The Pleasure Deriving From Pity and Fear

How is it possible for pleasure to derive from essentially painful emotions, like pity and fear? And this is a problem not limited to tragedy. So we enjoy going to see horror movies, all kinds of things that produce what are essentially painful emotions,. but it seems we derive pleasure from them. This has puzzled lots of philosophers. How is this possible? One tempting answer is to appeal to catharsis. That's, once you're done with pity and fear, the relief you get is pleasurable. Another thought is to appealing to the notion of understanding that Aristotle talks about.