Question

Assume that the risk-free interest rate is 9% per annum with continuous compounding and that the dividend yield on a stock index varies throughout the year. in february, may, august, and november, dividends are paid at a rate of 5% per annum. in other months, dividends are paid at a rate of 2% per annum. suppose that the value of the index on july 31 is 1,300. what is the futures price for a contract deliverable on december 31 of the same year?

Answer 1

The futures price for a contract deliverable on December 31 is $1,331.34.

Step-by-step explanation:

To calculate the futures price for a contract deliverable on December 31, we need to discount the expected dividends. In February, May, August, and November, dividends are paid at a rate of 5% per annum, and in other months, dividends are paid at a rate of 2% per annum. The value of the index on July 31 is 1,300.

To calculate the futures price, we need to determine the present value of the expected dividends. Assuming continuous compounding, we can use the formula:

Futures Price = Spot Price * (e^((r-d)*t))

Where:

• Spot Price = 1,300
• r = Risk-free interest rate = 9% per annum
• d = Dividend yield = (5% * 4 + 2% * 8) / 12 = 3.17% per annum
• t = Time until delivery date = 5/12 year (from July 31 to December 31)
• e = Euler's number, approximately 2.71828

Substituting the values into the formula:

Futures Price = 1,300 * (e^((0.09-0.0317)*(5/12)))

Futures Price = 1,300 * (e^(0.0583*(5/12)))

Futures Price = 1,300 * (e^0.0244)

Futures Price = 1,300 * 1.024647

Futures Price = $1,331.34