It is July 30, 2005. The cheapest-to-deliver bond in a September 2005 Treasury bond futures contract is a 13% coupon bond, and delivery is expected to be made on Februarys 4 and August 4 each year. The term structure is flat, and the rate of interest with semiannual compounding is 12% per annum. The conversion factor for the bond is 1.5. the current quoted bond price is $110. Calculate the quoted futures price for the contract.
There are 177 days between February 4 and July 30 and 182 days between February 4 and August 4. The cash price of the bond is, therefore:
110 + 177/182 x 6.5 = 116/32
The rate of interest with continuous compounding is 2 1n 1.06 = 0.1165 or 11.65% per annum. A coupon of 6.5 will be received in 5 days (= 0.01366 years) time. The present value of the coupon is
6e^-0.01366x0.1655 = 6.490
The futures contract lasts for 62 days (= 0.1694 years). The cash futures price if the contract were written on the 13% bond would be
(116.32 – 6.490)e^0.1694x0.1165 = 112.02
At delivery there are 57 days of accrued interest. The quoted futures price if the contract were written on the 13% bond would therefore be
112.02 – 6.5 x 57/184 = 110.01
Taking the conversion factor into account the quoted futures price should be:
It is July 30, 2005. The cheapest-to-deliver bond in a September 2005 Treasury bond futures contract is a 13% coupon bond, and delivery is expected to be made on Februarys 4 and August 4 each year. The term structure is flat, and the rate of interest with semiannual compounding is 12% per annum. The conversion factor for the bond is 1.5. the current quoted bond price is $110. Calculate the quoted futures price for the contract.
답글삭제There are 177 days between February 4 and July 30 and 182 days between February 4 and August 4. The cash price of the bond is, therefore:
답글삭제110 + 177/182 x 6.5 = 116/32
The rate of interest with continuous compounding is 2 1n 1.06 = 0.1165 or 11.65% per annum. A coupon of 6.5 will be received in 5 days (= 0.01366 years) time. The present value of the coupon is
6e^-0.01366x0.1655 = 6.490
The futures contract lasts for 62 days (= 0.1694 years). The cash futures price if the contract were written on the 13% bond would be
(116.32 – 6.490)e^0.1694x0.1165 = 112.02
At delivery there are 57 days of accrued interest. The quoted futures price if the contract were written on the 13% bond would therefore be
112.02 – 6.5 x 57/184 = 110.01
Taking the conversion factor into account the quoted futures price should be:
110.01/1.5 = 73.34
The future contract의 해당 만기일이 문제에서 생략되었다.(출제자의 실수?) 우리가 cash futures price를 알려면 cost of carry 모형을 써야하는데 말야... 거기서 중요한 만기를 모르니...
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