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Homework answers / question archive / Assume that the risk-free interest rate is 7% per annum with continuous compounding and that the divided yield (also in % per annum with continuous compounding) on a stock index varies throughout the year
Assume that the risk-free interest rate is 7% per annum with continuous compounding and that the divided yield (also in % per annum with continuous compounding) on a stock index varies throughout the year.
In February, May, August, and November, dividends are paid at a rate of 9% per annum. In other months, dividends are paid at a rate of 3% per annum.
Suppose that the value of the index on July 31 is 1,426. What is the futures price for a contract deliverable on December 31 of the same year?
Computation of futures price for a contract deliverable on December 31 of the same year:
The futures contract lasts for five months. The dividend yield is 3% for three of the months and 9% for two of the months. The average dividend yield is therefore
Average Dividend Yield = (3%*3+9%*2) / 5 = 5.40%
Futures Price = 1426*e (0.07-0.054)*(5/12)
= 1,426*1.00668894
Future Price = $1,435.54
