Callable bond: Type of bond which provides issuer of the bond with right, but not obligation, to redeem bond at some point before the date of maturity at a prefixed price.
For an issuer, when rates fall it makes more sense to call the bond and issue new bond at lower rates. Hence, when rates fall the price of the bond is somewhat capped by callability provision. Thus bond price does not exceed call price if rates fall but price falls when rate rise similar to a straigth plain vanilla bond.
Due to the risk of receiving lower rates in future, the investor demands higher rates and hence the bond price is lower than a straight bond.
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