Capped Bond

[Hanuman]

Hi,

Per the question in CFAI book:

One-year Libor annually, set in arrears, capped at 5.00%. What is the price of the bond?

Solution is :

105 6.368% 106.368 98.71 105 4.5027% 99.381 3.000% 5.0092% 105.0092 99.697 99.99 105 3.5419% 99.996 3.940% 103.94 100.00

For Year 1 and 4.5% my Price is ( (5+(0.5*98.71+0.5*99.99))/(1+.045027)) = 99.85. What am I doing wrong?

Also for year three why have they discounted 103.94 and not the coupon payment of 105?

I ahv realized that for floor and capped bond they normally take the forward rate and add it to 100 (100+3.94) during the last year. Not sure about the logic. But in other scenario its normally 100+ coupon.

Thanks

[iceman_1212]

@Hanuman

For Year 1 and 4.5% my Price is ( (5+(0.5*98.71+0.5*99.99))/(1+.045027)) = 99.85. What am I doing wrong?

Also for year three why have they discounted 103.94 and not the coupon payment of 105?

It’s a floating rate bond set in arrears where coupon is capped (i.e., not fixed) to 5%, so the coupon payment at time t+1 is equal to the smaller of (1) the interest rate at time t (i.e., the previous period), and (2) 5.00%. As a result, in year 3 (for the bottom-most node), the assumed coupon payment is equal to the interest rate in year 2, i.e., 3.9404, which is smaller than 5.

So for year 1 and 4.5%, the price is ( ( 4.5027 +(0.5*98.714+0.5*99.991))/(1+.045027)) = 99.381

[Hanuman]

@iceman\_1212

@Hanuman

For Year 1 and 4.5% my Price is ( (5+(0.5*98.71+0.5*99.99))/(1+.045027)) = 99.85. What am I doing wrong?

Also for year three why have they discounted 103.94 and not the coupon payment of 105?

It’s a floating rate bond set in arrears where coupon is capped (i.e., not fixed) to 5%, so the coupon payment at time t+1 is equal to the smaller of (1) the interest rate at time t (i.e., the previous period), and (2) 5.00%. As a result, in year 3 (for the bottom-most node), the assumed coupon payment is equal to the interest rate in year 2, i.e., 3.9404, which is smaller than 5.

So for year 1 and 4.5%, the price is ( ( 4.5027 +(0.5*98.714+0.5*99.991))/(1+.045027)) = 99.381

Thanks for the reply…this is helpful…sorry for the way question was posted.Should have doubled checked the formattting

[S2000magician]

I’m not certain about that reading’s definition of “set in arrears”. To my mind, that should mean that the coupon rate is set at the end of the period, when it’s paid, not at the beginning of the period (which I would expect to be called, “set in advance”). I’m going to write CFA Institute about that one.

[S2000magician]

I just heard back from CFA Institute, and they agree that their definition of “set in arrears” is incorrect; what they’re describing should be called, “set in advance, paid in arrears”.

Whew!

They said that they’ll correct it.