Consider a 6 month futures contract on the S&P 500. Assume the stocks underlying the index provide a 2.85% dividend yield per annum. The index is currently priced at 2420 and the continuously compounded annual risk-free rate is 3.5%.
A. What would be the arbitrage free price of the Future contract? That is what is F0(T)?
B. It is now 90 days into the contract. Interest rates have moved up slightly to 3.75% and the dividend yield is still 2.85. The current price of the index is 2439. Determine the price of the Futures contract and the profit in dollar terms, assuming you bought the contract at the price calculated in part A.
C. At expiration the index is at 2459. Interest rates are down to 3% and the yield on the S&P 500 has increased to 3.2% per annum. What is the price of the contract and calculate total dollar profit.