You are not able to drag and drop files between Mac OS X Virtual Machine and Mac OS X host (your Mac) and vice versa in Parallels Desktop 9 (and earlier versions).
Drag and Drop is not supported for Mac OS X Virtual Machines in the Parallels Desktop 9 (and earlier versions). Shared clipboard is not supported too.
For more details please see page # 171 of Parallels Desktop 9 User's Guide
Instead of that, please use Shared Folders:
Open virtual machine configuration > switch to Options tab > Sharing > set Share Folders: to whether Home folder only or All disks.
- In virtual machine open Finder > in the top menu bar go to Finder > Preferences > General tab > and tick Connected servers.
Now, the shared drive will appear on the virtual machine Desktop.