Some cor porate bonds are issued as callable bonds. These are bonds issued that contain an option exercisable at the discretion of the issuer to “call” or redeem the bond at a par ticular price. The exact call conditions are often more complicated than this but we will look at the case of a single call price where in the event of the issuer calling the bond it buys back all issued bonds.
This call option alters the way in which the bond’s price changes. We will use a 15-year bond with a coupon rate of 4.5% trading at $8000. The call price is $10 000, the bond’s par value. In effect while the issuer of the bond has sold a bond the buyers of the bond have also written a call option to the issuer.
(The reader should bear in mind that corporates cannot in practice issue bonds with such long terms but the longer term makes it easier to see the how the bond’s value is affected by the presence of the option.)
As yields-to-maturity fall the value of the vanilla bond rises. The position for the writer of the call option is opposite. As the bond’s price rises the writer’s losses increase. These are shown in the first of the following two char ts.
As the holder of the bond and the writer of the call option are the same party we can get the price of the callable bond by simply adding together the two positions. The effect is a form of price truncation, as yields fall and the bond’s price approaches that of the call price fur ther price increases are truncated.
We can express this as follows:
Value of callable bond = Value of equivalent straight bond − Value of call option
The exact terms of the call option vary in terms of call price and call schedule. Some bonds are issued with a schedule of possible call dates, call price on each date and may specify a maximum percentage of the issue that can be called on each date. When comparing yields-to-maturity of callable bonds to other bonds one of two yields is used:
Yield-to-call. The yield-to-call is the yield of the bond assuming it is called at the call price at the next call date.
Yield-to-worst. The yield-to-worst is used for callable bonds with a schedule of call dates and call prices. The yield-to-worst is the yield-to-call for the call for the combination that is most disadvantageous to the holder of the bond.
Callable bonds have lower value than equivalent vanilla bonds. When issued pricing has to reflect the “premium” paid to the writer of the call option. Callable bonds always have lower yield-to-maturity than their vanilla equivalent.