Please answer all parts (a) through (d) and specify the parts.

5. Clean Price - A 2 year semi-annual (m = 2) coupon bond is issued on 1/1/2020 and matures on 1/1/2022 with semi-annual coupon rate of 4% per annum and coupon dates 7/1/2020, 1/1/2021, 7/1/2021, 1/1/2022, leading to 4 coupon periods consisting of 182, 184, 181, 184 days respec- tively. Date Remaining Accrual Coupons (N) Fraction (w) P(C, y, N, m) 4 0 1 4 1 182 1/1/2020 1/2/2020 6/30/2020 7/1/2020 7/2/2020 4 3 3 181 182 0 1 184 1.019889 1 1.000108 12/31/2021 1 183 184 1.01989 (a) Keeping its semi-annual yield constant at 4%, graph its daily price from 1/1/2020 to 12/31/2021, using Act/Act for fractional periods. The price ramps up from 1/1/2020 to 6/30/2020 and drops (almost 2%) from 6/30/2020 to 7/1/2020 with no change in yields. The drop is simply due to 1 fewer remaining coupons. (b) Traders prefer to see quote a smooth price function if yields have not changed, and accordingly subtract accrued interest, wC/m from the true price (PV of remaining cash flows) to come up with the (artificially smoothed) clean price. Graph the clean price of bond over the same period. The true price (first graph) is called the Gross, Dirty, Invoice Price. (c) Graph the clean and dirty price of a discount bond, C y=3% 5. Clean Price - A 2 year semi-annual (m = 2) coupon bond is issued on 1/1/2020 and matures on 1/1/2022 with semi-annual coupon rate of 4% per annum and coupon dates 7/1/2020, 1/1/2021, 7/1/2021, 1/1/2022, leading to 4 coupon periods consisting of 182, 184, 181, 184 days respec- tively. Date Remaining Accrual Coupons (N) Fraction (w) P(C, y, N, m) 4 0 1 4 1 182 1/1/2020 1/2/2020 6/30/2020 7/1/2020 7/2/2020 4 3 3 181 182 0 1 184 1.019889 1 1.000108 12/31/2021 1 183 184 1.01989 (a) Keeping its semi-annual yield constant at 4%, graph its daily price from 1/1/2020 to 12/31/2021, using Act/Act for fractional periods. The price ramps up from 1/1/2020 to 6/30/2020 and drops (almost 2%) from 6/30/2020 to 7/1/2020 with no change in yields. The drop is simply due to 1 fewer remaining coupons. (b) Traders prefer to see quote a smooth price function if yields have not changed, and accordingly subtract accrued interest, wC/m from the true price (PV of remaining cash flows) to come up with the (artificially smoothed) clean price. Graph the clean price of bond over the same period. The true price (first graph) is called the Gross, Dirty, Invoice Price. (c) Graph the clean and dirty price of a discount bond, C y=3%