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?