# Bond (Not James Bond) Q

Compare the price of option-free bond and option-embedded bond in the following scenarios. List them from High to Low: P(free); P(callable); P(putable) 1. Yield level equal to coupon rate. 2. Yield level lower than coupon rate. 3. Yield level higher than coupon rate.

P>F>C for all 3 scenarios?

I really got confused… How to effectively sort this out? Thx much.

I’m not exactly sure, but I’ll give it a shot. * A putable bond § is a benefit to the bondholder. As a result, the bondholder has to pay a premium for that added benefit. * A callable bond © is a benefit to the bond issuer. As a result, the bond issuer has to make that bond less expensive relative to option-free bonds. * An option-free bond (F) doesn’t give an added benefit to the bondholder or issuer, and should be priced somewhere between a callable and a putable bond. So, when yield and coupon are equal, the price is… P > F > C ******************************* When yield is lower than the coupon rate, the value of the callable bond decreases for the bondholder since the issuer is more likely to be called by the issuer. The market value of the putable bond and the option-free bond should be the same, but the value of the put option isn’t for free and has to cost something to the bondholder. Hence… P > F > C ******************************* When yield is higher than coupon rate, the value of the put option begins to take effect and maintains the price of the putable bond above an option-free bond. At this point the market value of the option-free bond and callable bond should be the same. However since the callable bond always gives an advantage to the issuer, then… P > F > C

Thanks for your insight, tozerrt.

This is a red herring problem. Yields and coupons have nothing to do with it. A puttable bond gives a bond put to the holder. A callable bond makes him short a bond call. I would always like to have a bond put. I would never want to be short a bond call. So P > F > C always…