Valuation of a Convertible Bond in an Arbitrage Free Framework

Valuation of a Convertible Bond in an Arbitrage Free Framework

Recall that according to the arbitrage-free framework, the value of a bond with an embedded option is equal to the sum of the arbitrage-free values of its parts.

The arbitrage-free approach can be used to value convertible callable or putable bonds. Each component of the bond, including straight bond, call option of the stock, and call and/or put option on the bond) can be valued separately.

$$\text{Value}_{\text{convertible bond}} = \text{Value}_{\text{straight bond}}+\text{Value}_{\text{call option on the issuer’s stock}}$$

$$ \begin{align*} & \text{Value of convertible bond} \\ & = \text{Value of straight bond} + \text{Value of call option on the issuer’s stock} \end{align*} $$

$$ \begin{align*}\text{Value of convertible bond} & =\text{Value of straight bond}\\&+\text{Value of call option on the issuer’s stock}\end{align*}$$

$$\begin{align*}\text{Value of collable convertible bond} & =\text{Value of straight bond}\\&+\text{Value of option on the issuer’s stock}\\&-\text{Value of issuer’s call option }\end{align*}$$

$$\begin{align*}\text{Value of collable putable convertible bond } & =\text{Value of straight bond}\\&+\text{Value of call option on the issuer’s stock}\\&-\text{Value of issuer’s call option}\\&+\text{Value of investors put option}\end{align*}$$

Question

The value of a callable putable convertible bond is most accurately expressed as:

  1. Value of straight bond + Value of call option on the issuer’s stock.
  2. Value of straight bond + Value of call option on the issuer’s stock +Value of issuer call option – Value of investor put option.
  3. Value of straight bond + Value of call option on stock – Value of issuer call option + Value of investor put option.

Solution

The correct answer is C.

$$ \begin{align*} & \text{Value of callable putable convertible bond} \\ & = \text{Value of straight bond} \\ & + \text{Value of call option on stock} \\ & – \text{Value of issuer call option} \\ & + \text{Value of investor put option} \end{align*} $$

Reading 30: Valuation and Analysis of Bonds with Embedded Options

LOS 30 (p) Describe how a convertible bond is valued in an arbitrage-free framework.

Shop CFA® Exam Prep

Offered by AnalystPrep

Featured Shop FRM® Exam Prep Learn with Us

    Subscribe to our newsletter and keep up with the latest and greatest tips for success
    Shop Actuarial Exams Prep Shop Graduate Admission Exam Prep


    Daniel Glyn
    Daniel Glyn
    2021-03-24
    I have finished my FRM1 thanks to AnalystPrep. And now using AnalystPrep for my FRM2 preparation. Professor Forjan is brilliant. He gives such good explanations and analogies. And more than anything makes learning fun. A big thank you to Analystprep and Professor Forjan. 5 stars all the way!
    michael walshe
    michael walshe
    2021-03-18
    Professor James' videos are excellent for understanding the underlying theories behind financial engineering / financial analysis. The AnalystPrep videos were better than any of the others that I searched through on YouTube for providing a clear explanation of some concepts, such as Portfolio theory, CAPM, and Arbitrage Pricing theory. Watching these cleared up many of the unclarities I had in my head. Highly recommended.
    Nyka Smith
    Nyka Smith
    2021-02-18
    Every concept is very well explained by Nilay Arun. kudos to you man!
    Badr Moubile
    Badr Moubile
    2021-02-13
    Very helpfull!
    Agustin Olcese
    Agustin Olcese
    2021-01-27
    Excellent explantions, very clear!
    Jaak Jay
    Jaak Jay
    2021-01-14
    Awesome content, kudos to Prof.James Frojan
    sindhushree reddy
    sindhushree reddy
    2021-01-07
    Crisp and short ppt of Frm chapters and great explanation with examples.