# Binomial tree rates

Why do we use the forward rates in a binomial tree lattice and not the spot rates?

I understand forward-spot are related geometrically, but what is the rationale in a binomial tree? Is this a matter of choice or what?

Think about how we use a binomial interest rate tree: we check at each coupon date to see whether an embedded option will be exercised or not. To do so, we need the value of the bond at each node. To do that, we need to discount the value from the subsequent nodes. To do that . . . we need forward rates.

Ipso facto.

It’s these little things that help integrate the various concepts picked up during readings. Like cement mortar in building.

Hi S2000magician, I have a question regarding the interest rates used in a binomial model to value bonds without embedded options vs. the interest rates used in a binomial model to value bonds with embedded options.

I understand the logic that forward rates are used in a binomial model to value bonds with embedded options. Are spot rates used in a binomial model to value bonds without embedded options? Can you explain why or why not? Thanks!

You use the same tree to value callable bonds, putable bonds, straight fixed-rate bonds, and straight floating-rate bonds.

You use forward rates because the valuation is done step-by-step, moving one period at a time.

Appreciate the quick response and clarification, thank you!

My pleasure.