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 $110 per share, and the price of a 3-month call option at an exercise price of $110 is $6.53. 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 $110? (The stock pays no dividends.) 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?

Answer 1

(a) From the put-call parity, we know that
P = C – S + [X / (1 + r) ^T ]. Thus,
P = $6.53 - $110 + [$110 / (1.08) ^1/4]

P = $6.53 - $110 + [$110 / 1.019]

P = $6.53 - $110 + $ 107.95 = $ 4.48

(b)  Total cost of straddle would be $6.53 + $4.48 = $ 11 , and this is the amount by which the stock would have to move in either direction for the profit on the call or put to cover the investment cost (not including time value of money considerations). If time value of money were taken into account, stock price would need to swing in either direction by $11 x (1.08)^1/4 = $ 11.21.