Princess Raven

Considering it had to specify whose graveyard it's going to but not whose banish pile, then I assume since it was your card that it would go to yours by default.

You can't have your cards in your opponent's GY, any time they would be sent there, they go back to your own GY instead, so simply, banishing a card your opponent owns would put it in their banished pile.

Yes, it would go to your banished area, since you own the card. For it to be treated as an opponent's banished card it would require it to be part of the banishing effect to override the mechanic. And even then, a funny thing is that there is no official distinction for the player's respective "areas" or "piles", so you can't just write "If this card is banished, it is sent to the opponent's banished pile/area/whatever instead". It would require a different approach, something on the lines of "this card is banished, it is treated as in the opponent's possession".