B3. A puttable bond

a. ABC, Ltd. is considering issuing a simple coupon bond with a maturity of 2 years that pays a coupon of 5% per annum, in annual payments. At the moment, the one-year spot rate is 6% with quarterly compounding. The forward rate that starts applying in 1 year and pays off in 2 years is 7% with quarterly compounding. There is no default risk. What would be a fair price at which the company could issue this simple coupon bond? [11 marks]

b. ABC is considering making the bond puttable, that is, to embed a put option in the bond. ABC estimates that the implied volatility for such an option should be 13%. i. What is the value of the put option? ii. Suppose ABC issued the puttable bond. Who would have the right to exercise the put option? Hence, what would be the price of the puttable bond? [12 marks]

c. ABC is also considering making the bond callable, that is, to embed a call option in the bond. ABC estimates that the implied volatility for such an option should be 13%. i. What is the value of the call option? ii. Suppose ABC issued callable bond. Who would have the right to exercise the call option? Hence, what would be the price of the callable bond? [12 marks]