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Modeling Convertible Bonds with Two Correlated Underlying Assets

Article Quant Q&A · Author: Dennis
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Summary

The document raises modeling questions about a convertible bond whose value depends on two assets. It asks how a pricing model should incorporate each asset’s volatility and their correlation, and whether a binomial framework commonly used for options can also be applied to convertible bonds.

It also highlights a practical calibration challenge: estimating correlation when one underlying is a private company, especially when that company is a subsidiary of a listed firm. The post supplies no worked model or resolution. Its only response points to an external paper, so the modeling assumptions and proposed methods cannot be assessed from this text alone.

Key ideas

  • A two-asset convertible bond model must account for both underlying volatilities and their correlation.
  • The post asks whether a binomial option-pricing framework can be adapted to convertible bonds.
  • Historical stock prices can inform correlation when both companies are listed.
  • Correlation estimation is less direct when an underlying company is private, including a private subsidiary.
  • The post offers a paper reference but no explanation or evidence about its method.

Tags

Fixed incomeDerivatives pricingVolatilityStatistics
Full text
# A question about pricing convertible bond with two different underlying assets


# 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.

## Answer by Dora (score 1)

https://quant.stackexchange.com/a/20731

Here is a new paper written by Tim Xiao at

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2400101

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.