From the PIlot/Controller Glossary:
CLEARED FOR THE OPTION− ATC authorization for an aircraft to make a touch-and-go, low approach, missed approach, stop and go, or full stop landing at the discretion of the pilot. It is normally used in training so that an instructor can evaluate a student’s performance under changing situations.
Full stops are authorized under a clearance for the option. If a controller says that they are not, politely suggest that he check the definition in the P/CG.
If you tell the controller how your approach will terminate then there's no need to be cleared for the option. In such a case, make your original request for your desired type of approach and landing. The option is for situations where the pilot has not yet decided the intended result of the approach.
Once cleared for the option, there is no need to further clarify your intentions if you intend to make a touch-and-go, low approach, missed approach, stop and go, or full stop landing. If it was important to the controller to know, he would have asked or restricted the clearance.
You never need a clearance for a go-around.