The current price of Watson Corporation stock is $10. In this year, this stock price can either increase by 20% or decrease by 10% every six months. Watson pays no dividend. The effective quarterly risk-free interest rate is 2%, which will remain constant forever. You will calculate the price of a one-year European put option on Watson stock with a strike price of $10 following the steps below.

(a) Construct a binomial tree to show the evolvement of the stock price in this year and show the payoff of the put option. (2 marks)

(b) Calculate the risk-neutral probability based on the binomial model constructed in Part (a) (2 marks)

(c) Calculate the price of the put option using the risk-neutral binomial model.