The common stock of the P$.$U$.$T$.$T$.$ Corporation has been trading in a narrow price range for the past month, but you are convinced it is going to break far out of that range in the next six months. You do not know whether it will go up or down, however. The current price of the stock is $$100$ per share, and the price of a six$-$month call option at an exercise price of $$100$ is $$10.$

Required:

If the semiannual risk$-$free interest rate is $3\%,$ what must be the price of a six$-$month put option on P$.$U$.$T$.$T$.$ stock at an exercise price of $$100?($The stock pays no dividends.$)$

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