Adding embedded options to a bond allow issuers to manage interest rate risk and improve the initial coupon rate.
A callable bond gives the issuer the option to call the bond. The call option can be a European-style option (the option can only be exercised on a single day immediately after the lockout period), an American-style option (the option can be exercised at any time after the lockout period), or a Bermudan-style option (the option can be exercised at fixed dates after the lockout period).
Putable bonds all the investor to sell the bond back to the issuer prior to maturity. A related bond is an extendible bond, which allows the investor to extend the maturity. An extendible bond can be evaluated as a putable bond with longer maturity (i.e., the maturity if the bond is extended). A two-year, 3% bond extendible for an additional year at the same coupon rate would be valued the same as an otherwise identical three-year putable (European style) bond with a lockout period of two years.
There are more complex options that can be embedded into a bond. An estate put allows the heirs of an investor to put the bond if the original investor dies. The value of this bond is based on the life expectancy of the investor. A sinking fund bond is a provision that requires the issuer to periodically retire the portions of the bond issue, reducing the credit risk of the bond.