Suppose the S&P is trading at a level of 1000. Using continuously compounded rates, calculate the futures price for a contract expiring in three months, assuming expected dividends to be 2% and the interest rate for futures funding to be 5% (both rates expressed as continuously compounded rates)

Suppose the S&P is trading at a level of 1000. Using continuously compounded rates, calculate the futures price for a contract expiring in three months, assuming expected dividends to be 2% and the interest rate for futures funding to be 5% (both rates expressed as continuously compounded rates)
A . $1,007.50
B . $1,000.00
C . $1,007.53
D . $1,012.58

View Answer

Answer: C

Explanation:

The futures price of the contract will be the future value of the spot price, calculated at a net rate equal to the cost of funding the futures position, less any dividends or other distributions. Also note that when rates are continuously compounded, Future Value = Present Value x (exp(rate x time)).

Therefore in this case the futures price for the S&P = 1000 * exp((5%-2%)*3/12) = 1007.53