The option-free bond price tree is as follows:
|
100.00 |
|
A ==> 99.74 |
|
| 99.81 |
|
100.00 |
|
100.16 |
|
100.00 |
As an example, the price at node A is obtained as follows:
PriceA = (prob × (Pup + coupon/2) + prob × (Pdown + coupon/2))/(1 + rate/2) = (0.5 × (100 + 3) + 0.5 × (100 + 3))/(1 + 0.0653/2) = 99.74. The bond values at the other nodes are obtained in the same way.
The calculation for node 0 or time 0 is
0.5[(99.74 + 3)/(1+ 0.063/2) + (100.16 + 3)/(1 + 0.063/2)] =
0.5 (99.60252 + 100.00969) = 99.80611
