5. Clean Price (5pts) - 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 ($w$) $P(C, y, N, m)$
1/1/2020 4 0 1
1/2/2020 4 1/182
...
6/30/2020 4 181/182 1.019889
7/1/2020 3 0 1
7/2/2020 3 1/184 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.