Parachute usage is covered in 14 CFR 91.307. Section (c) of this regulation applies to aircraft during aerobatic maneuvers. It states:
"(c) Unless each occupant of the aircraft is wearing an approved parachute, no pilot of a civil aircraft carrying any person (other than a crewmember) may execute any intentional maneuver that exceeds --
(1) A bank of 60 degrees relative to the horizon; or
(2) A nose-up or nose-down attitude of 30 degrees relative to the horizon."
Note that this regulation states that, during aerobatic flight, all persons in the aircraft must have a parachute whenever people OTHER THAN CREWMEMBER(S) are carried. Therefore, when the only person on board is the pilot, and no others are carried, a parachute is not required. However, when a passenger is carried in an aircraft during aerobatics, all persons on board INCLUDING crewmember(s) are required to be wearing parachutes.