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3. (12 marks) (Yield curve and swap pricing) Assume that you observe the following yield curve for for government's coupon paying bonds There are a total of 30 bonds. For the k-th bond, k-1,... ,30, the maturity is k years The face value is $100.000 and the coupon rate for the k-th bond, k = 1, . The prices of the bonds are given in the following table , 30, is 4% Table 1: Bond prices prices prices prices 1 98,828.981711 89,083.930121 81,633.1317 297,812.0511 12 87,944.5962 22 81,287.3700 3 96,937.896913 86,976.358423 81,087.7608 4 I 96,159.9962 14 | 85.9284188 24 | 80.919.5136 5 95,269.2339 15 84,982.506525 80,780.7515 6 94,353.56691684,248.25892680,669.7282 7 93,276.0334 17 83,540.8304 27 80,584.8196 892,237.883718 82,911.522828 80,524.5143 9 91,261.0455 19 82,417.092329 80,487.4060 10 90,214.059720 82,009.074230 80,472.1856 Assume that all the coupon payments are made annually. Use continuous compounding a. (4 marks) Modify the Newton iteration program that you developed for Assignment 1 to compute the yield to maturity (YTM) for each bond. Submit a table similar to Table 1 with the "price" column being replaced by the "YTM" column filled with the computed YTMs Plot YTMs vs maturities and comment. You may find the Matlab function plot useful. For the initial guess, choose 10%. Use the stopping criteria n+1 n

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