As per this post on Oracle forums expdp can be used to export your own schema without any special privileges:
It all depends on what you want that user to be able to export/import. If all that use is exporting/importing is their own objects, then they don't need any raised privs. If you want that user to be able to export objects owned by other schemas, then they would need the exp_full_database and in order to import, they would need imp_full_database.
However I just can't get it to work. Directory object is required to be specified otherwise expdp displays error:
ORA-39145: directory object parameter must be specified and non-null
But creating directories requires
CREATE ANY DIRECTORY system privilege.
How then can I export my own schema as a normal user?