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 $$120$ per share, and the price of a $6$ month call option at an exercise price of $$120$ is $$5\mathrm{.}20.$

Required:

a$.$ If the semiannual risk$-$free interest rate is $5\%,$ what must be the price of a $6-$month put option on P$.$U$.$T$.$T$.$ stock at an exercise price of

$$120?($The stock pays no dividends.$)$

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?

Complete this question by entering your answers in the tabs below.

Required A

If the semiannual risk$-$free interest rate is $5\%,$ what must be the price of a $6-$month put option on P$.$U$.$T$.$T$.$ stock at an exercise

price of $$120?($The stock pays no dividends.$)$

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

Price of a six$-$month put option on P$.$U$.$T$.$T$.$ stock