I was able to do something similar by applying the following:
{% Documents["/" + CurrentDocument.NodeAliasPath.Split("/")[1]].GetValue("MyField") |(identity)GlobalAdministrator%}
In my case, I wanted to pick a specific (top level) page to inherit a field from. This won't automatically give you the parent page in your structure, but it would allow you to consistently pick a parent no matter how many pages you nest.
Grabbed from an answer on this thread