# value of a putable bond using Node method...?

Can someone please help. What is a good way to think about this problem? Breakdown? 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) 98.00. D) 99.52. Your answer: B was incorrect. The correct answer was C) 98.00. The putable bond price tree is as follows: 100.00 A ==> 98.27 98.00 100.00 99.35 100.00 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), 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.

I wouldn’t pay attention to the math that they provided. The only reason I would have picked B is because the price is currently 98, and the put option is a benefit to the bond owner. Therefore, since all interest rates given are higher than the coupon the value of the puttable bond has to be lower than par.

Wyantjs well I think you actually have to do the calculation because if the value would have came out to be higher then 98, then that would be your answer since its higher then the value of the put option. I’m not following the math on the break down though… any suggestions?

The way this problem is pasted is giving me a headache. But if you get a value less then 98 the value will be 98 b/c of the put.

Dancingqueen, youre right not the best job of pasting. Yes its clear that you would use the higher of the put value and the one calculated. However my question is what is the logic behind this calculation??? 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.

I got the same calculation as in the example. What is your problem exactly?

This question is posted earlier. I think its just badly phrased. It says semiannual spreads yet according to the answer you the are annual and you have to divide by 2.