A callable bond gives the issuer the right to buy back the bond early, which is therefore detrimental to the bondholder. It therefore reduces the callable bond price in comparison to an option-free bond. A more general way to view the callable bond price is:
Callable Bond = Option-free Bond - Call option
Embedded call options will increase in value when interest rate volatility rises. Therefore, a callable bond will fall in value. Remember the price of a callable bond is the difference between an option-free bond and a call option.
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