Don't want to upset the folks that don't believe in correcting misbehavior. But in my opinion, he needs a very firm hand ( and I don't mean in the mouth) to fix the problem. You may want to talk to a good trainer to get some pointers. Or have someone ride him for you that is use to dealing with a stallion. A stallion can be a stick of dinomite waiting to explode so be carefull trying to chastise him your self until he gets more accustom to discipline.

Good Luck

I'd ride with a short crop, or bat.  A squeal gets a tap, then a swat if the tap dosen't work.  You are looking to break his train of thought and if you can't seem to do it kindly then you need to keep bumping it up a notch until you get his attention.  If you pick the fight you must win it...  If anything bad happens drop the darned thing(bat).  Put yellow tape around the handle so you can find it later.  It shouldn't take long for him to figure out that vocalizing is BAD.

Studs are very tricky, like teenage boys.  You must stop this squealing before he figures out you don't know how to stop him.  Then he'll do whatever he darned well pleases because he's already getting away with stuff.

Unless he has superiour quailites that lead to to keep him a stallion, then I'd geld him.  its not fair to him to be punshing him for a natural stallion- like behavior when it would be a non-issue by gelding him.  he'd be a nicer pleasure/trail horse for you not having to deal with stallion behaviors which can get much worse than just squealing. 

Other than that- you must never let a stallion know you're not as strong as he is. The the game is up and you'll no control at all. keeping his mind busy  by sidepassing, leg yeilding,circling,backing up in circles, etc can help. giving him a swat can have its draw backs, especially if he has no respect for you, he might fight back. I'd get some help with someone with stallion experience. Or better yet, give the guya  break and cut him.