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LOS e: Illustrate the relations among the values of a callable (putable) bond, the corresponding option-free bond, and the embedded option.

For a callable bond, the value of an embedded option is the price of the option-free bond:

A)	plus the price of a callable bond of the same maturity, coupon and rating.

B)	minus the price of a callable bond of the same maturity, coupon and rating.

C)	plus the risk-free rate.

The value of the option embedded in a bond is the difference between that bond and an option-free bond of the same maturity, coupon and rating. The callable bond will have a price that is less than the price of a non-callable bond. Thus, the value of the embedded option is the option-free bond’s price minus the callable bond’s price.

Suppose that the value of an option-free bond is equal to 100.16, the value of the corresponding callable bond is equal to 99.42, and the value of the corresponding putable bond is 101.72. What is the value of the call option?

The call option value is just the difference between the value of the option-free bond and the value of the callable bond. Therefore, we have:

Call option value = 100.16 – 99.42 = 0.74.

How is the value of the embedded call option of a callable bond determined? The value of the embedded call option is:

A)	equal to the amount by which the callable bond value exceeds the option-free bond value.

B)	the difference between the value of the option-free bond and the callable bond.

C)	determined using the standard Black-Scholes model.

The callable bond is equivalent to the option-free bond except that the issuer has the option to call the bond at the call price before maturity. Therefore, for the holder of the bond, the bond is worth the same as the option-free bond reduced by the value of the option.

Which of the following is equal to the value of the putable bond? The putable bond value is equal to the:

A)	option-free bond value plus the value of the put option.

B)	option-free bond value minus the value of the put option.

C)	callable bond plus the value of the put option.

The value of a putable bond can be expressed as V_putable = V_nonputable + V_put.

A)	option-free bond value minus the value of the call option.

B)	callable bond value minus the value of the put option minus the value of the call option.

C)	callable bond plus the value of the embedded call option.

The value of a bond with an embedded call option is simply the value of a noncallable (V_noncallable) bond minus the value of the option (V_call). That is: V_callable = V_noncallable – V_call.

How does the value of a callable bond compare to a noncallable bond? The bond value is:

Since the issuer has the option to call the bonds before maturity, he is able to call the bonds when their coupon rate is high relative to the market interest rate and obtain cheaper financing through a new bond issue. This, however, is not in the interest of the bond holders who would like to continue receiving the high coupon rates. Therefore, they will only pay a lower price for callable bonds.

A callable bond and an option-free bond have the same coupon, maturity and rating. The callable bond currently trades at par value. Which of the following lists correctly orders the values of the indicated items from lowest to highest?

A)	Embedded call, callable bond, $0, option-free bond.

B)	Embedded call, $0, callable bond, option-free bond.

C)	$0, embedded call, callable bond, option-free bond.

The embedded call will always have a positive value prior to expiration, and this is especially true if the callable bond trades at par value. Since investors must be compensated for the call feature, the value of the option-free bond must exceed that of a callable bond with the same coupon and maturity and rating.

A callable bond, a putable bond, and an option-free bond have the same coupon, maturity and rating. The call price and put price are 98 and 102 respectively. The option-free bond trades at par. Which of the following lists correctly orders the values of the three bonds from lowest to highest?

A)	Option-free bond, putable bond, callable bond.

B)	Putable bond, option-free bond, callable bond.

C)	Callable bond, option-free bond, putable bond.

The put feature increases the value of a bond and the call feature lowers the value of a bond, when all other things are equal. Thus, the putable bond generally trades higher than a corresponding option-free bond, and the callable bond trades at a lower price.