Putable Bond Valuation

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BHahesy

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This might be the bone head question of the day… but here it goes.
Question from Q-Bank:
Using the following tree of semiannual interest rates what is the value of a putable semiannual bond that has one year remaining to maturity, a put price of 98 and a 4 percent coupon rate?
The bond is putable today.
——-7.59%
6.35%
——-5.33%
A) 98.75.
B) 97.92.
C) 99.52.
D) 98.00.
The correct answer was D) 98.00.
As an example, the price at node A is obtained as follows:
PriceA = max{(prob * (Pup + coupon/2) + prob * (Pdown + coupon/2))/(1 + rate/2), putl price} = max{(0.5 * (100 + 2) + 0.5 * (100 + 2))/(1 + 0.0759/2),98} = 98.27.
The bond values at the other nodes are obtained in the same way.
The price at node 0 = [.5*(98.27+2) + .5*(99.35+2)]/ (1 + 0.0635/2) = $97.71 but since this is less than the put price of $98 the bond price will be $98.
___________________________________________________________
The answer provided makes complete sense… but when the question states “Using the following tree of SEMIANNUAL interest rates” I was thrown off and assumed I did not need to take the rate and divide by 2. Can anyone provide thoughts/insight into why the question was not stated as “Using the following tree of interest rates”? Am I the only one that misinterpreted the rates as stated in this question?
I know this is a semiannual bond… but my question is how do I know if I need to take rate/2 in these situations?
Thanks in advance for all thoughts/comments.
 
Of course. Didn’t you pass level 1?
A 4 percent coupon is 2 percent, twice per year, unless told otherwise.
 
I am not talking about the coupon… I am asking about the interest rates.
Why in this specific example did we divide the interest rate by 2 when the the question states these are semiannual interest rates?
Maybee I am just reading this wrong or looking into the wording of the question too much…
 
Ahhh, I see.
But the answer is: yes, a semiannual interest rate still means div by 2. Just another convention I suppose.
 
Thanks… I really do not want to make silly mistakes like this on the exam.
 
Those must be annual rates. The value of the bond at the second step of the tree is the 102 due at maturity discounted for 6 mo at the 6 mo interest rate (semiannual rate).
If these were already semi-annual rates and you were using the 1/2 of the semi-annual rates to discount the maturity value, you would be discounting a 6 month CF by a 3 month discount rate. Doing so would not make any sense.
That would be like saying $110 in one year is worth $105 now, assuming a 10% annual discount rate.
Sometimes Schwesser isn’t very clear in the way their questions are presented, I would assume that this is one of those cases. I’m sure the exam will be more clear.
 
I’m confused by this q bank question. It states that the bond has 1 year remaining to maturity and the bond appears to be a 2 year bond from the tree yet the answer calculates the value at node 0. Why would we be calculating the value at time 0 when we are currently at the end of year 1? Or am I missing something?
 
stevoDE wrote:
I’m confused by this q bank question. It states that the bond has 1 year remaining to maturity and the bond appears to be a 2 year bond from the tree yet the answer calculates the value at node 0. Why would we be calculating the value at time 0 when we are currently at the end of year 1? Or am I missing something?
Click to expand...
Anyone?
 
It’s a semiannual-pay bond; it has one year – two semiannual periods – till maturity.
 
S2000magician wrote:
It’s a semiannual-pay bond; it has one year – two semiannual periods – till maturity.
Click to expand...
Ah, of course. Thanks.
 
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