How Does Teddy Die?

(Sorry about the weird formatting)

For me, the ending of Salinger's short story "Teddy" came across as an unexpected shock. Even if the reader had picked up on earlier hints dropped by Teddy, I don't think that many people fully expected the story to end in the way it did.
But going off that, how does the story end?
Upon first glance, it seems that Teddy dies. For one, Teddy hints that something important "will either happen today or February 14, 1958 when I am sixteen." This 'thing' becomes clearer later in the story, as Teddy (oddly) explains in great detail a hypothetical situation where he dies.
"I have a swimming lesson in about five minutes. I could go downstairs to the pool, and there might not be any water in it. This might be the day they change the water or something. What might happen, though, I might walk up to the edge of it, just to have a look at the bottom, for instance, and my sister might come up and sort of push me in. I could fracture my skull and die instantaneously." 
And in that famous, ambigious closing scene, we hear piercing screams from the pool, "clearly coming from a small, female child." This seems to suggest that a) Teddy and his sister are indeed at their swimming lesson, and b) something horrifying has happened.
If we as readers believe that Teddy is truly a spiritual genius who can outsmart professors at institutions around the world, then perhaps this whole situation is more believable. Maybe Teddy can truly predict his death.

But even if we accept this ending, it raises a few, important questions. For one, is it possible that Booper  murders Teddy? If Teddy knows that he's about to die why doesn't he try and stop it?
Both are sinister and chilling to think about. Maybe Booper and Teddy's relationship is more strained than just a "sibling rivalry". Or maybe Booper is truly evil. If we believe Teddy's intellegence is real, then it really isn't a far stretch to consider that Booper is a malicious child. Or heck, maybe Booper was just predetermined to kill Teddy when she was born. As for why Teddy does not try to avoid his inevitable death, it makes the most sense to assume that he believes that death—and dying, is not a big deal. He truly thinks he will be reincarnated again.

Another explanation of the last scene is that Teddy commits suicide.
From this point of view, we regard Teddy's genius with skepticism. After all, what ten-year old truly behaves like Teddy? Perhaps Teddy is actually a very mentally disoriented child, who has conjured a whole different world in his head. If we consider the people around Teddy—his parents, Bob, and Booper—they all seem much more different and removed.
Early on in the story, Teddy complains that he was only reincarnated as an American because he could not stay focused while meditating in his earlier life. Based on this detail, it would make sense for Teddy to be frustrated and even feel trapped in his current situation. Perhaps Teddy jumps into the empty pool himself in an attempt to escape from the confinements of his American life.

One last possibility to consider is that Booper is the one who dies (I didn't consider this until someone brought it up in class). It depends how closely you want to read into the text, but the last paragraph states that the piercing female scream seems to "reverberate within the four tiled walls." Maybe Salinger literally means "within"—that Booper screams as she falls into the empty pool.

There's no doubt that Salinger keeps the ending very ambiguous. A few of his other short stories have ended similarly, causing the reader to ponder (at times, with great frustration) what has actually happened, and what will happen.

How do you guys read the ending of "Teddy"?