A callable bond gives the issuer of a bond an option to call, or redeem, a bond before its formal term. A putable bond allows the holder of the bond to sell it back to the issuer before term. We can express the value of these two types of bond in the following way:
Value of callable bond = Value of equivalent straight bond ? Value of call option
Value of putable bond = Value of equivalent straight bond + Value of put option
Callable bonds are affected by what is called negative convexity. As yields fall and the price starts to approach the call price the price–yield curve flattens. The reason for this is simple. If yields fall further the issuer is likely to call in the bond in which case holders will only receive $10 000.
This situation is reversed with putable bonds. If prices of an equivalent straight bond fall below the put price the price of the putable bond will remain at the put price as the holder has the right to sell the bond back to the issuer at this price.
This truncation effect occurs with callable bonds because the bond’s price–yield curve has negative convexity as the price approaches the call price.