A stock is trading at $100 and in a year's time it will either double to $200 or halve to $50...

The_Wisdom_of_Crowds is all very well but I prefer Terry Pratchet's IQ of the Mob:

The IQ of the Mob is equal to the IQ of its dumbest member divided by the number in the Mob.

This probably also applies to English Football Teams.... but I have no proof..

You can also add that the PUT will have the same price as the CALL since the put call parity

C(t) + K * B(t,T) = P(t) + S(t)

C= Call price
P= Put price
K= Strike Price (100)
B= Interest rate (which is 0 in this case)
S= Spot Price (100)

Sorry if I came across as a bit of an ar$e in my earlier post. I only write these things to make myself feel more important.

KSG, a senior option trader should work this out in 1 minute, but we are only mortals. In fact, to answer correctly you need to know what an oprion trader does not do: take risks. If he buys an option (because a client wants to sell) he will pay 33.33, borrow 0.6666 of the stock, sell it on the market @ 100 for a gain of 66.66 and deposit with his treasury 33.33 at zero interest rate. He will then carry a net gain of 33.33 to expiry of the option, when he also needs to buy the stock back from the market, give it back to the lender and, finally, pocket the payoff of the option. If the stock goes up, he will pay 133.33 for the stock (200x0.6666), make 100 from the option (200-100) and, finally, "use" the precious 33.33 that he had gained at trade date to offset the loss (=> net gain = 0). If the the stock goes down, he will pay 33.33 from the stock (50x0.6666), make nothing from the option and, again, "use" the precious 33.33 that he had gained at trade date to offset the loss (=> net gain = 0). So what does the trader do in order to benefit the society? (1) anable market making and (2) pay taxes (this part of the answer might be slightly unrelated to the question).

Yeah good thinking IT guy - you made some good reasoning especially by testing the edge case of 99% real world probability of the stock halving.

The fact is risk neutral pricing isn't particularly intuitive - most people only understand it if they have studied it in finance or whatever. If you were prepared to sell your options to mr senior options trader for say $30 he'd buy them off you all day long because he knows he can extract $33 from them no mater what happens. :-)