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 $6$ months. You do not know whether it will go up or down,

however. The current price of the stock is $$105$ per share, and the price of a $6$ month call option at an exercise price of

$$105$ is $$10\mathrm{.}55.$

Required:

a$.$ If the semiannual risk$-$free interest rate is $3\%,$ what must be the price of a $6-$month put option on P$.$U$.$T$.$T$.$ stock at an

exercise price of $$105?($The stock pays no dividends.$)$

b$.$ 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?

ANSWERS PLEASE