What is the easiest way to price single barrier options using binomial tree? I found This method. Is this method good or maybe should I use another one? Does this price converge to price from BS model?
This may not be answering your question - but it is worth noting that valuing barrier options on a binomial / trinomial tree is at best problematic. It is difficult to enforce the boundary conditions because nodes will not typically sit on the barrier itself, necessitating some kind of probability-weighted interpolation - which is unlikely to be numerically stable. Greeks will be even worse. Strongly suggest you look at PDE approaches which are the industry-standard for Barrier options. Google "barrier options PDE" - there's a tonne of literature out there.