Assume a one-period binomial model in which the initial stock price is S = 60 and in each period the stock price can go either up by a factor of u = 7 3 or down by a factor of d = 2 3 . Assume that the simple interest rate over one time period is r = 1 3 .

(a) Determine the fair price of the European put option with strike K = 60.

(b) Assume that instead of the price determined in part (a), the European call option is trading at 11. Prove that there is an arbitrage and explain how the arbitrage can be achieved