friday and the ex-dividend is this Wednesday, the stock is not extremely volatile and the dividend is 0.5%. In this situation , how likely is it in practice that you will be assigned early?
The % likelihood of course depends on how large the differential is between the div and extrinsic. If it's a close call between exercising or not, then it's obviously tough to predict how likely you are to be assigned. That said, if it's a no-brainer exercise, then I would put the odds north of 95% (maybe 99%+ (been out of this market for a while)). If the percentage was any lower you could work a div arb strategy, but I highly doubt that's the case since it was marginally profitable 15 years ago.
The proper metric is to compare the value of the dividend to the put value on that strike and include your cost of carrying the stock if you exercise. If the dividend you receive minus the cost of carry is more than the put, you can exercise the call, buy the put, end up with stock+put which is a synthetic call, for less money. You should include all costs in your formula including any change in margin. Bob