Problem 1

The price of gold is currently $1,250 per ounce. The forward price for delivery in one year is $1,320 per ounce. An arbitrageur can borrow money at 3% per annum. Is there an arbitrage opportunity? What trades should the arbitrageur make? Assume that the cost of storing gold is zero and that gold provides no income.

Problem 2

The current price of a stock is $92, and three-month call options with a strike price of $95 currently sell for $3.50. An investor who feels that the price of the stock will increase is trying to decide between buying 100 shares and buying 1,600 call options (16 contracts). Both strategies involve an initial investment of $9,200. How high does the stock price have to rise for the option strategy to be more profitable than outright purchase of the stock?