A callable bond is the sale of a call option by the investor to the issuer as it allows the issuer to repurchase the bond from the time it becomes callable until the maturity date. The purchaser of a callable bond effectively enters into two transactions:
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Purchase of a non-callable bond for which they pay some price.
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Sale of a call option to the issuer for which they receive the option price from him.
The net price paid by a callable bondholder is given by,
Value of the callable bond = Value of the non-callable bond - Value of the call option.
It can be seen in Figure 1 that the difference between the price of the non-callable bond and the callable bond is the price of the embedded call option. Though we have simplified the situation for explanatory purposes, in practice it is not easy to define the price of a callable bond like this. The issuer may call the bond at the first call date or any time thereafter or any subsequent coupon anniversary. Thus, the investor has sold a strip of call options to the issuer. The price of the call option may vary with the date the option is exercised by the issuer. But it is always easier to describe the investor's position as a combination of a long position in non-callable bond and a short call option.