Question

Consider a 6 month futures contract on a Dow Jones Industrial Index. Stocks underlying the index have dividend yield of 2% per annum. The current value of the index is $1,383 and interest rate is 5% per year compounded continuously. What is the appropriate value of the futures price? Be sure to carry your answer out 2 decimal places and you do not need to include the $ sign. For example, if your answer is $1,402.7855 then just type 1402.79 in the answer box.

Answer 1

Price of Future = S e^(r-d)t= 1383* e^(5%-2%)*6/12 = 1383*1.01511= 1403.90

Where S: Spot price at the beginning
r: Risk-free interest rate
d: dividend yield
t: time to maturity


In the above solution, it has been assumed that the given dividend yield is compounded continuously.
However, if we consider that the dividend yield is compounded discreetly and the risk-free rate is compounded continuously, we will have to convert this discrete interest rate into a continuous compounding rate.

(1+r)ⁿ = e^Rn
1+r = e^R (taking nth root on both sides)
(1+0.02) = e^R
1.02 = e^{R
Taking Log on both sides}
R= ln(1.02)
R= 0.0198 = 1.98%
Plugging in this number in the formula

Price of Future = S e^(r-d)t= 1383* e^{(5%-1.98%)*6/12} = 1383*1.01511= 1404.04