How can I get my parents to trust me to have a boyfriend?

My Parents are ultra strict and say I cant have a BF till Im 18. I think this is a bit OTT. I am a good teenager (15) I dont drink or smoke or sneak out, I do my homework and pass all subjects at school and help around the house, but my parents seem to think I have no self control and that I cant handle a BF and that I will get pregnant. How can I convince them I am mature and sensible enough to have a BF? All I want to do is go to the movies with this person and hang around in public places, not completely alone. Is this reasonable? Thanks :)