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The following problem can be understood as an extension/modification of the textbook example of Hull (Options, Futures and other derivatives, chapter 27.4, 9th Edition), which is related to convertible bonds.

My questions is the following:

Based on the determination of the value of the convertible bond in t=0 (going from the end values to the left, in the example from Hull, this is 106.93), how do I calculate the yield to maturity of the bond? My initial guess is that, based on the term of the bond, the value would just be: (value of the bond/initial value)^(1/n)-1, where n is the term of the bond, the value of the bond is the calculated convertible bond in t=0, i.e. 106.93, and the initial value is the issue value of the bond, i.e. 100 in the example. Assuming a term of 1 year, the yield to maturity for the bond would be 6.93%, but somehow I'm really unsure whether this "internal rate of return calculation" is right for the case at hand.

Is there a "standard" method to convert the value of an option into its respective part of the yield to maturity of the underlying?

I hope my question is straight forward.

Thank you for your help.

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  • $\begingroup$ What does the yield of a convertible bond really represent? For a regular bond the thing is that the value at expiry is always known, contrary to the CB case, therefore something as FaceValue / InitialValue cannot be computed without assumptions $\endgroup$
    – KT8
    Jan 29 at 18:22
  • $\begingroup$ Well, in the original Hull Model, the problem is "solved" by a trinomial model, where you determine the value at the end of the term and then calculate backwards, based on the conversion and the expected value of the bond (taking into account the default probability etc.). So based on this, you can determine the market value in t_0. $\endgroup$
    – PAS
    Jan 29 at 18:42
  • $\begingroup$ I see for pricing, but I dont see where the concept of yield appears here $\endgroup$
    – KT8
    Jan 29 at 22:08
  • $\begingroup$ My goal is, to determine the yield that a rational agent would expect / would be willing to pay or receive, given the calculated face value and the initial value of the convertible (assuming that he can convert the bond into equity any time). $\endgroup$
    – PAS
    Jan 30 at 6:19
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    $\begingroup$ Convertible bonds are traded on price terms, not yield terms. Even when straight bonds are traded in yield terms, that's merely a convenience and the back office handles conversions to prices. So I agree with @KT8 -- the concept of yield is fraught for converts (except in the special case where conversion/call probability is vanishingly low). $\endgroup$
    – Brian B
    Jan 31 at 16:57

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