# Interest Rate Trees

How does one find the interest rates for each node of the interest rate tree? I understand how to find the spot rates based on the benchmark par curve, and then the implied forward rates. Seems like in the practice problems they always give you at least one interest rate for each T and then ask us to calculate the others based on e^2(standard deviation). Is this always the case? Either they will always give us one interest rate for each period or I completely missed how to figure out the interest rates for each period without being given one of the nodes already. If anyone could help with this it’d be much appreciated.

They’ll always give you the interest rate on at least one node at each time.

You can solve for the rates algebraically if you want, but in practice you usually use something like Excel’s Goal Seek or Solver to do it. In the curriculum the author explicitly says that they used Solver to get the values.

Thanks. Yeah I recall them saying that, but then they talk about calculating the updated rates for the option adjusted spread using the par curve and I wasn’t sure if that was something we’d need to do from scratch. Anyhow, sounds like not. Thanks again.

you can also stuff in the middle rate given in the answers and see if the numbers work out.

the s2000 method ™

You made me burst out laughing!

Thank you, Simon! What a great way to start the week!