Convertible Bonds

CFA Level II Fixed Income
#1

Hi All,

I was soving the following question - please have a look.

Question:

For a convertible bond with a call provision, with respect to the bond’s convertibility feature and the call feature, the Black-Scholes option model can apply to:

A.)neither features.

B.)both features.

C.)only one feature

Correct answer: C)

Explanation: The Black-Scholes model applies to the convertibility feature just as it does to the common stock. The Black-Scholes model is not appropriate for the call feature because the volatility of the bond cannot be assumed constant.

Could someone please explain what this explaiantion is meaning? Why Black scholes model applies to convertability feature (why it does apply to common stock?)?

Thanks many times,

Anush

#2

The convertibity of the bond is juts a call option to the stock (converting the bond to stock).

THe reason it doesnt apply to the call option of the bond is because the assumption of BSM is constant volatility.

#3

Hi - Thanks for the response.

Why BSM applies to the call option on the stock? Stock return volatility is not constant as well - or I`m mistaken here somehwere?

Thanks

Anush

#4

https://www.analystforum.com/forums/cfa-forums/cfa-level-ii-forum/9760689

#5

Hi 125 mph - thanks for the link, though it does not reply to the point why BSM holds for stocks but not for bonds, this is the point I don`t understand.

#6

Why we can assume that the vola vor stocks is constant but for bonds we cant - this is exactly what Im not understanding.

#7

The volatility in the bond is related to interest rates.

BSM was has an assumption of constant risk free rate. Talk to mr. black and mr. Scholes to invent a better algorithm.

The assumed interest rate was constant, hence the bonds cant be valued using BSM.

That is violated with bonds but not necessary with stocks. Anything interest rate related, you cannot calculate.

#8

:smiley: thanks for the explanation - very helpful.