The common stock of the Orange Incorporated has been trading in a narrow price range for the past month, and you are convinced it is going to break far out of that range in the next three months. You do not know whether it will go up or down, however. The current price of the stock is $100 per share, and the price of a three-month at-the-money put option on Orange Incorporated is $5.

a. If the risk-free interest rate is 2% per year, what must be the price of a 3-month at-the-money call option on the Orange Incorporated stock? (Note: ATM options are the options for which the strike price is equal to the current stock price.) The stock pays no dividends.

b. What would be a simple options strategy to exploit your conviction about the stock prices future movements? To receive a full credit, you should i. Identify which options are involved in your strategy ii. Construct a payoff table and show it in this exam iii. Show payoff of your strategy on a graph

c. How far would the price of the Orange Incorporated have to move in either direction for you to make a profit on your initial investment?