Question

The common stock of the P.U.T.T. Corporation has been trading in a narrow price range for the past month, and you are convinced it is going to break far out of that range in the next 3 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 3-month call option at an exercise price of $120 is $8.89. a. If the risk-free interest rate is 8% per year, what must be the price of a 3-month put option on P.U.T.T. stock at an exercise price of $120? (The stock pays no dividends.) (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. A straddle 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? (Round your intermediate calculations and final answer to 2 decimal places.)

Answer 1

A) according to put call parity:

price of put option = call option - stock price + [future value / (1 + risk free rate)ⁿ]

put = $8.89 - $120 + [$120 / (1 + 8%)¹/⁴] = $8.89 - $120 +$117.71 = $6.60

B) you have to purchase both a put and call option ⇒ straddle

the total cost of the investment = $8.89 + $6.60 = $15.496, this way you can make a profit if the stock price increases higher than $120 + $6.60 = $126.60 or decreases below than $120 - $6.60 = $113.40