THis question was easy enough, but the question mentions "By using the Black Sch or otherwise....." I tried a Binomial model out for valuation of the two call options , one at 100 and one at 200, and calculated the answer based on the up and down formulae in the tables, the narrive at q etc etc etc but I didnt arrive at the correct answer that I would have got if Id have just used the B S formula...... Should the two agree with each other or have I just screwed the maths up? If not, what is the other method? 5 step? Cheers.
The question says "Using the portfolios from i, or otherwise". You are told to assume that the Black-Scholes holds so you can't use a binomial model here. It doesn't really make sense to talk about the 5-step method being an alternative to these 2 models. Just to be clear for your understanding: 1) The 5-step method is a proof that the fair price of ANY derivative is the discounted value of its expected payoff under Q. This proof works in both discrete time and continuous time. 2) OK, a call option is then a type of derivative. 3) We can use the result of the 5-step method to derive a fair price of this call option... a) If we do this in discrete time, what we get is called "the binomial model" b) If we do this in continuous time, we are just copying what Black and Scholes did before - no surprises that we get their model. Good luck! John
