Option Pricing. The stock is trading at 10 now. The 1-period risk free rate is 5%. In the first period, the stock can go up by 20% or go down by 10%. In the second period, the stock can go up by 10% or go down by 10% if the stock goes up in the first period. However, in the second period, the stock can go up by 30% or go down by 10% if the stock goes down in the first period. Consider an at-the-money (ATM) European call option.

(a) Draw the stock price tree and the payoffs of the option price tree.

(b) What's the fair price of the option today?

(c) In this part of the question, assume that the stock pays a 10% dividend in the first period. Consider an at-the-money (ATM) American call option. What's the fair price of the American option today?