Convertible Bond Valuation: Bond Plus Option Versus Binomial Models

Summary

The note compares a bond-plus-equity-option approach to valuing convertible bonds with a binomial approach that models both debt and equity features. In the simpler method, the value is treated as the sum of a straight bond and a call option on the underlying shares, with the option valued using a model such as Black–Scholes.

The approaches are equivalent under restrictive conditions: default is not possible and the bond’s terms are very simple. In more realistic cases, default risk and detailed contractual terms matter. A binomial framework can account for the possibility that the embedded conversion option disappears upon default, which the basic bond-plus-option treatment does not capture. The note offers a conceptual comparison rather than implementation guidance or a detailed model specification; professional valuation may use more sophisticated models.

Key ideas

• The bond-plus-option approach decomposes a convertible into a straight bond and an equity call option.
• That simple decomposition can match a binomial model when default is impossible and bond terms are very simple.
• Default risk can affect whether the conversion option retains value.
• A binomial framework can represent complex terms and the loss of conversion value on default.

Tags

# What is the difference between the methods (listed in content) in pricing convertible bond?


# What is the difference between the methods (listed in content) in pricing convertible bond?












To price the convertible bond, one of the models is the bond plus equity option method. That is, the value of convertible bonds is evaluated by finding the value of the straight bond and the value of call option on the underlying asset by option pricing model, i.e. Black Scholes Model.

Another model is the binomial model which takes account of equity and debt component, as advocated by K. Tsiveriotis and C. Fernandes (1998).

My question is, what is the difference between two methods? Thanks...

## Answer by Brian B (score 1)

https://quant.stackexchange.com/a/8804

If there is no chance of default, and you have an extremely simple set of terms and conditions (T&C) on the bond, then the two are equivalent.

In the real world T&C are complex for all bonds currently traded, and default is important. Therefore something closer to the binomial model, which allows the embedded option to disappear in the event of default, is called for.

In practice, professionals use more sophisticated models like the offerings from Monis or Kynex.

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