Consider the financial market with N = 1, M = 1, r = 0, S1(0) = 100, S1(1) = 130, 110, or 80, all with positive probability.
(a) Find all possible risk-neutral probability measures.
(b) Consider a 1-year call option with a strike price of 100. (This is known as an ‘at-the-money' option). Find the range of possible prices for this option that will avoid arbitrage.
(c) If the price of the option in part (b) is 12, find an arbitrage opportunity.