Summer Affair(1971)

A very young Ornella Muti plays a rich girl who falls for an older hippie boy. Her parents don't approve and try to stop her from seeing him so they run away to a villa (Her parents') by the sea. Later they are shipwrecked on a deserted island. The plot focuses on the efforts of the police to figure out where the girl is, which is set against the developing relationship between the two young people.