Confused by Seemingly Different Calculations for 'Bond Value at a Node'

CFA Level II Fixed Income
#1

In Reading 36: The Arbitrage-Free Valuation Framework, they introduce the equation for finding the bond value at a node on a binomial interest rate tree.

The equation is: Bond Value = [(VH + C)/(1 + i) + (VL + C)/(1 + i)] x (1/2),

where VH = bond’s value if the higher forward rate is realized, VL = bond’s value if lower rate is realized, C = Coupon payment

Where I’m getting confused is in the BB & EOC problems for Reading 36 vs Reading 37, where they seemingly add another coupon payment to the equation above in reading 36, but not in reading 37 (for example, BB example 3 on p83, EOC problem 10 on p 102, contrasted against EOC problem 4 or 5 on p 173)

Hoping one of the smart people here can help clarify the problem :slight_smile:

TL;DR

Bond Value at Node in Reading 36 = [(VH + C)/(1 + i) + (VL + C)/(1 + i)] x (1/2) + C (Why?)

Bond Value at Node in Reading 37:= [(VH + C)/(1 + i) + (VL + C)/(1 + i)] x (1/2)

#2

Hi MRL,

I am looking at both examples and still unsure of what your issue is. Either way both methods will reconcile.

Looking at the far right node, you will take the par value of 100 and add the coupon on. Say 4.5 (so 104.5) The first node to the left will be 104.5/R. Take the answer and see if it needs to be called. If so mark it to 100 and add the coupon on. Repeat down the node, then add the nodes x 0.5 and discount back again. Coupons are added at every node but time 0 to get your price.

If you carefully work through both the examples you have suggested in your issue you will see it is the same method.