The common stock of the XYZ Corporation 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 3 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 3-month call option at an exercise price of $100 is $10.

a. If the risk-free interest rate is 10% per year, what must be the price of a 3-month put option on XYZ stock at an exercise price of $100? (The stock pays no dividends.)

b. What would be a simple options strategy to exploit your conviction about the stock prices future movements? How far would it have to move in either direction for you to make a profit on your initial investment?