Valuing Capped or Floored Floating Rate Bonds.

CFA Level II
#1

Hi,

If I am given a IR-tree and the following information:

* one year Libor annually, set in Arrears, capped at 5%.

I understand that if the rate at one node is higher than 5%, i use 5%.

But how do I know what the coupons are based on this information?

It is based on EOC R37. Q16

N0 = 3%

N1u = 4.5027%

N1d = 3.5419%

N2uu = 6.3679%

N2ud= 5.0092%

N2dd = 3.9404%

#2

Coupons are the rates x par, because the floating bond is reset at every payment date.

So with backward induction based on your tree you start with 105 105 and 103.9404. You discount these with the interest rates (untouched when you use them for discounting. And you go on like this. Rates at node 1 are less than the cap so you don’t need to modify them further.

#3

Schweser does not even mention this! Be careful in this case you dont get a lattice model

#4

Thanks a lot for your reply. I did not completely get it.

on the n2uu do I discount 105 at 6.37% or at 5%?

on N1u is the coupon 4.5027?

#5

Are you sure about this?

Most floating rates are set in advance, paid in arrears.

#6

That is what it says. Question 15-16 in Reading 37, CFAI.

Do you have any inputs to how I calculate the value of the bond in this situation, based on the IR-tree above?

#7

According to their answer, they’re lying.

I’ll e-mail CFA Institute and ask them why this isn’t mentioned in their errata.

#8

Thank you. Much appreciated, please let me know what they respond.

#9

I got an e-mail from Wanda at CFA Institute today. She said that her investigator checked and it’s correct as written.

So . . . I looked at the curriculum and, sure enough, the author of reading 37 says right up front that the term “set in arrears” means that the the rate is set at the beginning of the period and paid at the end.

Of course, this contradicts both other readings (swaps, for example) and common usage: the proper description is set in advance, _ paid _ in arrears.

I suggested that they ask the author to change his term to conform to common usage. We’ll see, but I’m not hopeful.

#10

When you calculate the coupon you take into account the cap, i.e. if the interest rate is higher than the cap you use the cap, if it’s lower than the cap you use the interest rate.

For discounting to t-1 you use the interest rate unchanged, because it is the prevailing interest rate so for PV calculation you do not modify it.