Given instruments in the following table Instrument 6m (182 day) T-Bill 2y Treasury 3y Treasury 5y Treasury 7y Treasury 10y Treasury Semiannual coupon rate Market yield Market price 0.75% 1.40% 2.00% 2.50% 2.90% 3.20% T (years) 0 a. Extract the semiannual discount factors for 10 years using the bootstrap method with linear and log-linear interpolation in discount factors. b. On the same graph, plot the semiannual zero-coupon yields (Formula 2.8 with w=0)) for 6m, 1y,.... 10y maturities for linear and log-linear interpolation methods. c. Using the discount factor curve from the log-linear interpolation, compute the price of a 5-year, 1% semiannual coupon bond and convert the price using Formula 2,5 to a semiannual yield. Do the same with a semiannual coupon rate of 8% to observe the coupon effect on yields. Hint: See Table 2.5 TABLE 2.5 Hint for bootstrap problem. 0.5 *** 2 7.5 0% 1.375% 2.125% 2.5% 3% 3.25% 9.5 10 Linear Zero rate Log-linear Zero rate DF DF 1 1 0.9962083 0.761% 0.9962083 0.761% 0.9724397 1.402% 0.9724406 1.402% 99.62083% 99.95086% 100.36222% 100% 100.62942% 100.42501% 0.7987633 3.018 % 0.7980435 3.031% 0.7373020 3.234 % 0.7366574 3.243% 0.7219367 3.285 % 0.7220633 3.283% FORMULA Pz(y, N, m) = D(T) = 1 (1+y/m)N-w (2.8) P(C, y, N,m) = P = N C/m 1 (1+y/m)i (1+y/m)N + i=1 1 1 = = ( -+y/my) + (1+y/m}\\ 1 y (2.5)