Hi AllI am studying binomial trees on Hull ( 7th edition, ch. 11 ) as a way of pricing my options.In the chapter I see in the first example 2 data are given : the 2 expected/possible prices for a stock after 3 months ( stock might end at $22 or stock might end at $18 ).My simple question ( I am newbie ) is what methodology should I look into to roughly estimate these 2 values?I would use volatility but if I use a method like GARCH(1,1) I am referring to a value that might change daily; I need a volatility to be estimated for longer horizon.Can you suggest some way to approach such calculation (if I it makes sense) or some reading where I can get an estimation for those 2 prices good for binomial trees?ThanksMnstn

The future prices of the underlying in a binomial tree are generated by successive multiplications of the initial observable price by up and down factors. These up and down factors are in turn simple functions of volatility and time. Only the volatility parameter is unknown and exegoneous to the model, all other parameters of the model are observable. Once a value for the volatility is specified (to get started just choose a 'reasonable' non-negative number) the prices of the underlying at all future nodes are easily computed.There is no need to forecast any prices.

Hi David JNI thank you for your response and it is now clear that the volatility is the variable that has the major impact on the tree because it is used to calculate 'u' and 'd'. I have a point about it: Hull uses a btree with a volatility assumed constant but I might think some scenarios where this doesn't apply. Right now I have In mind intra-day trading or special days where market prices are particularly variable.How to deal with this a case i.e. how to mix a changing volatiliy to a btree? Is there some special math tool available other than splitting the tree in sub-trees where in each the volatility is kept constant?I am reading right now this paper Recombining Trinomial Tree for Real Option Valuation with Changing Volatility and I hope it could be useful someway also for btrees.

QuoteI have a point about it: Hull uses a btree with a volatility assumed constant but I might think some scenarios where this doesn't apply. Right now I have In mind intra-day trading or special days where market prices are particularly variable.just because the market is volatile doesn't mean that volatility is not constant.

Hi daveangelyou are right and sorry for the bad sentence.By the way I did really mean btrees where I might have volatility changing..intra day or across trading days.Is there any advanced btree used that is worth to have a look at?The more I dig and the more I find tons on papers on the subject.Last one I found is this oneA binomial tree approach to stochastic volatility driven model of the stock price