12. A stock is presently selling at a price of $50 per share. After one time period, its selling price will (in present value dollars) be either $150 or $25. An option to purchase y units of the stock at time 1 can be purchased at cost cy.

(a) What should c be in order for there to be no sure win?

(b) If c = 4, explain how you could guarantee a sure win.

(c) If c = 10, explain how you could guarantee a sure win.

(d) Use the arbitrage theorem to verify your answer to part (a).