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I have a question regarding the pricing of convertible bond.

If I value the convertible bond with two different underlying assets, how can I incorporate two volatility and the correlation in the model?

So far, I can find the reference of setting up the binomial model as in P.160 to P. 162 in Peter James - Options Theory. However, this binomial model is applied to price options and I am not sure whether I can use the binomial model to price convertible bonds as well.

Also, if one of the underlying is non-listed company and the other is listed company, how can I assess the correlation between that non-listed company and the listed company? If two companies are listed companies, I can easily compute the correlation of the stocks based on historical price data. On the other hand, it is different story if one of the company is non-listed. In addition, if the non-listed company is the subsidary of the listed company, how can I assess the correlation between such non-listed company and the listed company?

Finally, is there any reference to describe the pricing of convertible bond with two different underlying assets?

Thanks.

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You'll get a better-quality answer if you are more specific about the terms and conditions (T&C) of the bond. In particular, if the holder chooses to convert, is the mixture of assets the conversion happens into determined by the holder, the issuer, or a formula? –  Brian B Apr 25 at 13:26
    
How does the conversion work for the private company? What is the strike based on? –  PBD10017 Apr 26 at 5:34
    
To PBD10017: If the strike price is fixed, so how can I value the CB? Thanks. –  Dennis Apr 27 at 7:51
    
Dennis, you can definitely use a binomial tree to value the optional component of the bond. However you're not saying how the conversion works. I see two alternatives 1) you convert into a portfolio of two companies or 2) you have a choice into which you convert. Both have solutions. You also don't mention how the price of the non-listed company is determined. It would be really helpful to know this so we can give you a meaningful response. –  PBD10017 Apr 28 at 12:49

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