yield volatilty of a BDT tree

[Mc Lovin]

Can someone explain these? I am having trouble following and would like to know what is expected for the exam. Thanks!

[Eagle.K.Y]

in general, u just need to remember, in one column(year) of tree, the ratio of 2 nodes "next to" each other(upper node and down node) is exp{2*sigma_i*sqrt(h)}.

But, be careful, such equation is assumed that sigma is for n-year opt on h-year bond. So, if the question asks about n-year opt on m-year bond, where m is not equal h, you should find the forward rates(upper and lower) corresponding to m-year bond, then to find the sigma. (good example in ASM PracExam10, cant remember question index, but question is asking 3-month opt on 6-month bond, where h=3month in the BDT tree)