Binominal tree - Value at a node

CFA Level II Fixed Income
#1

Hi all,

I’m little confused by this topic of valuing a bond at a node.

The formula should be this:
image

My question is - why coupon is discounted?

When I’m doing exercise examples I never discount coupon at a node, and get to correct answer at the end.

e.g. lets take this example, of 8% annual coupon bond
image

So at time 1 high node is calculated as follows:
image

So the coupon is not discounted as suggest by the formula above.

Hope I managed to explain this clearly. :slight_smile:

Thank you!

#2

The coupon they mention is the coupon paid at the next coupon date. In your tree, for example, to compute the value at time 1 you average the values at the up and down nodes at time 2, add the coupon paid at time 2, then discount it to time 1.

#3

Thanks. But following on this example - when calucalting the Value at Time 1, I’m not discounting the cupon paid in Time 2.

e.g. To compute value at higher node for Time 1 (6.00%) - I’m averaging values from higer and lower node from Time 2 (108.93 and 109.89) and discouting it at 6.00% rate and then just adding coupon of 8. Coupon is not discounted.

#4

You are, in fact.

The problem with their formula is that you’re discounting the value at the low node and the value at the high node by the same discount rate, which is not how binomial interest rate trees work. The value at node t is:

Value_t = \left(0.5\times\frac{C + VH}{1 + r_{t+1,H}}\right) + \left(0.5\times\frac{C + VL}{1 + r_{t+1,L}}\right)

In your original formula the coupon is discounted, and in the correct formula that I offered above it is discounted.

1 Like
#5

Yes, I believe I understand now. Thank you magician!

#6

Good to hear.

My pleasure.