# Fixed Income Binomial Tree

Will the question in the main CFA exam ask us to construct the binomial tree or will the tree be given?

Thanks

You can’t build a binomial tree on the exam.

Oh, sure: you could solve for the (two) time 1 forward rates using the quadratic formula (which, of course, you’ve memorized), then solve for the (three) time 2 forward rates using Ferrari’s formulae for solving a cubic equation (which were originally discovered by del Ferro and Tartaglia, and published by Cardano), then solve for the (four) time 3 forward rates using Cardano’s formulae (another of Ferrari‘s brainchildren published by Cardano), but after that point, you’re stuck: Abel (building on the work of Ruffini) – and, later, Galois – proved that there is no general algebraic solution to quintic (fifth-degree) and higher-order equations.

In short, it’s not particularly practical for a 3-minute question in an item set.

Wow… first sentence was very helpful thanks.

Yeah the section on calibration had me pretty confident that we wouldn’t be required to actually build one of these things from scratch come exam day haha…! Understand what they are implying, the relationships between rates at the different nodes, and how to use them to value bonds with options, caps, floors etc etc and I think we’ll be OK

One possibility is that they could give you a tree with one or more forward rates missing and expect you to fill them in. However, they would need to give you at least one rate at each time, and at least two rates at one time (so that you can determine the volatility).