Consider a European put option on a non-dividend-paying stock with a strike price of $100 and an expiration in one year costs $0.31. The stock price is $90 and the risk-free rate is 8% per year.

(1) What is the lower bound of the put option?

(2) Is the put option over-valued or under-valued?

(3) What strategy should an arbitrageur implement in order to take advantage of this opportunity, and how much is the profit? Use the following table to show your positions on date t (today) and the expiration day T.

Action	Cash flow at t	Cash flow at T
		if ST X	if ST < X
		ST =120	ST = 80
Hint: Long or Short Stock? ----------------
Hint: Long or Short Put? ---------------
Hint: Borrow or Lend? ---------------
Total