How does one calculate the value of a callable bond?

The value of a callable bond is calculated by taking the value of a regular bond and subtracting the value of the call option. This approach reflects the bondholder's perspective, as the presence of a call option gives the issuer the right to redeem the bond before its maturity, often at an unfavorable time for the bondholder.

A regular bond's value is based on the present value of its cash flows, which typically include periodic interest payments and the principal amount at maturity. However, when a bond is callable, the investor faces the risk that the bond may be redeemed early, usually when interest rates decline. This early redemption limits the potential appreciation that a bondholder might realize if they had held the bond to maturity.

The call option inherently reduces the bond's value for the investor because they might miss out on future cash flows if the bond is called. Therefore, the callable bond's value diminishes by the value of the call option that the issuer holds, leading to the calculation: value of a callable bond = value of a regular bond - value of a call option.

In summary, understanding the interplay between regular bonds and call options is crucial for valuing callable bonds appropriately, which is why the subtraction approach is the correct method for this calculation.