Question 6 (31 points) The current on-the-run yields for Orange Corporation are as follows: Maturity (years) Yield to Maturity (%) Market Value 1 2 100 2 4 100 Assume that each bond is an annual-pay bond. Each bond is trading at par, so its coupon rate is equal to its yield to maturity. Answer the below questions.

(a) Using the bootstrapping methodology, complete the following table (4 marks): Year Spot Rate (%) One-Year Forward Rate (%) 1 -- 2

(b) i) Using the spot rates, what would be the (theoretical) value of a 2 year 6% option-free bond of this issuer? (4 marks) ii) Without doing calculation, will you expect the corresponding yield to maturity of this 2 year 6% option-free bond to be higher or lower than that of the 2 year on-the-run? Why? (3 marks)

(c) i) There is another 2 year 6% bond of the same issuer in the market but it is callable at par in 1 year, calculate its fair value using the binomial model (which assumes that one-year rates undergo a lognormal random walk), the interest rate tree is as below: (7 marks) At node N, we have: r0 = 2% At node NL, we have: r1 = 5.5154% At node NH, we have: r1 = 6.7365% ii) What is the value of the call option? (3 marks)

(d) Name two other alternatives the issuer has should it do not want to pay upfront (or through higher coupon) for the call option in c) above? That is, it pays only when it exercises the right. (4 marks)

(e) Should there be a 2 year zero coupon bond trading in the market at 90% of par value, is it considered to be cheap or expensive? Describe the arbitrage opportunity if any? (6 marks)