A 2 -year semiannual coupon bond is issued on \(1 / 1 / 2020\) and matures on \(1 / 1 / 2022\) with a semiannual coupon rate of \(4 \%\) per annum and coupon dates 7/1/2020, 1/1/2021, 7/1/2021, 1/1/2022, leading to four coupon periods consisting of \(182,184,181\), and 184 days, respectively.

(a) Keeping its semiannual yield constant at \(4 \%\), graph the 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 one fewer remaining coupons.

(b) Graph the clean and dirty price of the bond from 1/1/2020 to \(12 / 31 / 2021\) when its yield is held at \(5 \%\), resulting in a discount bond, \(C

(c) Graph the clean and dirty price of the bond from 1/1/2020 to \(12 / 31 / 2021\) when its yield is held at \(3 \%\), resulting in a premium bond, \(C>y\).

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Date 1/1/2020 1/2/2020 6/30/2020 7/1/2020 7/2/2020 12/31/2021 Remaining Coupons (N) 4 4 4 +33 1 Accrual Fraction (w) 0 1/182 181/182 0 1/184 183/184 P(C, y, N, m) 1 1.019889 1 1.000108 1.01989