The present price of a stock is 100. The price at time 1 will be either 50, 100, or 200. An option to purchase y shares of the stock at time 1 for the (present value) price ky costs cy.

(a) If k = 120, show that an arbitrage opportunity occurs if and only if c >80/3.

(b) If k = 80, show that there is not an arbitrage opportunity if and only if 20 ≤ c ≤ 40.