FI Interest Rate Tree Shortcut

CFA Level II
#1

Hi all,

I was wondering if there could be a shortcut to valuing bonds with embedded options on an interest rate tee and would like some input:

Let’s say the coupon rate is 5% on a callable (at par) three year bond. If I look at the interest rate tree, can I always assume that the bond will be called (ergo value will be par at that node) whenever the interest rate is below the coupon rate because in that case the bond will be trading above par?

This would make calculations quicker, as you will only need to calculate the value at time step t where i > c.

Any thoughts on this?

#2

Given the typical assumption from the curriculum (that it will be called always, and only, when the option is in the money), yes.

But I’d read the vignette to make sure that that’s the case, and that it’s callable at par.

#3

Thanks for the input. Obviously I wouldn’t bet on it but if all necessary assumptions hold, this is a way to speed things up, especially if there are 3 or more periods.