2) A stock has been trading in a narrow range around S50 per share for months, and you believe it is going to stay in that range for the next 3 months. The price of a 3-month put option with a strike price of $50 is $4. The risk-free (annually compounded) interest rate is 10% per year. a) What must be the arbitrage-free price of a 3-month at-the-money call option on the stock with a strike price of S50? b) What would be a simple options strategy using ONLY a put and a call to exploit your belief about stock price movement in the next 3 months? What is the maximum profit you can make on this strategy? How far can the stock price move, and in what direction, to make you lose money? c) How can you create a position involving a put, a call, and a riskless bond that would mimic the payoff structure as the stock at expiration? d) What should be the arbitrage-free stock price if there is no arbitrage opportunity, assuming the premium for a 3-month call option with a strike price of $50 is 6.18