I noticed that LAB is up big today, no doubt helped by a big short position. It occurred to me, who is the specialist for a specialist firm's stock? Wouldn't it be a conflict for them to handle their own stock?
I do not believe that you are allowed to be a specialist in your own stock due to the conflict of interest that you state. LAB does not list itself as a client on their website: http://www.labranche.com/clients.html