Value of a capped floater

CFA Level II Fixed Income
#1

This question is blowing my mind. Please help

Forward IR tree

0 - 2%

1 - 5.7798% and 3.8743%

2 - 6.0512% and 4.0562% and 2.7189%

Par value is $100 . Cap rate is 4%. FInd the value of the capped floater.

#2

Clarification - I’m calcuating a value of 98.705 which apparantly is incorrect.

#3

I don’t think anybody is going to calculate it for you.

Why don’t you write up the steps instead?

#4

Sure. Tree …6.0512 …5.7798… 2%…4.0562 …3.8743… …2.7189 Starting at Upper right Node (2,U,U): - Cap is in the money - 100 + 4 = 104 / 1.060512 = 98.07 Far Right Middle Node (2,U,L) - Cap is in the money - 100 + 4 = 104 / 1.040562 = 99.95 Far Right Lower Node (2,L,L) - Cap is not in the money - 100 + 2.7189 = 102.7189 / 1.027189 = 100 ------------------------------------------- Middle Upper Node (1,U) - Cap is in the money - 98.07 + 4 = 102.07 / 1.057798 = 96.49 - 99.95 + 4 = 103.95 / 1.057798 = 98.27 - (96.49 + 98.27) / 2 = 97.38 Middle Lower Node (1,L) - Cap is not in the money - 99.95 + 3.8743 = 103.82 / 1.038743 = 99.95 - 100 + 3.8743 = 103.8743 / 1.038743 = 100 - (99.95 + 100) / 2 = 99.98 Initial Node: - Cap is not in the money - 97.38 + 2 = 99.38 / 1.02 = 97.43 - 99.98 + 2 = 101.98 / 1.02 = 99.98 - (97.43 + 99.98 ) / 2 = 98.71 Does this look correct ?

#5

No. You’re discounting the final payoffs.

The values in the time 2 nodes should be:

  • (2,U,U): 104
  • (2,U,L): 104
  • (2,L,L): 102.7189

Carry on from there.

#6

Thanks for responding, but now I’m now more confused. =\

This bond has a three year maturity. I thought At time 3 (maturity), the values should be the final payoffs - (104,104 and 102.7189) - And then we proceed with backward induction, taking the cap rate under consideration.

Schweser is giving me a final answer of $97.82. I just can’t seem to understand the logic here.

#7

are the question use 5.7798% or 5.5598% ?

please also give me the specific reference from which schweser

Thanks

#8

Its 5.7798%…my error. I updated the post.

It’s from the q-bank though. They are getting a value at the Node (1,U) of 95.59 which is causing all this confusion. (as opposed to my calculation of (1,U) of 97.38 from above)

#9

You hadn’t mentined the maturity earlier; I thought that it was a 2-year maturity.

I get $98.70.

Perhaps Schweser made a mistake.

#10

My bad for not clarifying!

But good! I’m glad I’m not going crazy. Thanks for taking a look!

#11

Hi Kos,

do you mind if you try first the same question on EOC no 15 (Curriculum Reading 44) ?

Tree (exhibit 6)

…………………6.3679% …….4.5027%……. 3%……………5.0092% …….3.5419%……. …………………3.9404%

#12

Yes - Just did the calculations and got the same answer as the CFAI solutions.

I’m concluding schweser just dropped the ball on this particular question

#13

Your calculations are fine.

What’s the solution written in the textbook?

#14

glad to hear that…the tricky part of this IMO : floating rate that pay LIBOR in arrears smiley