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101 Concepts for the Level I Exam

Essential Concept 67: Relationships between the Values of a Callable or Putable Bond, Straight Bond, and Embedded Option


An embedded option represents a right that can be exercised by the issuer, by the bondholder, or automatically depending on the course of interest rates. Embedded options can be:

  • Simple: call options, put options etc.
  • Complex: estate put, sinking fund bonds etc.

A call option decreases the value of a bond to an investor. Therefore,

  • Value of callable bond = Value of straight bond – Value of issuer call option
  • Value of issuer call option = Value of straight bond – Value of callable bond

A put option increases the value of a bond to an investor. Therefore,

  • Value of putable bond = Value of straight bond + Value of investor put option
  • Value of investor put option = Value of putable bond – Value of straight bond

The value of any embedded option increases with interest rate volatility. The greater the interest rate volatility, the higher the chances for the embedded option to be exercised.

A call option is more likely to be exercised when interest rates fall. Hence, the value of an embedded call option is higher if the yield curve is downward sloping.

A put option is more likely to be exercised when interest rates rise. Hence, the value of an embedded put option is higher if the yield curve is upward sloping.