Pick a new password
Bad. You pick something from an existing collection. In the case of password you don't really
pick one - the phrase does not correspond to the action.
Change your password
The 'your' is verbose. What other password than yours you may change?
That's way you 'add to basket' and not 'add to your basket' or 'add to your basket on this amazon site'; and that's why you 'edit' and not 'edit this post'.
The brain is associative machine; if the 'edit' link is next to a post, gestalt principle of proximity has it that 'edit' means 'edit the post closest to the link' and not 'edit the post two posts below'.
Same goes for writing - "Leonardo da Vinci was born in Italy. He also died there." and not "Leonardo da Vinci was born in Italy. Leonardo da Vinci also died in Italy."
I don't accept the argument that 'your' makes it more friendly. What's more, you want to be friendly in marketing copies, but when it comes to task-based behaviour you want to be concise.
Short. Straight to the point. Clear.
It doesn't matter much
Despite all that is said above, I do feel the need to assert that a user who wishes to change her password would care little about these variations - all three options will do the job.
But if you define usability as the amount of effort a user has to expand in order to perform a task, and effort includes cognitive interpretation effort, then the "Change password" is the most usable one.