In the previous post, we outlined the main steps in pricing a convertible bond using the Binomial Tree approach. In this follow-up post, we provide a hypothetical example of a straight convertible bond.
The specifics of the hypothetical convertible bond are as follows,
| INPUTS | |
| Stock price | 100 |
| Volatility | 0.25 |
| Risk Free Rate | 0.02 |
| Risky Rate (risk free+credit spread) | 0.08 |
| Coupon | 0.06 |
| Maturity (in years) | 5 |
| Conversion ratio | 10 |
Using the formula provided in the previous post, we calculated the up and down moves, and probability of the up move. The results are
| MODEL PARAMETERS | |
| dt | 1.00 |
| u | 1.28 |
| d | 0.78 |
| Probability Up | 0.48 |
Once the tree parameters are calculated, we next build the tree, and then work backward from the end nodes in order to obtain the convertible bond’s price at time zero. As the final result, the bond price is $1319 (per $1000 notional)
To see the details of the calculations of the tree, follow the instruction at the bottom of this page. Note that this is a simplified example. In real life, convertible bonds are usually more complex. They often include features such as call, put, contingency conversion options. The call and put options can be implemented using the formula given in the previous post.
I hope that this and previous posts demystified a little bit the complexities of convertible bonds. Let us know if you have any questions.
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