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 $125 per share, and the price of a 3-month call option at an exercise price of $125 is $6.93

a. If the risk-free interest rate is 5% per year, what must be the price of a 3-month put option on P.U.T.T. stock at an exercise price of $140?

b. What would be a simple options strategy to exploit your conviction about the stock price

Answer 1

A) according to put call parity:

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

put = $6.93 - $125 + [$140 / (1 + 5%)¹/⁴] = $6.93 - $125 +$138.30 = $20.23

B)

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

the total cost of the investment = $6.93 + $20.23 = $27.16, this way you can make a profit if the stock price increases higher than $125 + $20.23 = $145.23 or decreases below than $125 - $20.23 = $104.77