What are Bonds with Embedded Options?
A provision in financial security (usually bonds) is known as an embedded option. The bond issuer borrows money from bondholders and pays fixed payments to them for a set time at a fixed (or variable) interest rate.) The only constraint is that the possibilities cannot be mutually exclusive in this situation.
Examples of Bonds with Embedded Options:Callable Bond : A callable bond is when the issuer has the right to buy the bond back from investors at a specific price in the future. When interest rates have fallen, and the issuer can refinance at lower, more advantageous rates, the issuer will often desire to buy back the bond. As a result, the price appreciation on the upside in response to lower rates is limited and capped at the call price. A popular way to determine the effective lifetime of a callable bond is to utilise the bond's duration calculated as though it will not be called in the future. This, however, is erroneous because it excludes the possibility of the bond being called.
For example, consider a 7-year bond that can be called in four years, with a 43% probability of being called. The effective duration would then be calculated as
D=0.43D called+0.57(D not called)
Putable Bond: A putable bond gives the bondholder the right to sell the bond back to the issuer at a predetermined price. The effective duration of a putable bond is calculated similarly to callable bonds.