The common stock of the Hartz Company 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. If the risk-free interest rate is 10% per year, what must be the price of a 3-month put option on Hartz stock at an exercise price of $100? 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? and then please answer following too: Show that Black-Scholes call option hedge ratios also increase as the stock price increases. Consider a 1-year option with an exercise price of $40, on a stock with an annual standard deviation of 15%. The T-bill rate is 7% per year. Find N(d1) for the stock price $35, $40, and $45.