Question 1: The current interest rate is 5 percent per year. You can treat it as 2.5% per six months. You can borrow or lend at this interest rate. The futures contract for gold six months in the future is selling for $346.30, whereas the futures contract 12 months in the future is selling for $360.00. Is there an arbitrage opportunity here? If so, how would you exploit it?
Question 2: A stock is currently selling for $100 per share. It does not pay a dividend. Each month it either goes up by 5% or it goes down by 2%. There is no necessary relationship between what happens one month and what happens the next. There are call options available that expire exactly three months from now. They have an exercise price of $104. Assume that the interest rate is 6 percent per year or one-half percent per month. Using the two-state approach, determine the value of these call options. That is, determine what they should sell for today. {Hint: you probably want to use a spreadsheet and calculate what the options will be worth three months from now (under various outcomes), then two months from now, then one month from now, and then now}.