The price of the embedded option comprises two components. The first is the value of the same bond assuming it has no embedded option (option-free bond), the second part is the value of the embedded option.
The two very common embedded options are call and put options. Under call option, the issuer has right to call or prepay the bonds and issuer may do this when interest rate decreases. In put option, bondholder or investor has right to return the bonds to the issuer for pre-decided price and investor may do this when interest rate increases. Now let us look into the price/yield relationship for both types of embedded options.
Figure 1: Price/Yield Relationship for a Callable Bond and an Option-Free Bond