A common stock of the put corporation has been trading in a narrow price range for the past month, but you're 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 $$100$ per share and the price of a six month call option atexercise price of $$100$ is $$10$ a semi annual risk free interest rate is $3\%.$ What must be the price of a six month put option on put stock at an exercise price of $$100$ what would be a simple option 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?