Suppose the current price of a share of stock is $75 and that it will change to either $20, $50 or $200 in the future. Let $c be the price to buy an option to buy the stock for $100 in the future.
a) Set up the equations for the expected gains for buying stock and buying options if p1 = P ($20), p2 = P ($50), and p3 = P ($200).
b) Set the two equations in (a) equal to zero and solve for p1 and p2. The solutions will be in terms of c.
c) Find the values of c for which no arbitrage opportunity exists (for what values of c does a solution to the system exist?).