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

Q1. For a callable bond, the value of an embedded option is the price of the option-free bond:

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

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

C)   plus the risk-free rate.

Q2. 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?

A)   0.64.

B)   0.21.

C)   0.74.

Q3. 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.

Q4. 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.

LOS e: Illustrate the relationship among the values of a callable (putable) bond, the corresponding option-free bond, and the embedded option. fficeffice" />

Q1. For a callable bond, the value of an embedded option is the price of the option-free bond:

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

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

C)   plus the risk-free rate.

Correct answer is A)

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.

Q2. 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?

A)   0.64.

B)   0.21.

C)   0.74.

Correct answer is C)

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.

Q3. 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.

Correct answer is B)

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.

Q4. 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.

Correct answer is A)

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

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