Question

Problem 26-9 Futures prices

Calculate the value of a six-month futures contract on a Treasury bond. You have the following information:

• Six-month interest rate: 11% per year, or 5.40% for six months.
• Spot price of bond: 91.00.
• The bond pays a 9% coupon, 4.50% every six months.

Answer 1

Futures price is given by the formula:

F = S*e^(r-q)t , where S is the spot price, r is the interest rate, q is the income rate (dividend or coupons) and t is the time period

In our question the given information is:

S= $91, r = 11%, q=9%, and t = 6 months = 6/12 = 0.5 year

substitute these values in the formula above:

F = 91*e^(11%-9%)*0.5 = $91.9146