You want to determine if an arbitrage opportunity exists in the option market. You gather the following information regarding a non-dividend paying stock: The current price of the stock is S0 = 50. Its volatility is 20% per annum. There is a put option with maturity of 18 months and strike K = 45 that trades at $4. The continuously compounded risk-free rate is r = 0:02. (A) Considering a one-period binomial model, compute the future price of the stock in the up and the down states. (5 points) (B) Compute and B to create a replication portfolio. (5 points) (C) Compute the price of the put option and explain why there exists an arbitrage opportunity. (5 points) (D) Briefly explain which transactions you would use to exploit this arbitrage opportunity. (5 points) (E) Using the put-call parity, what should be the price of the corresponding European call? (5 points)