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.
