# What is the difference between the methods (listed in content) in pricing convertible bond?

To price the convertible bond, one of the models is the bond plus equity option method. That is, the value of convertible bonds is evaluated by finding the value of the straight bond and the value of call option on the underlying asset by option pricing model, i.e. Black Scholes Model.

Another model is the binomial model which takes account of equity and debt component, as advocated by K. Tsiveriotis and C. Fernandes (1998).

My question is, what is the difference between two methods? Thanks...

• I notice you are providing comments as answers. Stop doing this. The moderators have had to turn your "answers" into comments. Also, I notice you keep creating new Stack Exchange accounts for each post. Again, stop doing this. I've had to put-in requests to have your accounts merged. Just pick one account and write comments. Sep 4, 2013 at 13:21

If there is no chance of default, and you have an extremely simple set of terms and conditions (T&C) on the bond, then the two are equivalent.

In the real world T&C are complex for all bonds currently traded, and default is important. Therefore something closer to the binomial model, which allows the embedded option to disappear in the event of default, is called for.

In practice, professionals use more sophisticated models like the offerings from Monis or Kynex.

• However, bond does default risk as it is considered in the credit spread in bond discounting rate when evaluating the bond value. In my conjecture, for the case of using option model, the intrinsic value of the option is assigned to the equity part and the bond is assigned to the debt part. For the case of separating equity and debt component, the conversion value is assigned to the equity part and the redemption value or call value is assigned to the debt part. Does it relate to the difference in defining the equity and debt component in two method? Sep 3, 2013 at 9:16
• If you separate the bond and option components then you cannot deal properly with the fact that default affects both. When I need to explain it to traders who don't understand the math, I generally express it in terms of discount rates for the option component, which in theory would need to vary with the probability of both exercise and default as the underlying moves. As a matter of fact, primitive approaches to converts pricing in the 1980s and early 1990s did just that. Sep 3, 2013 at 14:07
• To Brian B: I get our comment. For binomial model with equity and debt component, the equity and debt component are discounted by risk-free and risky rate respectively. Therefore, there is still one component not affected by the default risk. In addition to this, the value of CB at each node is governed by the well-known decision rule, (i.e. max(min(roll,call),conv) or min(max(roll,conv),call) and the equity and debt components are also more or less affected by that. Is there any other difference or rationale to support the consideration of default risk in binomial model? Sep 4, 2013 at 1:21