Consider the following two-period binomial model, and each period is three months. The current stock price is $50, the annual interest rate is 8%, and the stock price may go up by 10% per period or down by 10%.

Price a European call on the stock with exercise price $51

Price a European put on the stock with exercise price $51

Price an American call on the stock with exercise price $51 P

rice an American put on the stock with exercise price $51

Using the following graph, calculate the hedge ratio and risk neutral probability p for the following binomial tree, then determine the option price for each node and the above four cases.