Today is January 3. Your friend David has just bought a futures contract on a stock index, and the contract specifies one year to expiration. The current share price is $80, and the annually compounded interest rate is 10%. The stock will pay quarterly dividends of $2 during the next year, with dividends payments on the following dates:
- January 25
- April 25
- July 25
- October 25
Assume that this is a non-leap year.
a. What is the futures price on this contract on January 3?
b. What is the cost-of-carry on this futures contract on January 3?
c. What is the value of this futures contract on February 17 if the spot price turns out to be $90 on that day?
d. Suppose that, instead of paying a quarterly dividend of $2, the stock index has an annual dividend yield of 10%. The continuously compounded interest rate is 10.52%. What is the price of the index futures on January 3? What is its value on February 17 when the index turns out to be $90?
