Explain how a callable or putable bond's value links to the value of its embedded option and of the equivalent straight bond
The idea
An embedded option is valued as the difference between the bond with the option and the same bond without it. For a callable bond the issuer owns the call, so in value terms callable = straight − call, and call = straight − callable. For a putable bond the holder owns the put, so in value terms putable = straight + put, and put = putable − straight. The same logic applies to floaters, where the issuer owns a cap and the holder a floor: capped = straight floater − cap and floored = straight floater + floor. A callable bond is therefore never worth more than the straight bond, and a putable bond never less. Measuring an option against par rather than against the straight bond is the usual mistake.
Formulas
Value of an embedded call option
call value = straight bond value − callable bond value
- call value
- what the issuer's right to redeem early is worth
- straight bond value
- the same bond valued with no call
- callable bond value
- the bond valued with the call, capping each node at the call price
Value both bonds on the same tree. At each node where the call is exercisable, the callable value is the lower of its computed value and the call price, which is how the option takes value away from the investor.
In the app: 2 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.
Take the free diagnostic →More in Valuation and Analysis of Bonds with Embedded Options
- Explain bonds and other debt securities that contain embedded options
- Explain how to apply the arbitrage-free approach when valuing a bond that contains embedded options
- Explain the effect of interest rate volatility on what a callable or putable bond is worth
- Explain the effect of shifts in the yield curve's level and shape on what a callable or putable bond is worth
- Use an interest rate tree to work out what a callable or putable bond is worth
- Explain how option-adjusted spreads are computed and what they are used for
- Explain the effect of interest rate volatility on option-adjusted spreads
- Work out a callable or putable bond's effective duration and explain what it means
- Contrast the effective durations of straight, callable and putable bonds
- Explain how one-sided and key rate durations help assess the rate sensitivity of bonds that contain embedded options
- Contrast the effective convexities of straight, callable and putable bonds
- Work out what a floating-rate bond with a cap or a floor is worth
- Set out the key characteristics of a convertible bond
- Work out the parts that make up a convertible bond's value and explain what they mean
- Explain how to value a convertible bond within an arbitrage-free framework
- Weigh the risk and return profile of a convertible bond against the profiles of a straight bond and the underlying common shares