The common stock of the CALL Corporation has been trading in a narrow range around $ 50 per share for many months, and you are convinced that it is going to stay in that range for the next three months. The price of a three- month put option with an exercise price of $ 50 is $ 4. The stock will pay no dividends for the next three months.
a. If the risk- free interest rate is 10 percent per year, what must be the price of a three- month call option on CALL stock at an exercise price of $ 50 if it is at the money?
b. What would be a simple options strategy using a put and a call to explain 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?
c. How can you create a position involving a put, a call, and risk- free lending that would have the same payoff structure as the stock at expiration? What is the net cost of establishing that position now?