Question 13 Bond Pricing [20 Points] Imagine to be working on the fixed income desk of a hedge fund or investment bank. You have two monitors in front of you: on one monitor you can see realtime prices of the zero coupon bond market. Prices of zero coupon bonds (ZCB) with face value equal to 1000 are reported in the second column of the table below, for a maturity equal to n-years. On the other monitor, you are given the real-time market prices of coupon bonds, which are reported in column 3 and 4 in Table 1. At the moment, you are tracking two U.S. Treasury (UST) bonds, both maturing in 3 years and with $100 principal or par value but with different coupon rates: bond "UST 5\%" pays a 5% fixed annual coupon and bond "UST 2\%" pays a 2% fixed annual coupon. For simplicity of the calculations, we will assume that the coupons are paid once a year, not semi-annually, and in both cases, the first coupon will be paid in exactly 1 year from now. Therefore, the cash-flows generated by these two bonds are given in the third and fourth columns of Table 1. a) Calculate the 1, 2 and 3 year spot rates. (6 points) b) Calculate the prices of the UST 2% and the UST 5% bond assuming there are no arbitrage opportunities in the market. (6 points) c) Using your answer to part B, suppose that in fact bond "UST 5\%" is trading at \$105.00. Sketch out an arbitrage: ( 8 points) i. Which quantities of which instruments do you have to buy and sell? Be very precise about the quantities you would purchase and sell. ii. Compute the arbitrage profit