The common stock of the C$.$A$.$L$.$L$.$ Corporation has been trading in a narrow range around $$120$ per share for months, and you believe it is going to stay in that range for the next $6$ months. The price of a $6-$month put option with an exercise price of $$120$ is $$8\mathrm{.}89.$

Required:

a$.$If the semiannual risk$-$free interest rate is $4\%,$ what must be the price of a $6-$month call option on C$.$A$.$L$.$L$.$ stock at an exercise price of $$120$ if it is at the money? $($The stock pays no dividends.$)$

b$.$What would be a simple options strategy using a put and a call to exploit your conviction about the stock price$$s future movement? What is the most money you can make on this position? How far can the stock price move in either direction before you lose money?

c$.$How can you create a position involving a put, a call, and riskless lending that would have the same payoff structure as the stock at expiration? What is the net cost of establishing that position now?