Hi everybody! I'm reading the chapter 3 about option pricing in "FINANCE Paul Wilmott Introduces Quantitative Finance" , in 3.17 VALUING BACK DOWN THE TREE,  an example says" with S = 100, δt = 1/12, r = 0.1(risk free rate), and σ = 0.2... Using these numbers we have u = 1.0604, v = 0.9431 and p' = 0.5567( where δt stands for time step, u for the upper underlying asset price after on tiem step, v for the lower price, and p' for risk neutral probability). ”
But, according to the formulas  u = 1 + σ(δt)^0.5, v = 1 - σ(δt)^0.5 and p'=1/2 + r(δt)^0.5/2σ, I got u = 1 + 0.2 (1/12)^0.5 = 1. 0577, v = 1- 0.2(1/12)^0.5=0.9423 and p’= 0.5 + 0.0722=0.5722. Could u please tell me if I have made any mistakes in the calculation? Thanks!

You are v observant! I use two different algorithms, but haven't explained this!

There are three parameters to choose, u, v and p. But only two parameters to match, drift and vol. So there is one degree of freedom and an infinite number of possible choices! In the text I use the one that looks simplest, just for teaching purposes. 

They give different answers for finite dt but for infinitesimal dt they'd give the same. 

Sorry about the confusion!

Dear Paul, thank u very much for your quick reply and now I finally understood the issue and get more interest in studying with your masterpiece. Thanks!