Cannot set permissions on Parallels volume
Typically when you mount an NTFS volume in OS X (or Linux for that matter) the permissions are determined at the time the volume is mounted. You'll probably find that all files within your volume are set with identical "-rw-rw-rw-" permissions and all folders are set with identical "drwxrwxrwx" permissions.

Some software for mounting NTFS volumes will allow you to change the these volume wide permissions with arguments to the mount command. For example, with OSXFUSE you can set umask, fmask and dmask arguments when you mount an NTFS volume that will allow you to specify the permissions you want to see. However if there is documentation on how to do this with Parallels Mounter I'm unable to find it.