I have a question With conducting a binomial tree to back into the bond price today. If the price fall under the put price at year 0. You bring the price back to the put price. But when you do the same process to value a callable bond and the price is above the call price at year 0, why don’t you bring back down the value of the bond to the call price?
You do. (Assuming, of course, that it’s immediately callable.)
Is there an example that makes you think that you don’t?
Using the following tree of semiannual interest rates what is the value of a putable bond that has one year remaining to maturity, a put price of 99, coupons paid semiannually with payments based on a 5% annual rate of interest? 7.59% 6.35% 5.33% A) 98.75. B) 97.92. C) 99.00. Your answer: C was correct! The putable bond price tree is as follows: 100.00 A → 99.00 99.00 100.00 99.84 100.00 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)), put price] = max[(0.5 × (100 + 2.5) + 0.5 × (100 + 2.5)) / (1 + (0.0759 / 2)) ,99] = 99.00. The bond values at the other nodes are obtained in the same way. The calculated price at node 0 = [0.5(99.00 + 2.5) + 0.5(99.84 + 2.5)] / (1 + (0.0635 / 2)) = $98.78 but since the put price is $99 the price of the bond will not go below $99.
These 2 I got so confused…
This bond is not callable today.
Ok thanks. So if its callable or putable immediately, then I should adjust the value at time 0. Thx a lot
My pleasure.
Yup.
Glad to help.