2. (40 pts) Suppose the current price of a share of stock is $100 and that it will change to either $25 or $200 in the future. a) (15 pts) Find the price, $c, to buy an option to buy a share of stock for $100 in the future so there is not an arbitrage opportunity. b) (15 pts) Suppose the price of the option is $10. An investor can buy or sell x shares of stock and y shares of option. Find x and y such that the investor always makes the same (positive) profit regardless of stock price in the future. Should the investor be buying or selling stock? c) (10 pts) Plot the region (on an xy-plot) that includes all schemes that make money regardless of stock price in the future, mark the line which represents the scheme you found in part (b).