Like most Hollywood jobs, it depends how much you’re working and the difficulty of the stunts you're performing. If you're in the union (SAG—Screen Actors Guild), you'll make around $800 a day when working on a scale union production. Plus, you might get paid a "stunt adjustment" that takes into account how dangerous the stunts are that you were asked to perform.
Unfortunately, you can't just multiply that by 365, because it's often hard to get regular work doing this sort of thing. There are about a billion people in Hollywood (that's just a completely uneducated guesstimate) and everyone is vying for jobs in the industry. In a slow month, you may only get a few days of work. You're also going to be self-employed, which means you've got to go out there and get gigs yourself.
Any production you're working on will have its own stunt insurance, but you're also going to want to go out and get yourself some regular health insurance, as you want to be covered during the periods of time that you aren't juggling Ginsu knives…because that's probably when you're going to have some freak accident that involves you slamming your hand in your car door.
It's a tough business and a real grind, but if you’re a top notch performer and you’re great at selling yourself (hopefully you don't have to resort to selling yourself in that way, but you wouldn't be the first), then you have a chance to make some real bank.