- franklau0125
**Posts:**34**Joined:**

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...

amongst other things, bond + warrant does not consider default risk. T&F does I think.

knowledge comes, wisdom lingers

- franklau0125
**Posts:**34**Joined:**

However, bond does default risk as it is considered in the credit spread in bond discounting rate when evalauting 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?

Last edited by franklau0125 on September 2nd, 2013, 10:00 pm, edited 1 time in total.

And if you calculate the convertible bond as straight bond + the kind of option you can trade on market, you neglect the fact that when you exercise the embedded option you are paying out, not cash, but a bond. Numeraire matters.

- franklau0125
**Posts:**34**Joined:**

I got your reply.But what I think is that, if I calculate the convertible bond as straight bond + the kind of option and the kind of option is valued by option pricing model based on intrinsic value approach (even using binomial tree), then the intrinsic value is just multiplied by (Principal amount / conversion price). By doing so, I think I do not neglect the fact that when I exercise the embedded option I am paying out a bond.Then, it seems that there is no difference in defining the equity and debt component in two methods and it seems that default risk is still considered in the model, by taking account of risky bond discount rate.Is there any reference that explain the valuation of convertible bond using straight bond + the kind of option or equity/debt method by T&F? Thanks...

I think besides the credit risk in the instrument itself the stock and spread dynamics are obviously correlated. I wonder whether that is the difference between the two approaches, the first one "ignores it" or assumes it is static, while the other approach recognizes spreads are blowing out as the stock approaches zero!

- franklau0125
**Posts:**34**Joined:**

I have a comment about the two method after running the algorithm. I doubt that the intrinsic value may not be appropriate in pricing the convertible bond (conversion option). Here is my claim,In the past few days, I tried to use the binomial tree to price the conversion option based on intrinsic value approach and using the decision rule max(min(call,roll),conv), I found that the value of conversion option is smaller than that based on total value approach. Hence, the CB valued is smaller. I guess the reason is that if the option is exercised, only the intrinsic value is discounted but in fact intrinsic value is not only the part to be discounted by risk-free rate. When the conversion option is exercised, the whole CB should be discounted by risk-free rate. Hence the option valued is smaller and using intrinsic value approach to value the CB is not correct, is my claim right?Could anyone justify my claim? Thanks.

Note that the method "bond + option" works with a fixed strike, while the exercising of the option at time t depends on the corresponding bond price at t.

Last edited by kpacu on October 11th, 2013, 10:00 pm, edited 1 time in total.

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