Dear experts, I am seeking a newbie help on understanding binomial tree construction from Hull, page 392 (I have uploaded a snapshot of that page here: http://www.2shared.com/photo/nIw4omBd/Hull.html). I understand that according to binomial tree construction, there are 2 possible realization in time interval dt viz "Su", "Sd" (current price is "S").Then in that page Hull says that percentage difference is those realization are u & d. Here my question is: how it can be justified? shouldn't the percentage difference be (Su - S)/S= (u-1), and similarly (d-1)? Can somebody help me to understand that?Secondly, it says that expected percentage change is exp((r-q)*dt). Here if I assume GBM i.e. dS/S = rdt + sigma*z then, shouldn't expected percentage change will just be rdt?Can somebody please tell me what I am missing here?Thanks for your time

Hull is using "percentage change" loosely, he means the "logarithmic change" or the "multiplicative change"He considers a dividend paying stock so the GBM process is dS/S = (r-q)dt + sigma*dz . In an interval dt the shareholder receives a dividend dt * q and capital gains dt * (r-q) which add up to dt*r as theory requires.