How to price barrier options (binomial tree)

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?

• Rephrased a little bit differently: Yes, you could use a binomial tree for barrier option pricing, but you will have to use a very unwieldy number of steps in your tree. In my experience the challenge with barrier options is their $\Delta t \to dt$ behaviour: You need extremely small time steps to get towards reasonable prices when compared to quasi closed form PDE solutions. Thus, we see another challenge: You will also have problems when using numerical PDE schemes: Explicit schemes need a humongous amount of steps; implicit schemes introduce errors when pricing path-dependency. Dec 1 '20 at 8:53
• Do you know maybe Boyle, Lau (1994) method for pricing barrier options? They use $F\left(m\right)=\frac{m^{2}\sigma^{2}T}{\ln\left(\frac{S}{H}\right)^{2}}$ to find optimal number of time steps but I hae problem with understadning why they use formula like this Dec 23 '20 at 14:58