(10 Marks) Consider a multi-period model. An airline stock sells for $10 in year 0. Each year, the stock price increases in value by 30% if oil prices are low or decreases in value by 10% if oil prices are high. The annual risk-free interest rate is 3 percent. Calculate the arbitrage-free price in year 0 of an American call (buy) option on the stock with an exercise price of 15 in year 1, 2 or 3.