1. Calculate the dirty price and the clean price for a 5% coupon Treasury that p

Question

1. Calculate the dirty price and the clean price for a 5% coupon Treasury that pays interest on 2/15 and 8/15 of each year, matures on 8/15/2018 and settles on 9/20/2015. Show all calculations and include six decimal places.

Assume the following Treasury spot rate curve for this problem.

Date                Period              Years               Spot Rate

2/15/2016        1                      0.5                   2.0000%

8/15/2016        2                      1.0                   2.0500%

2/15/2017        3                      1.5                   2.1014%

8/15/2017        4                      2.0                   2.2043%

2/15/2018        5                      2.5                   2.2556%

8/15/2018        6                      3.0                   2.3604%

Explanation / Answer

Solution:

Coupon = 5%, Maturity date = 15th Aug 2018, Settlement date = 20th Sep 2015, Interest paid on 15th feb and 15th Aug, let the face value of treasury be $1000

Hence, clean price of the treasury at settlement date = $1221.555018

Now dirty price = clean price + accrued interest
Accrued interest is the = Coupon * number of days since last coupon date/365
Last coupon was paid on 15 Aug 2015 and settlement was done on 20th Sep 2015,

Hence, Number of days since last coupon = 35
Accrued interest = 5% * 1000 *35/365
                           =   $4.794521
Hence dirty price = 1221.555018 + 4.794521
                            = 1228.658170

Coupon Dates 15 Feb 16 15 Aug 16 15 Feb 17 15 Aug 17 15 Feb 18 15 Aug 18 Days since settlement 148 328 508 688 868 1048 Time (t) 0.411 0.994 1.411 1.994 2.411 2.994 Coupon (5%) + maturity amount 50 50 50 50 50 1050 Spot rate (r) 2.0% 2.05% 2.1014% 2.2043% 2.2556% 2.3604% Discounting (1/(1+r)^t 0.991892 0.980022 0.971081 0.957446 0.947640 0.932525 Present value 49.594598 49.001114 48.554029 47.872298 47.381993 979.150980 Sum of present values 1221.555018

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