I think the more complete answer is that an option expires at 1159 pm on expiration day. It will be auto assigned based on the closing price of the underlying compared to the strike price with 0.01 ITM initiating an auto assignment. If the buyer wishes to change what the auto assignment would normally do, he has until the earlier of 530ET or whenever his broker allows his request which is always earlier than 530 to allow time for the broker to meet the 530 deadline to initiate the change from or to assignment.