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 $90 per share, and the price of a 3-month call option at an exercise price of $90 is $7.00.

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 $90? (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). Using put-call parity, we have:

P = C - S + K/(1+rf)^t where C (call option price) = 7; S (current stock price) = 90; K (strike price) = 90; rf (risk free rate) = 8%; t (time to expiry) = 3/12 = 0.25

P = 7 - 90 + 90/(1+8%)^0.25 = 5.28

b). A straddle is formed by buying a call and put with same strike price and same time to expiry. So, total cost of straddle will be 7 + 5.28 = 12.28

In order to have a profit, the stock would have to move by the time value of this cost, in either direction, in order to break even.

So, amount by which stock price should move is 12.28*(1+8%)^0.25 = 12.52 (Answer)