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

Finance Mar 08, 2021

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?

Expert Solution

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

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