AFAIK, the only model that has some claim to statistical legitimacy is the log-Brownian (or geometric-Brownian) model, which gives a very broad probability distribution, having 50% chance above today's price, 50% below, for any future date.
50% chance above and 50% below, for any future date, are you serious ?
Yes. What will be the price on Nov 17, 2014, at 17:23:11 UTC? The log-Brownian model say that it will be more than 487.15 USD with 50% probability, less than that with 50% probability. (OK, there is some probability that it will be EXACTLY 487.15 USD,but it is very small.)
I do not know what the price will be but the log brownian model does NOT say that (I am just repeating myself here) ...
Look at a call closed formula price, N(d2) represents the probability of the call being in the money, if you put S=K (our example here) you are left with N(something negative) which means that the probability that the price ends up above current value is ... less than 50% !
And below current value is ... more than 50%.
Try to think about why, if you still dont understand in a few hours, feel free to ask me.
EDIT: forgot the "but" in first sentence