Consider a European put option on a non-dividend paying stock. The price for this put option has a lower bound: X 2 mar (0. (1+277-5) So R) Po 0, Po is put price today. X is the strike price, 7 is the maturity of the put option. R, is the risk-free rate and S, is the stock price today. Derive this lower bound for the put price. In your answer. make sure to include the following elements: 11 1. Define two investment strategies (portfolios) to compare 11. For each portfolio, determine the payoffs at maturity 7. Consider the events that S X and S, X, where S, is the stock price at time 7 Derive an inequality for today's prices of the two portfolios, and show that the lower bound for the put price follows from this inequality