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Unformatted text preview: ACTSC231 TUTORIAL PROBLEMSSOLUTION, WEDNESDAY, JULY 21, DC 1351, 4:305:20PM (1) You are given the following prices of $1,000 par value bonds with 10% annual coupons: $1,028.04 for 1 year term, $1,036.53 for 2 years term, $1034.47 for 3 years term Find the spot rates for t=1,2,3 that are implied by these bond prices. Solution 0.1. We can express the prices of given bonds in terms of the unit ZCB (zero coupon bond) prices denoted by B(t) where t is term. 1028 . 04 = 1100 B (1) , 1036 . 53 = 100 B (1) + 1100 B (2) , and 1034 . 47 = 100 B (1) + 100 B (2) + 1100 B (3) . Thus, we obtain B (1) = 0 . 93458 , B (2) = 0 . 857338 and B (3) = 0 . 777625 . Since B ( t ) = (1 + r t ) t where r t is the spot rate for the term t, we get r 1 = 7% , r 2 = 8% and r 3 = 8 . 75% . (2) The current term structure is as follows: r 1 = 6% ,r 2 = 8%, and r 3 = X %. A 3year bond with a 8% coupon payable annually has an annual effective yield rate equals to 9%. Assume the bond is redeemed at par and the face value is $100.equals to 9%....
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 Spring '09
 Chisholm

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