# A question about pricing convertible bond with two different underlying assets

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.

• 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? Apr 25, 2014 at 13:26
• How does the conversion work for the private company? What is the strike based on? Apr 26, 2014 at 5:34
• To PBD10017: If the strike price is fixed, so how can I value the CB? Thanks. Apr 27, 2014 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. Apr 28, 2014 at 12:49
• For the correlation component, if you don't have historical stocks, you could go on some estimate based on average correlations in the sector, or liken them to similar companies that are listed...
– will
Oct 9, 2016 at 9:40