1. The common stock of the P.U.T.T Corporation has been trading in a narrow range for the past month, and you are convinced it is going to break far out of that range in the next three month. You do not know whether it will go up or down, however. The current price of the stock is $100 per share, the price of a three-month call option with an exercise price of $100 is $8, and a put with the same expiration date and exercise price costs $5.

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

2. A call option on Jupiter Motors stock with an exercise price of $75 and one-year expiration is selling at $4. A put option on Jupiter stock with an exercise price of $75 and one-year expiration is selling at $2.50.

1. If the annual risk-free rate is 2% and Jupiter pays no dividends, what should the stock price be?
2. Is there an arbitrage opportunity if the stock price is $73? If so, how to exploit it?

3. Stock of Apple is currently selling at $200. Suppose in the next six months it can increase by 10% or decrease by 5%. The risk-free interest rate is 1% per six month period. Use the one period binomial option pricing model to value a European call option with strike price of $205 and time to maturity of six months.