Answer :
The futures price would be 98.52.
To determine the futures price of a bond futures contract, you need to calculate the present value of the bond's cash flows discounted at the appropriate rate.
In this case, the bond has a par value of $100, an annual coupon of $8, and a maturity date in 2 years. The futures delivery date is in 1 year, and the rates of return R(0,1) and R(0,2) are 5% and 10%, respectively.
The present value of the bond's cash flows can be calculated as follows:
- At time 1 (futures delivery date): receive $8 coupon payment
- At time 2 (maturity date): receive $100 par value + $8 coupon payment
The present value of these cash flows at time 0 (now) can be calculated using the formula:
[tex]PV = CF1 / (1 + r) + CF2 / (1 + r)^2[/tex]
where PV is the present value, CF1 and CF2 are the cash flows at time 1 and time 2, respectively, and r is the appropriate rate of return.
Substituting the values into the formula, we get:
[tex]PV = $8 / (1 + 0.05) + ($100 + $8) / (1 + 0.1)^2\\\\= $7.61 + $90.91\\\\= $98.52[/tex]
Hence, The futures price would be 98.52.
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