Please help me with this problem C2. I am posting the notes that might be helpful for you to solve the problem

C2. The yield of a semiannual coupon bond with 6% coupon rate and 30 months to maturity is 9%. (a) What are the price, duration and convexity of the bond? (b) If the yield moves down by 5 basis points, how will the price of this bond change? Problem 2 (515 pts) (a) Use bootstrapping to obtain a continuously compounded zero rate curve given that the price of a 6-month T-bill is 97.5, the price of a 12-month T-bill is 100, and the price of a 2-year T-bond with a 4% coupon rate is 108. The Treasury bonds pay semiannual coupons. (b) Use your zero-rate curve from part (a) to price a 20-month T-bond with a 3% coupon rate. What are the duration and convexity of this bond? So we have 108 = 2.0- 0.5.(0,0.5) + ze - r(o, 1 ) + 2.e + 102.e - 2x plug in to get: x = r(02) = - 0.000243 ( 2tr (0. 0.5) + (1-2+) . r(0,0) if outso.5 So, r(o,t) = j(2t-i)no.1) + 2(1-t). r (0, 0.5) it 0.5sts, ( + - 1) r (0, 2) + (2-+). r(o, 1 ) if ists2 Where r (0, 0.5 ) = 0. 050636 r ( 0, 1 ) = 0 r (0,2) = - 0.000243 and r(o. 0) is the overnight lending rate ( that you can assume to be O, since it was not mentioned ).101.5 b ) cash flow diagram: 1.5 1.5 1.5 From : O 2/12 8/12 14/ 12 20/12 r(0, 2/12) = 2. 4 r(0,0.5) = - r(o, 0.5) = 0. 016879 12 Y(o, #/12) = ( 2. 8 - 1) r(0, 1) + 2(1- 2) 160,0.5) = =160,0.5) = 0.033757. r ( 0, 14 / 12 ) = (14 -1 )1(0, 2) + (2-14 10, 1) = - r(0, 2) = - 0.000 041 r (0, 20/12 ) = (72 - 1) 16,2) + 42- 20) 1 10,1) = 2r(o, 2) = -0.000162 Now the price of the band is: - AB = Ice i=I B= 1.5.e- 2.r(0 2/12) + 1.5. e 12 2.r(0,8/12) 20(0, 20/12) + 101.5.0 12 B = 105.99 Next we find the yield. 105. 99 = 1.5. e 2. y - 12 + 15 . e 12-+ 15. e 14. y + 101.5. e B . Y Duration Y = 0. 0000587 D= = n B tic. e-yt. D = L. /1.5.2 + 1.5. -. e . 2-y 12 e y - 20 105 99 + 15 .-.0 12 +1015.20 - Dy by cash flow diagrams