Fixed Income Topic Test Desna Problem #4

P

pfunder33

New member
Joined
Jun 18, 2026
Messages
0
Reaction score
0
Aside from this topic test being really difficult (1/6). I had an issue with the CFAI answer for the binomial interest rate tree problem #4. I assume I am missing something obvious, but I don’t understand their calculations.
For example, why isn’t V(u,u) calculated as .5*(102.8+102.8)/1.0456 = 98.317?
And then why do they only add $2.80 at each of the preceding nodes instead of $5.60?
Thanks in advance.
 
I don’t have access to the test, but for the second question I’ll venture the guess that the coupon is paid semiannually, not annually; therefore, each 6 months you get half the coupon.
 
Unfortunately, it specifies annual payments. Thanks for the thought, though! Love your site.
 
1) They are doing what you are saying. However you need to add the coupon received at that period at the end which is not discounted.
2.)
Using a different set of benchmark bond values, Maalouf constructs the calibrated binomial interest rate tree shown in Exhibit 2. He shows Fujioka how to value a three-year, option-free, fixed-rate bond with a 2.8% coupon rate, annual payments, and a face value of 100 using this interest rate tree.
2.8% coupon, annual payments = 2.8 coupon 1x per year
2.8% coupon, semi-annual payments = 1.4 coupon 2x per year.
The curriculum does a funky job with the formulas explaining how to discount. I thought Wiley did a better job, but in the end you get the same answer. Luckily I have a background in FI or I would have been lost :/
 
This is really a notation issue. Their V(x,x) includes the current node CF whereas everywhere else I’ve seen it’s only the PV of the future CFs.
I did indeed get the same answer doing it “my way”.
Thanks
 
Yup, you will be receiving the CF on that date so you need to include it in the value.
 
Yes, I understand that, thanks.
Open up your Wiley fixed income book to a binomial interest rate tree problem and tell me if their “V(u,u)” includes the CF that occurs at that time/node. You will see what I mean.
It’s just a notation issue.
 
remember that
0.5 * 2.8 + 0.5 * 2.8 = 2.8 nonetheless
so a short cut would be to take (0.5 * Node 1 value + 0.5 * Node 2 Value)/(1+r) + 2.8
or even better
0.5 * [(Node 1 + node 2) / (1+r)] + 2.8 –
all shoiuld give you the same value
 
Yes, I understand that, thanks.
It’s just a notation issue.
 
Yeah I thought it was weird that Wiley presented it differently than the curriculum did. Confusing when you are trying to look at EOC answers and topic tests. I preferred how they did it but transitioning to CFAI was weird.
 
turbo989 wrote:
Yeah I thought it was weird that Wiley presented it differently than the curriculum did. Confusing when you are trying to look at EOC answers and topic tests. I preferred how they did it but transitioning to CFAI was weird.
Click to expand...
Actually, they both (and Kaplan) say that V(x,x) is equal to the PV of future cashflows with C being the coupon/current period CF.
The only time I’ve ever seen V(x,x) being equal to PV future CF + C is in this one answer explanation from CFAI.
 
If it’s a 3-year bond, we use only the current, year 1, and year 2 forward rates.
A fig for the year 3 rates.
 
Can you provide a pathwise valuation for th above mentioned bond using the given interest rate tree
Tx
 
You must log in or register to reply here.
Back
Top