As far as I know, the old ones are compatible with the newer versions of OS X. At least that's how it was with Mavericks. The system requirements for Desktop 9 state "OS X 10.9 Mavericks or later, OS X 10.8 Mountain Lion or later, OS X Lion 10.7.4 or later, or Mac OS X Snow Leopard v10.6.8 or later."
You see, you have that backwards. Yes, the current Parallels version runs on older OS versions. But the older versions of Parallels do not run on more recent OS X.
Which is what has turned this into essentially an annual subscription model, for anybody who adopts Apples next release.