When using the home, end, page up and page down movement keys in a text editor, the cursor stays in the same spot, even though the window has moved elsewhere.

I know that you can use the option modifier to move the cursor along, but is there a way to move the cursor where your window has moved to (without using the mouse)?

Another alternative would be to make these movement keys always behave as if the option modifier key is already pressed. Is this possible?