Yes, I do think that insurance companies will raise the cost of insurance, because you are a teenager(well that's what I'm guessing). But, it may go up even higher when you get your driver's license because you would be able to drive by yourself most of the time without a parent. And insurance statistics confirm that teenagers drive fast, wreckless, and less-experienced. So the good has to suffer because of the bad. So to answer your question, the rates will most likely go up, but not as much as if you were on your own insurance.
Neila222