3. (9 marks) a. Rogers (RCI) stock has been trading in a narrow range around $55 per share for several months and you believe it is going to stay in that range for the next 6 months. The price of a 4-month put option with an exercise price of $55 is $2.50. If the risk-free rate is 4% per year, what must be the price of a 4-month call option on RCI stock at an exercise price of $55 if it is at the money? (Assume no dividends) (2 mark) b. What would be a simple options strategy using a put and a call to exploit your conviction about the stock price's future movement? What is the most money you can make on this position? How far can the stock price move in either direction before you lose money? (3 marks) C. How can you create a position involving a put, a call, and riskless lending that would have the same payoff structure as the stock at expiration? What is the net cost of establishing that position now? (4 marks)