When I was with my girlfriend at around that age (bit older, 18/19), her parents allowed me to sleep in her bed in their house, on the understanding that nothing happened - that was never specifically said, however they trusted us to respect the fact it was under their roof. And we did respect it. And because of that, we earned the parents' trust.
Also, as has been said above, there is some inevitability about the fact that they will get it on at some point. You would hope that they are aware of taking precautions etc. As a parent, would you rather them do it in the safety and comfort of your house, or in the back of his car down some dark lane? That was a point that was made to my parents about my brother and his girlfriend, by her parents, when both sets of parents found out they'd been knocking boots under my parents' roof...[/QU