Very new to pricing models. Is there a general guideline when to use binomial tree and when trinomial tree is preferred? As far as I know, unlike binomial tree, trinomial tree only gives a range instead of a unique value. Thank you.
you have to be careful to distinguish between trinomial trees in a theoretical sense which do not give unique prices, and trinomial trees chosen as an approximation to the risk-neutral measure of the BS model. In the second case, they are an effective numerical method as are binomial trees.
Trinomial trees are more useful when you want to ensure nodes lie on a given level such as a barrier since this gives better convergence.
I discuss the theoretical point you are making at length in More Mathematical Finance. I have done paper on numerical comparisons as well, see my ssrn author page.